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Journal articles on the topic 'Constant deflection contour method'

Author: Grafiati

Published: 18 May 2024

Last updated: 31 July 2025

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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 (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 no

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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 (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-

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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 calcu

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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 anal

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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 (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 c

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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 (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 man

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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 (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 v

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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 (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 install

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10

Kirill, Trapezon, and Trapezon Alexandr. "CONSTRUCTION OF AN ALGORITHM TO ANALYTICALLY SOLVE A PROBLEM ON THE FREE VIBRATIONS OF A COMPOSITE PLATE OF VARIABLE THICKNESS." Eastern-European Journal of Enterprise Technologies 1, no. 7 (103) (2020): 26–33. https://doi.org/10.15587/1729-4061.2020.191123.

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The paper reports an algorithm to analytically solve one of the problems in the mechanics of elastic bodies, which is associated with studying the natural vibrations of a composite two-stage plate whose concave part is smoothly aligned with the part of a constant thickness. We have defined patterns for stating the boundary and transitional conditions, which should be taken into account when considering the natural vibrations of a two-stage plate. The ratios have been obtained, which make it possible to study the distribution of deflections and determine the values of amplitudes of the curved v

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11

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 (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 thr

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12

Kirill, Trapezon, and Trapezon Alexandr. "ANALYSIS OF FREE OSCILLATIONS OF CIRCULAR PLATES WITH VARIABLE THICKNESS BASED ON THE SYMMETRY METHOD." Eastern-European Journal of Enterprise Technologies 2, no. 7 (104) (2020): 12–18. https://doi.org/10.15587/1729-4061.2020.183319.

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Based on symmetry and factorization methods, a general analytical solution to the fourth-order differential equation has been derived for a problem on the free axisymmetric oscillations of a circular plate of variable thickness. The law of the thickness change is the concave parabola h=H<sub>0</sub>(1–μρ)<sup>2</sup>, where µ is a constant coefficient that determines the degree of plate concaveness. The solution has been given by the Bessel functions of zero and the first order of the actual and imaginary argument. A circular ring plate has been considered whose inner contou

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13

Manuylov, Gaik A. "THE APPROXIMATE SOLUTION FOR PLATES USING MODIFIED RAYLEIGH-RITZ METHOD." International Journal for Computational Civil and Structural Engineering 13, no. 4 (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

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14

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 cont

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15

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 (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.

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16

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 (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

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17

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 (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 fl

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18

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 constructe

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19

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 (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 compu

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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 (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

Reynolds, Robert, and Allan Stauffer. "Is Catalan’s Constant Rational?" Mathematics 10, no. 22 (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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22

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 (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 1.534

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23

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

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24

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 (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

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25

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 (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 categ

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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 (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

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27

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 (2023): 23–33. http://dx.doi.org/10.52326/jes.utm.2023.30(2).02.

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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 de

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28

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,

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29

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

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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 de

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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 (2022): 910. http://dx.doi.org/10.3390/mi13060910.

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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 fr

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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 (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 appli

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33

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 (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

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34

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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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 p

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35

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 s

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36

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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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 (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

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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 (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 igniti

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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

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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

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Wang, Tong, Jing Di, and Hongliang Zuo. "Long-Term Loading Experimental Research of Prestressed Glulam Beams Based on Creep Influence." Sustainability 14, no. 16 (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 def

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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 cr

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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

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Melnikov, Y. A. "Influence Functions of a Point Force for Kirchhoff Plates with Rigid Inclusions." Journal of Mechanics 20, no. 4 (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

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Vatulyan, Alexander O., and Ivan S. Kozachenko. "About the Deformation of the Lamina Cribrosa of the Eye." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 2 (222) (June 27, 2024): 21–32. http://dx.doi.org/10.18522/1026-2237-2024-2-21-32.

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Several problems pertaining to deformation of the circular elastic isotropic plate of variable rigidity in the presence of elastic support on the edge were study. In the first problem Timoshenko model was considered. In the second problem the deformation of a multilayer plate with piecewise constant Lame coefficient along the thickness coordinate which are assumed to be constant within one layer was researched, the Zig-zag method is used for modeling. The basis for constructing a solution for both problems is the use of Lagrange’s variation principle of plates, numerical solution constructed u

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Reynolds, Robert, and Allan Stauffer. "Definite Integral of Arctangent and Polylogarithmic Functions Expressed as a Series." Mathematics 7, no. 11 (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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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

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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 (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 approxima

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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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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 i

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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 (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 fi

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