Статті в журналах: "Constant deflection contour method"

1

Banerjee, M. M., and G. A. Rogerson. "On the application of the constant deflection-contour method in nonlinear vibrations of elastic plates." Archive of Applied Mechanics (Ingenieur Archiv) 72, no. 4-5 (July 1, 2002): 279–92. http://dx.doi.org/10.1007/s00419-002-0206-0.

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2

Wei, Zhao Cheng, Min Jie Wang, Wu Chu Tang, and Liang Wang. "Tool Deflection Error Regularization and Compensation in End Milling of Contour Surfaces." Applied Mechanics and Materials 217-219 (November 2012): 1341–45. http://dx.doi.org/10.4028/www.scientific.net/amm.217-219.1341.

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This paper presents a new approach of tool deflection error regularization and compensation in end milling of contour surfaces. The material removal rate (MRR) is adopted as the dominant factor of surface dimensional error. A mathematics model of determining the MRR in generalized contour surfaces machining is proposed. Feedrate scheduling methodology is applied to regulate a constant MRR along curved tool path. The expectation with the constant MRR is that it will potentially produce a constant surface dimensional error. Thus, the compensation can be conveniently achieved by offsetting the nominal finishing path. The desired MRR and corresponding offsetting value of finishing tool path are determined by a peripheral milling test. Machining results obtained in this study reveal that the proposed approach can significantly reduce the surface dimensional error and the smooth variation of feedrate can get a few variation of surface dimensional error. Comparing to the existing methods, the time-consuming iterative process in error compensation is omitted.

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3

Li, Dong, Zhi-Chao Lai, Ying Wang, and Zhou-Lian Zheng. "A non-contact method for estimating the pre-tension of a rectangular membrane structure." Insight - Non-Destructive Testing and Condition Monitoring 62, no. 8 (August 1, 2020): 464–70. http://dx.doi.org/10.1784/insi.2020.62.8.464.

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The stiffness of membrane structures widely used in modern buildings is provided by pre-tension, which means that any loss of pre-tension during service life may endanger structural safety and lead to engineering accidents. Therefore, the pre-tension of membrane structures needs to be estimated effectively and a corresponding estimation method is proposed in this study. Firstly, a theoretical model of a rectangular membrane structure is established using the constant deflection contour method (CDCM) to analytically derive a relationship between the pre-tension and the frequency. Then, the pre-tension is calculated using the frequency obtained experimentally by non-contact modal testing using a three-dimensional digital image correlation (3D-DIC) technique. Furthermore, the estimation method is validated by experimental study. The results show that the proposed method can provide a satisfactory assessment of the pre-tension in rectangular membrane structures and has significant potential to be utilised by industry.

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4

Surianinov, Mykola, Yurii Krutii, Dariya Kirichenko, and Oleksii Klimenko. "TO THE CALCULATION OF RING PLATES ON A VARIABLE ELASTIC BASE." Urban development and spatial planning, no. 83 (April 14, 2023): 304–13. http://dx.doi.org/10.32347/2076-815x.2023.83.304-313.

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The article examines the bending of ring plates on a variable elastic base. There are different models of elastic base. The simplest is the Winkler model, or the spring model. For beams on a constant elastic base, this model allows obtaining an exact solution, but not for slabs. The case is even more complicated when the elastic basis is variable. There is no single approach to building a universal analytical solution. Therefore, numerical calculation methods are used in engineering practice. The analytical method of direct integration and computer modeling in PC LIRA-CAD with subsequent calculations by the method of finite elements are used. Two examples are considered: a steel plate, which is rigidly clamped along the inner contour, and its outer contour is hinged, and a concrete slab, which is rigidly clamped along the outer contour, and its inner contour is hinged. The results of the numerical implementation show that the values of deflections when calculated by the author's method and the method of finite elements in PC LIRA-CAD practically coincide, and the difference in the values of bending moments reaches 10%. Moreover, the difference in deflections is manifested only in the fourth (and sometimes in the fifth) sign after the comma. It is noted that the method of direct integration demonstrated very high accuracy when solving numerous test problems that have an exact solution. The authors explain the discrepancy in the values of the bending moments obtained here by the semi-automatic breakdown of the finite-element mesh in PC LIRA-CAD. This statement is based on the fact that when the mesh is thickened in the circumferential direction, the results obtained by the two methods for determining the radial and circumferential bending moments are substantially converged.

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5

Surianinov, M. H., Y. S. Krutii, А. S. Karnaukhova, and О. M. Klymenko. "ANALYTICAL METHOD FOR CALCULATING ANNULAR PLATES ON A VARIABLE ELASTIC BASE." Modern construction and architecture, no. 2 (December 28, 2022): 37–43. http://dx.doi.org/10.31650/2786-6696-2022-2-37-43.

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The paper considers the application of the method of direct integration to calculations of annular plates and slabs on a continuous variable elastic base. Ring-shaped plates with variable geometric and mechanical parameters are increasingly used. Not only the elastic base, but also the plate thickness and cylindrical stiffness can be variable parameters here. The need for an analytical method for calculating such structures raises no doubts, since it makes it possible to evaluate the accuracy of finite-element analysis. To date, there are no proposals in the literature regarding a general analytical method for the calculation of annular plates on a variable elastic base. A detailed description of the algorithm of the direct integration method is not given in the paper, and all the calculation formulas for the annular plate are taken from the authors' already published article. The results of numerical implementation of this algorithm for specific examples are considered: a concrete plate, which is rigidly pinch on the inner contour, and its outer contour is free, and a steel plate, which is rigidly pinch on the outer contour, and its inner contour is free. To estimate the results of calculation by the author's method, computer modeling of the considered structures in PC LIRA-SAPR and their calculations by the finite-element method have been executed. The foundation reaction is described by Winkler model with a variable bedding factor. In the first case a bed factor is assumed constant, and in the second case it changes under the linear law. Calculations have shown that discrepancy between deflections calculated by the finite-element method and the author's method does not exceed 1 %, and the results of radial and circumferential moments calculation differ more considerably, amounting to 10 %. The authors explain this difference by the inaccuracy of the numerical analysis associated with the semi-automatic method of constructing a finite-element mesh, which should be made finer. The densification of the mesh in the manual mode of its partitioning significantly reduces the discrepancy between the results of calculating the deflections, radial and circumferential bending moments by the finite-element method and the author's method.

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6

Surianinov, M., Y. Krutii, D. Kirichenko, and O. Klimenko. "CALCULATION OF ANNULAR PLATES ON AN ELASTIC BASE WITH A VARIABLE BEDDING FACTOR." Mechanics And Mathematical Methods 4, no. 2 (December 31, 2022): 43–52. http://dx.doi.org/10.31650/2618-0650-2022-4-2-43-52.

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The application of the analytical method ‒ the method of direct integration ‒ to calculations of building structures in the form of circular plates and plates on a continuous variable elastic base is considered. It is noted that there are no proposals for a general analytical method for calculation of annular plates on a variable elastic base in the literature. And the need for such a method is obvious, since it makes it possible to estimate the accuracy of finite element analysis. A detailed description of the algorithm of the direct integration method is not given in the paper, and all the calculation formulas for the circular plate are taken from the authors’ already published article. The results of numerical implementation of this algorithm for specific examples are considered. In order to verify the results of calculations by the author’s method, computer modeling of the considered circular plates in PC LIRA-SAPR and their calculations by the finite element method have been performed. The reaction of the foundation is described by the Winkler model with a variable bedding factor. The calculation of a concrete slab that is rigidly pinched on the inner contour and articulated on the outer contour is performed. And calculation of a steel plate with rigid pinching on the outer contour and articulated on the inner contour. In the first case, the bedding factor is assumed constant, and in the second case, it changes according to the linear law. The calculations showed that the discrepancy between deflections calculated by the finite-element method and the author’s method does not exceed 1%, and the results of radial and circumferential moments calculation differ more considerably, amounting to 10%. The authors explain this difference by the inaccuracy of the numerical analysis associated with a semi-automatic method of constructing a finite-element mesh, which should be made finer. The densification of the mesh in the manual mode of its partitioning significantly reduces the discrepancy between the results of calculating the deflections, radial and circumferential bending moments by the finite-element method and the author’s method.

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7

Petrakov, Yury, and Yan Romanov. "Ensuring accuracy of contour milling on CNC machines." Mechanics and Advanced Technologies 7, no. 1 (April 13, 2023): 51–60. http://dx.doi.org/10.20535/2521-1943.2023.7.1.276162.

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Contour milling is characterized by quasi-stationary, which leads to the occurrence of a machining error caused by elastic deflections of the machining system. Moreover, such an error cannot be eliminated by sub-adjusting the control program "for size", since it not is constant and changes along the contour in a wide range. To ensure the accuracy of contour milling, a new method of combined control is proposed, which uses a posteriori information of machine verification measurements of the machined surface and a priori information of modeling the material removal process. In case of single manufacturing, the allowance on the last pass is divided into two parts, and after machining the first part, verifications are performed, then modeling and machining of the second half according to the corrected control program. In mass manufacturing, verifications are performed on the first part, and all subsequent ones are machined according to the adjusted control program. To obtain the necessary a posteriori information, the technology of machine verifications on CNC-machine with a three-coordinate probe according to standard control programs is proposed, and it is enough to perform two measurements or one, in the presence of surfaces inclined to the coordinate axes of the contour. A computer program was created, the core of which is a mathematical model of the process, which reproduces the structural diagram of the machining system closed behind two elastic deflections. The primary control file is loaded in G-codes with measurement data, and as a result of the process simulation, a new control file for the CNC-machine tool is formed, which eliminates the error from elastic deflections of machining system. Preliminary tests showed the possibility of increasing the accuracy of contour machining by more than 3 times.

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8

RAJASEKARAN, S., and K. NALINAA. "STABILITY AND VIBRATION ANALYSIS OF NON-PRISMATIC THIN-WALLED COMPOSITE SPATIAL MEMBERS OF GENERIC SECTION." International Journal of Structural Stability and Dynamics 05, no. 04 (December 2005): 489–520. http://dx.doi.org/10.1142/s0219455405001714.

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This paper presents a detailed treatment of the formulation of static, bucking and vibration analysis of non-prismatic thin-walled composite spatial members of generic section. The theory is limited to small strains, moderate deflections and small rotations. The torsional shear strain on the middle surface of the beam wall is zero for an open contour while it corresponds to constant shear flow for a closed contour. Rigorous expressions for strains based on membrane theory of shells are obtained through which the effect of nonlinear tapering is considered. Solutions for classical buckling and vibration analysis by the finite element method are discussed. Numerical integration by using Gaussian quadrature on the cross-sections for the computation of sectorial properties and stress resultants and over the length for the computation of flexural, geometric and mass matrices is suggested. Some examples are solved and critical bucking loads, natural frequencies and the corresponding buckled and mode shapes are obtained by the Jacobi iteration procedure.

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9

ASTAKHOV, Sergey A., and Vasiliy I. BIRYUKOV. "Buckling under the action of loading by aerodynamic and inertial forces during ground track tests of aviation equipment." INCAS BULLETIN 13, S (August 3, 2021): 5–12. http://dx.doi.org/10.13111/2066-8201.2021.13.s.1.

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The article analyses the choice of a rational layout of the test object with a propulsion system (PS). One of the design examples of calculating the longitudinal stability and strength of the structure is given. The purpose of the article is to solve the problem of bending the elastic line of a cantilever tubular rod with a hinged termination during tests of a propulsion system for various aircrafts. On the example, the estimates of the approximate test object, accelerated on the track to a speed of 1200 m/s, are carried out. The aerodynamic loading of the structure of the mobile track installation is considered using the methods of mathematical modelling and the development of an algorithm for the numerical solution of the problem of bending the elastic line of a cantilever tubular rod. The deflection from the forces of external and internal loads of the outer shell of a movable track installation is considered, provided that the diameter of the outer contour is equal to the minimum and it is constant along the entire length.

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10

Starovoitov, Eduard I., and Denis V. Leonenko. "Repeated alternating loading of a elastoplastic three-layer plate in a temperature field." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 21, no. 1 (February 24, 2021): 60–75. http://dx.doi.org/10.18500/1816-9791-2021-21-1-60-75.

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Axisymmetric deformation of a three-layer circular plate under repeated alternating loading from the plastic region by a local load is considered. To describe kinematics of asymmetrical on the thickness of the plate pack is adopted the hypothesis of a broken line. In a thin elastic-plastic load-bearing layers are used the hypothesis of Kirchhoff. A non-linearly elastic relatively thick filler is incompressible in thickness. It is taken to be a hypothesis of Tymoshenko regarding the straightness and the incompressibility of the deformed normals with linear approximation of the displacements through the thickness layer. The work of the filler in the tangential direction is taken into account. The physical relations of stress-strain relations correspond to the theory of small elastic-plastic deformations. The effect of heat flow is taken into account. The temperature field in the plate was calculated by the formula obtained by averaging the thermophysical parameters over the thickness of the package. The system of differential equations of equilibrium under loading of the plate from the natural state is obtained by the Lagrange variational method. Boundary conditions on the plate contour are formulated. The solution of the corresponding boundary value problem is reduced to finding the three desired functions: deflection, shear and radial displacement of the shear surface of the filler. A non-uniform system of ordinary nonlinear differential equations is written for these functions. Its analytical iterative solution is obtained in Bessel functions by the method of elastic solutions of Ilyushin. In case of repeated alternating loading of the plate, the solution of the boundary value problem is constructed using the theory of variable loading of Moskvitin. In this case, the hypothesis of similarity of plasticity functions at each loading step is used. Their analytical form is taken independent of the point of unloading. However, the material constants included in the approximation formulas will be different. The cyclic hardening of the material of the bearing layers is taken into account. The parametric analysis of the obtained solutions under different boundary conditions in the case of a local load distributed in a circle is carried out. The influence of temperature and nonlinearity of layer materials on the displacements in the plate is numerically investigated.

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11

Manuylov, Gaik A. "THE APPROXIMATE SOLUTION FOR PLATES USING MODIFIED RAYLEIGH-RITZ METHOD." International Journal for Computational Civil and Structural Engineering 13, no. 4 (December 31, 2017): 121–27. http://dx.doi.org/10.22337/2587-9618-2017-13-4-121-127.

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For thin elastic plates of arbitrary shape with a smooth pinched or hinged contour based on the modified Rayleigh-Ritz method, explicit expressions are obtained for the approximate values of the maximum deflection from a uniformly distributed load, the deflection at the point of application of the concentrated force, the critical force of uniform compression, and the first eigenfrequency. The lateral movements were approximated by special functions having level lines similar to the plate contour. The results of calculating the plate in the form of a pear-shaped oval are presented, which are in good agreement with the two-sided geometric estimates of the corresponding solutions

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12

Yuan, En Tao, Bing Shao, and Qui Xian Fei. "Slicing Contour Generation of Z-Constant Contour Machining for Subdivision Surface." Advanced Materials Research 225-226 (April 2011): 982–86. http://dx.doi.org/10.4028/www.scientific.net/amr.225-226.982.

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For the Z-constant contour machining, a slicing contour generation procedure for subdivision surface is presented. Subdivision surface defines a smooth surface as the limit of a sequence of successive refinements starting from an initial control mesh. It can easily generate smooth surfaces of complex arbitrary topology without intricate patch stitching and curve trimming. Instead of randomly intersecting each facet with a slicing plane and having to construct the slicing contour later, this paper takes full use of the topological information of subdivision surface to construct the slicing contour. The contour information is collected as marching from one effective edge to neighboring effective edge. Example shows our method is obviously easier and the complexity has been reduced

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13

Wang, Han, Hongfu Zuo, Zhenzhen Liu, Hang Fei, Yan Liu, and Zhiqiang Jiang. "Research on 3D reconstruction method of wear particle dynamic image based on multi contour space mapping." IOP Conference Series: Materials Science and Engineering 1207, no. 1 (November 1, 2021): 012017. http://dx.doi.org/10.1088/1757-899x/1207/1/012017.

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Abstract Aiming at the problems of current image monitoring methods of lubrication oil wear particles, this paper designs and builds a dynamic monitoring system for oil wear particles based on microfluidic microscopic images. A contour-based 3D reconstruction method of debris particle images is proposed. The image sequences of rotating wear particles tracked by a single target are used as data, and the contour of the wear particle is extracted and the data is stored. The minimum area external rectangle method is used to correct the rotation of the particle images for the problem of deflection. And an algorithm based on cylindrical coordinate space conversion is used to convert the discrete contour point data into three-dimensional space. Complete the 3D model reconstruction of microfluidic wear particles. The ability to analyse wear particles in oil online monitoring technology is improved, which also shows new ideas for wear status monitoring and fault diagnosis technology.

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14

YU, Chengguo, Zhili ZHANG, Xuqing NIE, and Long ZHANG. "A large-deflection deformation reconstruction method for semi-flexible plate nozzle based on strain-moment relationship." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 40, no. 6 (December 2022): 1312–19. http://dx.doi.org/10.1051/jnwpu/20224061312.

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To enhance the health detection capability of the semi-flexible plate nozzle in a supersonic wind tunnel, a large-deflection deformation reconstruction algorithm for a semi-flexible plate nozzle based on the strain-moment relationship is developed. The multi-jack semi-flexible plate nozzle in the supersonic wind tunnel is studied; its mechanical model of contour assembly is established. The differential equation of flexible plate contour curve is deduced, and the elliptic integral expression of the flexible plate deformation is given. Based on the deformation theory of a rectangular thin plate, the deformation reconstruction algorithm is modified, and its correction effect is simulated and analysed with the finite element method. The maximum deviation after correction is only 10.78% compared with that before correction. The 0.3 m semi-flexible plate nozzle is used as the experimental platform to carry out the experimental study. The experimental results show that under the 6 Mach number, the large-deflection deformation reconstruction results based on strain-moment relationship are in good agreement with the experimental results. The coordinate deviation of the nozzle throat position is about 6.12% compared with the structural deformation, thus verifying that the deformation reconstruction algorithm in this paper is effective and accurate.

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15

Linß, Sebastian, Philipp Schorr, and Lena Zentner. "General design equations for the rotational stiffness, maximal angular deflection and rotational precision of various notch flexure hinges." Mechanical Sciences 8, no. 1 (March 15, 2017): 29–49. http://dx.doi.org/10.5194/ms-8-29-2017.

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Abstract. Notch flexure hinges are often used as revolute joints in high-precise compliant mechanisms, but their contour-dependent deformation and motion behaviour is currently difficult to predict. This paper presents general design equations for the calculation of the rotational stiffness, maximal angular elastic deflection and rotational precision of various notch flexure hinges in dependence of the geometric hinge parameters. The novel equations are obtained on the basis of a non-linear analytical model for a moment and a transverse force loaded beam with a variable contour height. Four flexure hinge contours are investigated, the semi-circular, the corner-filleted, the elliptical, and the recently introduced bi-quadratic polynomial contour. Depending on the contour, the error of the calculated results is in the range of less than 2 % to less than 16 % for the suggested parameter range compared with the analytical solution. Finite elements method (FEM) and experimental results correlate well with the predictions based on the comparatively simple and concise design equations.

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16

Reynolds, Robert, and Allan Stauffer. "Is Catalan’s Constant Rational?" Mathematics 10, no. 22 (November 14, 2022): 4251. http://dx.doi.org/10.3390/math10224251.

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This paper employs a contour integral method to derive and evaluate the infinite sum of the Euler polynomial expressed in terms of the Hurwitz Zeta function. We provide formulae for several classes of infinite sums of the Euler polynomial in terms of the Riemann Zeta function and fundamental mathematical constants, including Catalan’s constant. This representation of Catalan’s constant suggests it could be rational.

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17

TURKOV, A. V., S. I. POLESHKO, E. A. FINADEEVA, and K. V. MARFIN. "RELATIONSHIP OF MAXIMUM DEFLECTIONS AND NATURAL FREQUENCIES VIBRATIONS OF ISOTROPIC CIRCULAR PLATES WITH INHOMOGENEOUS RESISTANCE CONDITIONS ON THE OUTER AND INNER CONTOUR." Building and reconstruction 98, no. 6 (2021): 36–42. http://dx.doi.org/10.33979/2073-7416-2021-98-6-36-42.

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The relationship between the maximum deflections from a static uniformly distributed load W0 and the fundamental frequency of natural transverse vibrations of a round isotropic plate of linearly variable thickness with thickening to the edge under homogeneous conditions of support along the outer contour, depending on the ratio of the thickness of the plate in the center to the thickness along the edge, is considered. According to the results of the study, graphs of the dependence of the maximum deflection and the frequency of natural vibrations of the plate on the ratio t1 / t2 are constructed. It is shown that for round plates of linearly variable thickness at t1/t2<1.1 coefficient K with an accuracy of 5.9% coincides with the analytical coefficient for round plates of constant thickness. Numerical studies shows that when the ratio of the thicknesses on the contour and in the center is equal to two, the difference in the coefficient K, which depends on the relationship between the static and dynamic characteristics of the platinum, is about 25% for hinged support along the contour and up to 37% for rigid support. This indicates a more significant effect of uneven mass distribution for such boundary conditions.

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18

Henning, Stefan, Sebastian Linß, and Lena Zentner. "detasFLEX – A computational design tool for the analysis of various notch flexure hinges based on non-linear modeling." Mechanical Sciences 9, no. 2 (November 20, 2018): 389–404. http://dx.doi.org/10.5194/ms-9-389-2018.

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Abstract. Notch flexure hinges are commonly used in compliant mechanisms for precision engineering applications and yet important rotational properties of a hinge like the bending stiffness, maximum angular deflection and rotational precision are difficult to predict accurately and simultaneously. There exist some closed-form equations and a few design tool approaches for calculating flexure hinges with particular geometries, but apart from that no comprehensive calculation program for the contour-specific analysis is known to the authors. Developed in MATLAB, this paper presents a novel computational design tool using a non-linear analytical approach for large deflections of rod-like structures to calculate the elasto-kinematic flexure hinge properties by numerically solving a system of differential equations. Building on previous investigations, four certain hinge contours are implemented, the circular, the corner-filleted, the elliptical, and the power function-based contour with different exponents. In addition to the theoretical approach and the implementation it is exemplarily shown, that finite elements method (FEM) results correlate well with the analytical design tool results. For a given deflection angle of 10° and a corner-filleted contour as an example, the deviations of the bending stiffness are between 0.1 % and 9.4 % for typical parameter values. The presented design tool can be beneficial for the accelerated and systematic synthesis of compliant mechanisms with optimized flexure hinges.

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19

Sun, Dechuan, Tianyou Luo, and Qiang Feng. "New Contour Design Method for Rocket Nozzle of Large Area Ratio." International Journal of Aerospace Engineering 2019 (December 20, 2019): 1–8. http://dx.doi.org/10.1155/2019/4926413.

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A rocket engine for space propulsion usually has a nozzle of a large exit area ratio. The nozzle efficiency is greatly affected by the nozzle contour. This paper analysed the effect of the constant capacity ratio in Rao’s method through the design process of an apogee engine. The calculation results show that increasing the heat capacity ratio can produce an expansion contour of smaller expansion angle and exit area ratio. A simple modification of Rao’s method based on thermally perfect gas assumption was made and verified to be more effective. The expansion contour designed by this method has much thinner expansion section and higher performance. For the space engine, a new extension contour type for the end section of the nozzle is proposed. The extension curve bent outward with increasing expansion angle increases the vacuum specific impulse obviously.

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20

Mazumdar, J., A. Ghosh, J. S. Hewitt, and P. K. Bhattacharya. "Elastic plastic analysis of shallow shells—a new approach." ANZIAM Journal 47, no. 1 (July 2005): 121–30. http://dx.doi.org/10.1017/s1446181100009810.

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AbstractA simple and efficient method for the analysis of the elastic-plastic bending of shallow shells is presented. The method is based upon the concept of contour lines of equal deflection on the surface of the shell, and uses Illyushin's theory of plastic deformation. As an illustration of the method, a technically interesting example of a shallow elliptic elastic dome is examined. Results are obtained for increasing loads and varying aspect ratios, and are illustrated graphically. The application of the method to other shell geometries is quite straightforward.

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21

Budi, Sigit Setijo, Agus Suprihadi, and Syarifudin Syarifudin. "Analisis Tegangan City Electric Car Torsi Beam Suspension Menggunakan Metode Finite Element Model (FEM)." Infotekmesin 12, no. 1 (April 13, 2021): 93–97. http://dx.doi.org/10.35970/infotekmesin.v12i1.463.

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The torsion beam is one of the most important parts of an electric car. The torsion beam can accept the loading of vehicle structures statically and dynamically. The movement of the vehicle, such as turning, turning with a bumpy road contour, affects the stress limit that the torsion beam can support. This study aims to simulate the effects of shifts such as deflection and stress on the use of a torsion beam suspension. The method used is a loading simulation using the Finite Element Model (FEM) model. The results showed that the maximum deflection effect occurred in the 2000N loading of 1.5347 mm, while the maximum stress effect occurred in the 2000N loading of 2342.57N.

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22

Chew, Kuew Wai, C. K. Leong, and Bok Min Goi. "Contour Data Acquisition System for Electric Vehicle Distance Estimation Method." Applied Mechanics and Materials 479-480 (December 2013): 503–7. http://dx.doi.org/10.4028/www.scientific.net/amm.479-480.503.

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The conventional distance estimation system only uses a constant speed and a constant level of road elevation to estimate the driving mileage for a vehicle. This technique leads to a low accuracy. In the current project, a new estimation technique namely; the Contour Positioning System (CPS) for an electric vehicle has been proposed. The CPS has a better estimation on the electric vehicle battery usage because of the consideration of road elevation, regenerative energy etc. In order to perform the CPS calculation, the elevation profile of the selected destination must be known. In this paper, the technique to extract the elevation profile i.e. latitude, longitude and altitude has been performed and evaluated using Google Maps or Google EarthÒ. This method enables the user to obtain the road information and compute the amount of energy needed to reach the said destination.

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23

Galbinean, Sergiu. "APPLICATION OF DISCONTINUOUS SOLUTIONS IN BOUNDARY ELEMENT METHOD FOR THE BENDING PROBLEMS OF KIRCHHOFF PLATES WITH AN ARBITRARY CONTOUR." Journal of Engineering Science 30, no. 2 (July 1, 2023): 23–33. http://dx.doi.org/10.52326/jes.utm.2023.30(2).02.

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Анотація:

The discontinuous solutions represent a new direction for the indirect Boundary Element Method (BEM) in the indirect formulation. Discontinuous solutions represent those functions, which when crossing certain lines, the transverse deflection, the slope angle, the bending moment and the generalized shear force may have jumps. These can be used to solve important problems for which the existing methods do not have solutions or a satisfactory accuracy, such as: plates of arbitrary contour, presence of defects, mixed boundary conditions, contact problems, infinite domains etc. In this paper, we describe the methodology of application and the numerical implementation of discontinuous solutions for the bending problems of plates with an arbitrary contour in the classical theory (Kirchhoff). For this purpose, programming codes were developed in the Matlab language, which allowed to calculate the displacements and efforts in the plate. The obtained results were compared with the Finite Element Method (FEM) for different mesh densities.

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24

Rajalingham, C., R. B. Bhat, and G. D. Xistris. "Natural Frequencies and Mode Shapes of Elliptic Plates With Boundary Characteristic Orthogonal Polynomials as Assumed Shape Functions." Journal of Vibration and Acoustics 115, no. 3 (July 1, 1993): 353–58. http://dx.doi.org/10.1115/1.2930356.

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The natural frequencies and natural modes of vibration of uniform elliptic plates with clamped, simply supported and free boundaries are investigated using the Rayleigh-Ritz method. A modified polar coordinate system is used to investigate the problem. Energy expressions in the Cartesian coordinate system are transformed into the modified polar coordinate system. Boundary characteristic orthogonal polynomials in the radial direction, and trigonometric functions in the angular direction are used to express the deflection of the plate. These deflection shapes are classified into four basic categories, depending on their symmetrical or antisymmetrical properties about the major and minor axes of the ellipse. The first six natural modes in each of the above categories are presented in the form of contour plots.

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25

Li, Zonghai, Yujie Duan, and Junji Jia. "Deflection of charged massive particles by a four-dimensional charged Einstein–Gauss–Bonnet black hole." Classical and Quantum Gravity 39, no. 1 (December 6, 2021): 015002. http://dx.doi.org/10.1088/1361-6382/ac38d0.

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Abstract Based on the Jacobi metric method, this paper studies the deflection of a charged massive particle by a novel four-dimensional charged Einstein–Gauss–Bonnet black hole. We focus on the weak field approximation and consider the deflection angle with finite distance effects. To this end, we use a geometric and topological method, which is to apply the Gauss–Bonnet theorem to the Jacobi space to calculate the deflection angle. We find that the deflection angle contains a pure gravitational contribution δ g, a pure electrostatic δ c and a gravitational–electrostatic coupling term δ gc. We find that the deflection angle increases (decreases) if the Gauss–Bonnet coupling constant α is negative (positive). Furthermore, the effects of the BH charge, the particle charge-to-mass ratio and the particle velocity on the deflection angle are analyzed.

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26

Setiawan, Asri Mulya, and Erniati Bachtiar. "Studi Kapasitas Lendutan, Daktalitas, dan Kekakuan pada Balok Beton Bertulang yang Diperkuat GFRP-S dengan Perendaman Air Laut Selama Satu Tahun." Indonesian Journal of Fundamental Sciences 5, no. 2 (November 18, 2019): 112. http://dx.doi.org/10.26858/ijfs.v5i2.11112.

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This study aims to analyze the deflection capacity, ductality and stiffness of reinforced concrete beam structures reinforced by GFRP with sea water immersion for 1 year. The test method used is a monotonic loading method that uses two simple supports over the test object and is pressed at a constant ramp actuator speed of 0.05 mm / sec until the concrete beam fails. The test results show that BF0 is more ductile compared to BF6 and BF12. This can be seen the existing deflection, where BF0 has a deflection that tends to be larger than the other beams. In BF0 specimens, the load that is able to hold is greater than BN specimens, but the resulting deflection is also greater

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27

Li, Wei Zhao, Xiao Min Huang, and Yan Li. "Rapid Assessment Method of Girder Bridge Carrying Capacity Based on Traffic Running Test." Key Engineering Materials 574 (September 2013): 11–19. http://dx.doi.org/10.4028/www.scientific.net/kem.574.11.

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The dynamic response under running vehicle of the bridge includes the static response. The frequency components of simple supported beam dynamic response under the uniform constant force and the harmonic force were discussed. A method using the low pass filter to extract the static displacement from dynamic response curves was proposed and extended to the continuous girder bridge. Simulation analysis describes the process of extracting static displacement. The results show that the method is effective to separate the static and dynamic compositions from the vibration deflection. The dynamic deflection curves of an actual bridge was studied to get the generalized influence lines and then vehicles were laid on them as the static load test program to estimate the static deflection. The results of research show the estimative deflection has high precision and meets the requirements of the bridge inspection. This method can replace the static load test for rapid assessment of the girder bridge.

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28

Sheng, Xian Jun, Ke Xin Wang, Ren Ke Kang, and Yong Qi Wang. "Analysis and Compensation Following Error of Feed Drive in CNC." Applied Mechanics and Materials 26-28 (June 2010): 591–97. http://dx.doi.org/10.4028/www.scientific.net/amm.26-28.591.

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In CNC machining, the constant following error was caused by the uniform motion of feed drive, which could induced contour error in the multi-axis movement, and the contour error would affect machining accuracy. In this paper, the produce principle of following error is analyzed, as well as the influences of following error on contour of linear and circular interpolation. The following error was compensated by velocity feedforward controller, and a new method for identifying coefficient of velocity feedforward controller is presented, based on the actual observed values of following error. The following error was eliminated after compensating with the proposed method.

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29

Yu, Chengguo, Xinyu Gao, Wenlin Liao, Zhili Zhang, and Guishan Wang. "A Highly Accurate Method for Deformation Reconstruction of Smart Deformable Structures Based on Flexible Strain Sensors." Micromachines 13, no. 6 (June 8, 2022): 910. http://dx.doi.org/10.3390/mi13060910.

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Анотація:

Smart deformable structures that integrate designing, sensing, and controlling technology have been widely applied in the fields of aerospace, robotics, and biomedical engineering due to their multi-functional requirements. The deformation reconstruction method essential for security monitoring and shape controlling, especially for the large deflection deformation, remains a challenge on accuracy and efficiency. This paper takes a wind tunnel’s fixed-flexible nozzle (FFN) plate as the research object to develop a highly accurate deformation reconstruction method based on sensing information from flexible strain sensors. The mechanical behaviors of the FFN plate with large deflection deformation, which is modeled as a cantilever beam, are studied to analyze the relationship of the strain and moment. Furthermore, the large deflection factor and shell bending theory are creatively utilized to derive and modify the strain–moment based reconstruction method (SMRM), where the contour of the FFN plate is solved by particular elliptic integrals. As a result, structural simulation based on ABAQUS further demonstrates that the reconstruction error of SMRM is 21.13% less than that of the classic Ko-based reconstruction method (KORM). An FFN prototype accompanied by customized flexible sensors is developed to evaluate the accuracy and efficiency of the SMRM, resulting in a maximum relative error of 3.97% that is acceptable for practical applications in smart deformable structures, not limited to the FFN plate.

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30

Xiao, Yi. "Large Deflection of Tip Loaded Beam with Differential Transformation Method." Advanced Materials Research 250-253 (May 2011): 1232–35. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.1232.

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This paper deals with large deflection problem of a cantilever beam with a constant section under the action of a transverse tip load. The differential transformation method (DTM) is used to solve the nonlinear differential equation governing the problem. An approach treats trigonometric nonlinearity is used in DTM. The results obtained from DTM are compared with those results obtained by the finite difference method and they agree well.

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31

Ma, Zihao. "Research on calculation strategy of perimeter of irregular objects." Highlights in Science, Engineering and Technology 49 (May 21, 2023): 220–26. http://dx.doi.org/10.54097/hset.v49i.8508.

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Image processing is a burgeoning subject in recent decades, which combines related theories with modern high technology to systematically study various image theories, technologies and applications. In the problem of industrial precision dimension detection, the edge of the obtained target image is rough and noisy due to the manufacturing accuracy, breakage and corrosion of the workpiece, which makes automatic detection difficult. Therefore, it has become a difficult problem to accurately extract the characteristic curve of the target edge in the development of industrial automatic detection system. Image measurement method has the advantages of non-contact, high speed, large dynamic range and rich information, and is widely used in the field of measurement. This paper introduces the principle of foot type three-dimensional contour measurement based on the light cutting method. Aiming at the composition of a multi CCD light cutting measurement system, a new method for high-precision extraction of the center line of the contour light band using the combination of central axis tracking and improved deflection measurement principle is proposed. The extraction and processing process of the light cutting surface contour image is described in detail, and through the coordinate transformation of the extracted center line, The complete profile data of the foot profile are obtained. The experimental results show that the processing effect of this method is satisfactory.

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32

Schierle, Stefan, Nils Straub, Peter Woias, and Frank Goldschmidtboeing. "Creep Compensation in an Electrostatic PDMS-Membrane Actuator with Flexible Silver Nanowire Electrodes." Proceedings 2, no. 13 (December 11, 2018): 1088. http://dx.doi.org/10.3390/proceedings2131088.

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An electrostatic membrane actuator with an elastomer membrane as movable part and silver nanowires (AgNWs) as flexible electrode material is built and characterized. A layered and modular actuator design facilitates simple and fast modification of actuator properties for characterization purposes. The tested actuators allow a membrane center deflection in the range of over 50 μm with applied voltages lower than 1 kV. The observable membrane center deflection exhibits a viscoelastic creep behavior. With the aim to achieve a more stable membrane deflection, a simple correction function was applied to the constant electrode voltage thus compensating the linear creep rate. With this method, the creep rate was changed from +0.27 μm/s to −0.08 μm/s. This method already improves the stability of the actuator deflection to a high degree.

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33

TURKOV, A. V., S. I. POLESHKO, E. A. FINADEEVA, and K. V. MARFIN. "THE RELATIONSHIP OF DEFLECTIONS AND FREQUENCIES OF NATURAL TRANSVERSE VIBRATIONS OF CIRCULAR ISOTROPIC PLATES OF VARIABLE THICKNESS ACCORDING TO THE LAW A SQUARE PARABOLA WITH A THICKENING TO THE CENTER." Building and reconstruction 99, no. 1 (2022): 59–66. http://dx.doi.org/10.33979/2073-7416-2022-99-1-59-66.

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Анотація:

The relationship between the maximum deflections W0 from a static uniformly distributed load q and the fundamental frequency of natural transverse vibrations ω of a round isotropic plate of variable thickness according to the law of a square parabola with a thickening in the center under homogeneous conditions of support along the outer contour, depending on the ratio of the thickness of the plate in the center to the thickness along the edge, is considered.According to the results of the study, graphs of the dependence of the maximum deflection and the frequency of natural vibrations of the plate on the ratio t2/ t1 are constructed. It is shown that for round plates of linearly variable thickness at t2/t1≤1.1, the coefficient K with an accuracy of 5.29% coincides with the analytical coefficient for round plates of constant thickness.

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34

Peng, Quancheng, Tengjiao Lin, and Hesheng Lv. "Calculation of optimum profile modification curve for gear pair based on complex potential method." Journal of Vibration and Control 25, no. 23-24 (September 5, 2019): 2921–34. http://dx.doi.org/10.1177/1077546319873464.

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The optimum profile modification curve of a gear pair is usually determined according to the fluctuation minimization of static transmission error (STE). For the calculation of STE, the potential energy method dismisses the correlative tooth deflection induced by gear body elastic coupling effects, and the finite element method requires high calculation cost. In order to simultaneously obtain high calculation accuracy and efficiency, the single tooth deflection is calculated through analytical integration about the Hertz contact pressure based on the conformal map method. The correlative tooth deflection is calculated based on the power series solution of the mixed boundary problem of an elastic annulus. Via combination of deflection compatibility and the force equilibrium condition, a contact analysis model of a spur gear pair is built. Based on the model, the STE is first calculated and compared with the finite element analysis result to verify the model rationality. Then, the optimum profile modification curve which renders constant STE is calculated. For a gear pair with the obtained modification curve, fluctuation of dynamic transmission error also decreases and the optimization effect is verified.

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35

Martinez-Cazares, Gabriela, Rafael Mercado-Solis, Yaneth Bedolla-Gil, and Diego Lozano. "Continuous Estimation of the Crack Growth Rate during Rotating‒Bending Fatigue Testing." Metals 9, no. 3 (February 28, 2019): 275. http://dx.doi.org/10.3390/met9030275.

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A method for estimating the crack growth rate in steel during rotating‒bending fatigue testing is presented. Constant deflection tests were conducted in which the initial load remained constant prior to crack nucleation, when it decreased as the crack grew. In the proposed approach, steel samples were sharp-notched to produce a characteristic circular fracture upon loading and the final fracture area was correlated with a ratio of the load prior to fracture and the initial load. In this method, the deflection imposed is a function of a material’s elastic modulus rather than its yield strength and the correlation obtained to estimate the average crack length as a function of the instantaneous load is independent of the applied stress or steel grade.

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36

Song, J., and M. Sunwoo. "Analysis of flame kernel development with Schlieren and laser deflection in a constant volume combustion chamber." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 216, no. 7 (July 1, 2002): 581–90. http://dx.doi.org/10.1243/095440702760178604.

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The purpose of this study is to investigate the relation between ignition systems (or energy) and flame kernel development. In this research, three different kinds of ignition systems and several different kinds of spark plug electrodes are designed and manufactured. The flame propagation velocity in a constant volume combustion chamber is measured by both a laser deflection method using an He-Ne laser and a Schlieren method using a high speed digital camera. In order to control the ignition energy, the dwell time is varied by a spark time controller. The results indicate that, when the ignition energy is increased by extending the dwell time, flame kernel growth accelerates. As the electrode gap width is increased, the breakdown energy is also increased, which stimulates the initial kernel development. The materials, diameter and shape of the electrode affect the discharged energy, the energy transfer efficiency and heat losses and, thus, these also affect the flame kernel development. The average difference in measurement of the flame velocity by the laser deflection method and Schlieren method is only 1.73 per cent. The laser deflection method is found to be preferable because it is more effective and employs simpler means for the analysis of flame kernel development.

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37

Borboni, Alberto, Diego De Santis, Luigi Solazzi, Jorge Hugo Villafañe, and Rodolfo Faglia. "Ludwick Cantilever Beam in Large Deflection Under Vertical Constant Load." Open Mechanical Engineering Journal 10, no. 1 (March 28, 2016): 23–37. http://dx.doi.org/10.2174/1874155x01610010023.

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The aim of this paper is to calculate the horizontal and vertical displacements of a cantilever beam in large deflections. The proposed structure is composed with Ludwick material exhibiting a different behavior to tensile and compressive actions. The geometry of the cross-section is constant and rectangular, while the external action is a vertical constant load applied at the free end. The problem is nonlinear due to the constitutive model and to the large deflections. The associated computational problem is related to the solution of a set of equation in conjunction with an ODE. An approximated approach is proposed here based on the application Newton-Raphson approach on a custom mesh and in cascade with an Eulerian method for the differential equation.

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38

Kamenev, I. V. "Verification of the mathematical modelof the deformed state of cylindrical CLT-panels." Вестник гражданских инженеров 20, no. 3 (2023): 25–32. http://dx.doi.org/10.23968/1999-5571-2023-20-3-25-32.

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In this paper, the verification of the mathematical model previously proposed by the author for studying the stress-strain state of multilayer cylindrical panels from CLT is carried out. For this purpose, the calculation results of the author's model of three shells of different geometry made of a different number of layers are compared with the calculation results of such structures obtained in PC «Lira-SAD».Structures fixed along the contour in a hinged and rigid manner were subjected to the action of a small evenly distributed transverse load, with the greatest possible panel deflections of 4 mm. The comparison of the deformed state was carried out by the biggest deflection and the deflection in the center of the shells, as well as by the shape of the deformed state of the structures. At the same time, there was studied the influence of the number of functions in the expansion in the Ritz method on the accuracy of the proposed mathematical model. It is shown that with 16 or more terms in the expansion, the deflection calculation error in comparison with the Lira-SAPR PC does not exceed 10%.

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39

Stanciu, Mariana Domnica, Ioan Curtu, and Teodor Mocanu. "Mechanical Behavior of Guitar Neck under Simple Bending Stress Analyzed with Finite Elements Method." Applied Mechanics and Materials 658 (October 2014): 225–30. http://dx.doi.org/10.4028/www.scientific.net/amm.658.225.

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This paper presents the results of the FEM analysis of the mechanical behavior of guitar subjected to simple bending. Deformation of guitar neck by string tension constitutes a quality defect of finished product - guitars, which affect the acoustic of instrument. The neck bending modified length guitar strings which leads to obtaining false sounds. Therefore, the aim of the research was to establish the stresses and strains state of the guitar neck in terms of varying the position and force size and contour conditions. It was found that both deflection and stress are maximum values when force is applied on joint area between neck and guitar body. Stiffening of the guitar neck by increasing section or by using stiffer material can conduct to lower displacements, irrespective deformations of guitar neck.

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40

Alebrahim, Reza, Nik Abdullah Nik Mohamed, Sallehuddin Mohamed Haris, and Salvinder Singh Karam Singh. "Vibration Analysis of Multi-Cracked Beam Traversed by Moving Masses Using Discrete Element Technique." Applied Mechanics and Materials 376 (August 2013): 220–23. http://dx.doi.org/10.4028/www.scientific.net/amm.376.220.

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The vibration analysis of a multi-cracked beam using discrete element technique (DET) was investigated in this study. Undamped simply supported beam was traversed by moving mass with constant speed and Euler Bernoulli beam theory was considered. Cracks are located in different positions and maximum deflection of mid-span was derived and compared. The results showed that increasing numbers of cracks in the beam causes more deflection while maximum deflection of beam takes longer time to build up. The results were validated by solving the equations generated using finite element method (FEM) and their comparison with already established results from previous similar studies (literatures) showed good agreement.

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41

Melnikov, Y. A. "Influence Functions of a Point Force for Kirchhoff Plates with Rigid Inclusions." Journal of Mechanics 20, no. 4 (December 2004): 249–56. http://dx.doi.org/10.1017/s1727719100003464.

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AbstractA semi-analytic method is proposed for two problem settings for a Kirchhoff plate containing an absolutely rigid circular inclusion and undergoing a transverse point force. The settings differ by the location (within and out of inclusion) of the force application point. In both cases, the plate's stress-strain state is simulated with a boundary value problem for the biharmonic equation stated over a doubly connected region whose inner contour represents the edge of the inclusion. Boundary conditions imposed on the inner contour bring some parameters which are found via the equations of static equilibrium of the inclusion. A modification of the Kupradze'smethod of functional equationsis proposed for obtaining influence functions of a point force for such plates. Green's functions of the biharmonic equation for appropriately shaped simply connected regions are employed. Numerical differentiation is never required in the computing of stress components and the latter are subsequently found with accuracy level comparable with that attained for the deflection function.

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42

Wen, Shifeng, Xiaohu Zeng, and Gongnan Xie. "A Numerical Procedure to Obtain the Creep Parameters of the Thermal Barrier Coating." Advances in Mechanical Engineering 6 (January 1, 2014): 920354. http://dx.doi.org/10.1155/2014/920354.

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Three-point bending creep test was used to understand the creep behavior of typical thin film/substrate systems—thermal barrier coating (TBC) systems. Firstly, a simplified model, which does not consider the local effect, has been set up to get an analytical relationship. The important result is that creep stress exponent of materials is equal to the creep load exponent of the steady-state deflection rate of BC specimens. Secondly, in order to consider the local effect of bending, the finite element method (FEM) has been carried out. FEM calculation shows that there is a steady stage of the creep deflection under a constant applied load. And the exponent of the steady-state creep deflection rate to the applied load is found to be equal to the creep stress exponent of materials. The creep constant of the materials can be obtained by a set of trials with assumed creep constants of materials and can be finally determined by the best fit method. Finally, the finite element results show that the influences of the friction, the thickness of TBCs, and the modulus ratio of TBC to the substrate on stress distribution are important.

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43

Wang, Tong, Jing Di, and Hongliang Zuo. "Long-Term Loading Experimental Research of Prestressed Glulam Beams Based on Creep Influence." Sustainability 14, no. 16 (August 11, 2022): 9937. http://dx.doi.org/10.3390/su14169937.

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In this paper, long-term loading tests of ten prestressed glulam beams were carried out for 45 days, using the loading method of three-point hanging heavy objects. We analyzed the influence of prestressed steel wire numbers and total preloading force on parameters such as failure mode of beams, variation of steel wire stress, and long-term deflection of mid-span. When the total prestress was constant and the number of steel wires was 2, 4, and 6, the total stress of steel wires decreased by 33.07%, 37.26%, and 50.04%, respectively, after long-term testing for 45 days. The ratio of mid-span deflection to total deflection was 61.5%, 54.8%, and 40.9% respectively. When the number of steel wires was constant and the values of total prestress were 0, 3.079 kN and 6.158 kN, the total stress decreased by 28.90%, 36.59%, and 36.63%, respectively, after long-term loading. The ratio of long-term deflection of mid-span to total deflection was 60.7%, 54.8%, and 39.3%, respectively. The more steel wires, the greater the value of total prestress and the loss of total stress, the smaller the mid-span long-term deflection. After the test, we analyzed and fitted the test data to obtain the specific numerical of the creep coefficient θ under normal conditions, and the formula for calculating the long-term stiffness of the glulam beams based on the creep effects is proposed.

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44

Averchenkov, Andrey, Inna Koloshkina, and Sergey Sheptunov. "Development and Optimization of Control Programs for 2.5-Coordinate Milling of Three-Dimensional Workpieces on CNC Machines." MATEC Web of Conferences 346 (2021): 01009. http://dx.doi.org/10.1051/matecconf/202134601009.

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The paper presents new methods for optimizing milling operations on CNC machines when programming in CAM-systems, in particular, a method for improving the efficiency of processing three-dimensional workpieces by 2.5-coordinate milling on CNC machines for contour machining and a method for improving the productivity of contour milling of products with a variable allowance at a constant optimal value of the chip thickness, with the provision of geometric parameters of surface quality. Mathematical dependences of the surface quality parameters on the milling conditions are determined. Algorithms of automated analysis are presented, and methods for designing such operations are developed.

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45

Reynolds, Robert, and Allan Stauffer. "Definite Integral of Arctangent and Polylogarithmic Functions Expressed as a Series." Mathematics 7, no. 11 (November 14, 2019): 1099. http://dx.doi.org/10.3390/math7111099.

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We present a method using contour integration to evaluate the definite integral of arctangent reciprocal logarithmic integrals in terms of infinite sums. In a similar manner, we evaluate the definite integral involving the polylogarithmic function L i k ( y ) in terms of special functions. In various cases, these generalizations give the value of known mathematical constants such as Catalan’s constant G, Aprey’s constant ζ ( 3 ) , the Glaisher–Kinkelin constant A, l o g ( 2 ) , and π .

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46

Ufe, M. M., S. N. Apebo, and A. Y. Iorliam. "Derivation and optimization of deflection equations for tapered cantilever beams using the finite element method." Nigerian Journal of Technology 39, no. 2 (July 16, 2020): 351–62. http://dx.doi.org/10.4314/njt.v39i2.5.

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This study derived analytical solutions for the deflection of a rectangular cross sectional uniformly tapered cantilever beam with varying configurations of width and breadth acting under an end point load. The deflection equations were derived using a numerical analysis method known as the finite element method. The verification of these analytical solutions was done by deterministic optimisation of the equations using the ModelCenter reliability analysis software and the Abaqus finite element modelling and optimisation software. The results obtained show that the best element type for the finite element analysis of a tapered cantilever beam acting under an end point load is the C3D20RH (A 20-node quadratic brick, hybrid element with linear pressure and reduced integration) beam element; it predicted an end displacement of 0.05035 m for the tapered width, constant height cantilever beam which was the closest value to the analytical optimum of 0.05352 m. The little difference in the deflection value accounted for the numerical error which is inevitably present in the analyses of structural systems. It is recommended that detailed and accurate numerical analysis be adopted in the design of complex structural systems in order to ascertain the degree of uncertainty in design. Keywords: Deflection, Finite element method, deterministic optimisation, numerical error, cantilever beam.

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47

Shi, Jiao, Jiaji Wu, Anand Paul, Licheng Jiao, and Maoguo Gong. "A Partition-Based Active Contour Model Incorporating Local Information for Image Segmentation." Scientific World Journal 2014 (2014): 1–19. http://dx.doi.org/10.1155/2014/840305.

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Анотація:

Active contour models are always designed on the assumption that images are approximated by regions with piecewise-constant intensities. This assumption, however, cannot be satisfied when describing intensity inhomogeneous images which frequently occur in real world images and induced considerable difficulties in image segmentation. A milder assumption that the image is statistically homogeneous within different local regions may better suit real world images. By taking local image information into consideration, an enhanced active contour model is proposed to overcome difficulties caused by intensity inhomogeneity. In addition, according to curve evolution theory, only the region near contour boundaries is supposed to be evolved in each iteration. We try to detect the regions near contour boundaries adaptively for satisfying the requirement of curve evolution theory. In the proposed method, pixels within a selected region near contour boundaries have the opportunity to be updated in each iteration, which enables the contour to be evolved gradually. Experimental results on synthetic and real world images demonstrate the advantages of the proposed model when dealing with intensity inhomogeneity images.

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48

Yazyev, Batyr M., Anton S. Chepurnenko, and Anzhelika V. Saibel. "MODELING OF STRESS-STRAIN STATE OF THICK CONCRETE SLABS TAKING THE CREEP OF CONCRETE INTO ACCOUNT." International Journal for Computational Civil and Structural Engineering 13, no. 4 (December 31, 2017): 140–48. http://dx.doi.org/10.22337/2587-9618-2017-13-4-140-148.

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In the article the derivation of the resolving equations for calculation taking into account creep of thick reinforced concrete plates is given. We use the hypothesis of a parabolic law for the distribution of tangential stresses over the thickness of a plate. The problem was reduced to a system of two differential equations with respect to deflection and the function of shear. An example is given of a calculation of a plate hinged on the contour loaded with a uniformly distributed load using a viscoelastic model of hereditary aging of concrete. The solution was carried out using double trigonometric series in combination with the Euler method for determining creep strains.

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49

Dandavate, Chetan. "False Engagements in AFM." Microscopy Today 7, no. 2 (March 1999): 26–27. http://dx.doi.org/10.1017/s1551929500063914.

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In scanning microscopes, like the Atomic Force Microscope (AFM), used in contact mode, scanning begins with engaging the tip with the sample at some contact force, which can be adjusted by the setpoint* (this is common to Digital Instruments' AFMs). It may differ for other brands. For a system that detects the motion of the cantilever with a laser beam, the setpoint basically gives an idea of the voltage difference between the top and bottom photo detectors, When the tip comes into contact, the feedback circuit adjusts the tip deflection according to the required contact force, This is the method commonly followed for the constant deflection method.

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50

Li, Zekun, Baolong Guo, and Fanjie Meng. "Fast Shape Recognition Method Using Feature Richness Based on the Walking Minimum Bounding Rectangle over an Occluded Remote Sensing Target." Remote Sensing 14, no. 22 (November 18, 2022): 5845. http://dx.doi.org/10.3390/rs14225845.

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Анотація:

Remote sensing target recognition has always been an important topic of image analysis, which has significant practical value in computer vision. However, remote sensing targets may be largely occluded by obstacles due to the long acquisition distance, which greatly increases the difficulty of recognition. Shape, as an important feature of a remote sensing target, plays an important role in remote sensing target recognition. In this paper, an occluded shape recognition method based on the local contour strong feature richness (contour pixel richness, contour orientation richness, and contour distance richness) to the walking minimum bounding rectangle (MBR) is proposed for the occluded remote sensing target (FEW). The method first obtains the local contour feature richness by using the walking MBR; it is a simple constant vector, which greatly reduces the cost of feature matching and increases the speed of recognition. In addition, this paper introduces the new concept of strong feature richness and uses the new strategy of constraint reduction to reduce the complex structure of shape features, which also speeds up the recognition speed. Validation on a self-built remote sensing target shape dataset and three general shape datasets demonstrate the sophisticated performance of the proposed method. FEW in this paper has both higher recognition accuracy and extremely fast recognition speed (less than 1 ms), which lays a more powerful theoretical support for the recognition of occluded remote sensing targets.

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