Journal articles: 'Arc-Length Solver'

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Reynolds, Quinn G., Thokozile P. Kekana, and Buhle S. Xakalashe. "A Computational Magnetohydrodynamic Modelling Study on Plasma Arc Behaviour in Gasification Applications." Mathematical and Computational Applications 28, no. 2 (April 12, 2023): 60. http://dx.doi.org/10.3390/mca28020060.

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The application of direct-current plasma arc furnace technology to the problem of coal gasification is investigated using computational multiphysics models of the plasma arc inside such units. An integrated modelling workflow for the study of DC plasma arc discharges in synthesis gas atmospheres is presented. The thermodynamic and transport properties of the plasma are estimated using statistical mechanics calculations and are shown to have highly non-linear dependencies on the gas composition and temperature. A computational magnetohydrodynamic solver for electromagnetically coupled flows is developed and implemented in the OpenFOAM® framework, and the behaviour of three-dimensional transient simulations of arc formation and dynamics is studied in response to different plasma gas compositions and furnace operating conditions. To demonstrate the utility of the methods presented, practical engineering results are obtained from an ensemble of simulation results for a pilot-scale furnace design. These include the stability of the arc under different operating conditions and the dependence of voltage–current relationships on the arc length, which are relevant in understanding the industrial operability of plasma arc furnaces used for waste coal gasification.

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Bharali, Ritukesh, Somdatta Goswami, Cosmin Anitescu, and Timon Rabczuk. "A robust monolithic solver for phase-field fracture integrated with fracture energy based arc-length method and under-relaxation." Computer Methods in Applied Mechanics and Engineering 394 (May 2022): 114927. http://dx.doi.org/10.1016/j.cma.2022.114927.

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Hou, Jiatong, Bo You, Jiazhong Xu, and Qiaomu Hu. "Numerical simulation for expansion of preform and optimization of preform in thermoset composites." Advances in Mechanical Engineering 13, no. 5 (May 2021): 168781402110170. http://dx.doi.org/10.1177/16878140211017002.

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The expansion of preform and the optimization of preform have become important steps in the molding process. At present, there are some questions in the expansion of thermoset composite material preform and precompression, for example, the inaccurate dimensions, cracks, and wrinkles. For the expansion of preform, the finite element inverse algorithm is used as the expansion algorithm, and then the initial solution is optimized by the arc length mapping method, the expansion of preform is realized by the iterative equation which is solved by the ABAQUS solver. The effectiveness of the expansion of preform is verified through the comparison between the finite element inverse algorithm with DYNAFORM. The optimization of the precompression process is researched in order to solved the problems of cracks and wrinkles in the integral precompression method of preform. Firstly, the precompression sequence is adjusted by the precompression method, and then the precompression direction is optimized by the genetic algorithm. Through numerical simulation, the maximum thinning rate is reduced to 13%, and the maximum thickening rate is reduced to 6%, which improve the problems of cracks and wrinkles of preform, and the effectiveness of the optimization method is verified.

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Shamal, Souad Jabbar, Luay Sadiq Al-Ansari, Ahmed Niameh Mehdy Alhusseny, and Adel Gharib Nasser. "Roughness Effect on Thermo-Elasto-Hydrodynamic Performance of a 170ᵒ -Arc Partial Journal Bearing." Journal of Engineering 27, no. 1 (January 1, 2021): 16–34. http://dx.doi.org/10.31026/j.eng.2021.01.02.

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In the current analysis, the effects of circumferential scratches along the inner surface of a 170ᵒ -arc partial journal bearing has been numerically investigated. Their impact on the thermo-elasto-hydrodynamic performance characteristics, including maximum pressure, temperature, deformation, and stress, has been examined thoroughly. The ANSYS Fluent CFD commercial code was employed to tackle the iterative solution of flow and heat transfer patterns in the fluid film domain. They are then applied to the ANSYS Static Structure solver to compute the deformation and stress resulted in the solid bearing zone. A wide range of operating conditions has been considered, including the eccentricity ratio ( ) and scratch depth ( ). In contrast, the bearing length-diameter ratio (L/D) and the rotation speed (N) have been fixed at 0.77 and 1500 rpm, respectively. The thermo-hydrodynamic pressure, temperature, stress, and deformation have all been computed. It was found that the scratch depth has a direct effect on the thermo-hydrodynamic performance of the partial bearings. Meanwhile, the deep central scratches are important, especially at scratch depth equal to 0.224 mm.

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Shamal, Souad Jabbar, Luay Sadiq Al-Ansari, Ahmed Niameh Mehdy Alhusseny, and Adel Gharib Nasser. "Roughness Effect on Thermo-Elasto-Hydrodynamic Performance of a 170ᵒ -Arc Partial Journal Bearing." Journal of Engineering 27, no. 1 (January 1, 2021): 16–34. http://dx.doi.org/10.31026/10.31026/j.eng.2021.01.02.

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In the current analysis, the effects of circumferential scratches along the inner surface of a 170ᵒ -arc partial journal bearing has been numerically investigated. Their impact on the thermo-elasto-hydrodynamic performance characteristics, including maximum pressure, temperature, deformation, and stress, has been examined thoroughly. The ANSYS Fluent CFD commercial code was employed to tackle the iterative solution of flow and heat transfer patterns in the fluid film domain. They are then applied to the ANSYS Static Structure solver to compute the deformation and stress resulted in the solid bearing zone. A wide range of operating conditions has been considered, including the eccentricity ratio ( ) and scratch depth ( ). In contrast, the bearing length-diameter ratio (L/D) and the rotation speed (N) have been fixed at 0.77 and 1500 rpm, respectively. The thermo-hydrodynamic pressure, temperature, stress, and deformation have all been computed. It was found that the scratch depth has a direct effect on the thermo-hydrodynamic performance of the partial bearings. Meanwhile, the deep central scratches are important, especially at scratch depth equal to 0.224 mm.

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Barbieri, Ettore, Federica Ongaro, and Nicola Maria Pugno. "AJ-integral-based arc-length solver for brittle and ductile crack propagation in finite deformation-finite strain hyperelastic solids with an application to graphene kirigami." Computer Methods in Applied Mechanics and Engineering 315 (March 2017): 713–43. http://dx.doi.org/10.1016/j.cma.2016.10.043.

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7

Soria, Antonio, and Pierre Pegon. "An arc length control procedure to solve parabolic problems." Computer Methods in Applied Mechanics and Engineering 106, no. 1-2 (July 1993): 27–50. http://dx.doi.org/10.1016/0045-7825(93)90183-x.

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Chucheepsakul, S., C. M. Wang, X. Q. He, and T. Monprapussorn. "Double Curvature Bending of Variable-Arc-Length Elasticas." Journal of Applied Mechanics 66, no. 1 (March 1, 1999): 87–94. http://dx.doi.org/10.1115/1.2789173.

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This paper deals with the double curvature bending of variable arc-length elasticas under two applied moments at fixed support locations. One end of the elastica is held while the other end portion of the elastica may slide freely on a frictionless support at a prescribed distance from the held end. Thus, the variable deformed length of the elastica between the end support and the frictionless support depends on the relative magnitude of the applied moments. To solve this difficult and highly nonlinear problem, two approaches have been used. In the first approach, the elliptic integrals are formulated based on the governing nonlinear equation of the problem. The pertinent equations obtained from applying the boundary conditions are then solved iteratively for solution. In the second approach, the shooting-optimization method is employed in which the set of governing differential equations is numerically integrated using the Runge-Kutta algorithm and the error norm of the terminal boundary conditions is minimized using a direct optimization technique. Both methods furnish almost the same stable and unstable equilibrium solutions. An interesting feature of this kind of bending problem is that the elastica can form a single loop or snap-back bending for some cases of the unstable equilibrium configuration.

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Kalitkin, N. N., and I. P. Poshivaylo. "Guaranteed accuracy for the Cauchy problem solved using the arc length method." Doklady Mathematics 88, no. 2 (September 2013): 601–4. http://dx.doi.org/10.1134/s1064562413050219.

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Gao, Liyang, and Weiguo Wu. "Forward kinematics modeling of spatial parallel linkage mechanisms based on constraint equations and the numerical solving method." Robotica 35, no. 2 (June 19, 2015): 293–309. http://dx.doi.org/10.1017/s0263574715000508.

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SUMMARYIn order to solve general kinematics modeling problems and numerical stability problems of numerical methods for spatial parallel linkage mechanisms, a general modeling method and its numerical solving algorithm is proposed. According to the need for avoiding direct singular configurations, valid joint variable space and valid forward kinematics solutions (VKSs) are defined. Taking numerical convergence near singular points into account, the pseudo-arc length homotopy continuation algorithm is given to solve the kinematics model. Finally as an example, the joint variable space of the general Stewart platform mechanism is analyzed, which is proved to be divided into subspaces by direct singular surfaces. And then, forward kinematics solutions of 200 testing points are solved separately using the pseudo-arc length homotopy continuation algorithm, the Newton homotopy continuation algorithm and the Newton–Raphson algorithm (NRA). Comparison of the results shows that the proposed method is convergent to the same solution branch with the initial configuration on all the testing points, while the other two algorithms skip to other solution branches on some near singular testing points.

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Larionov, Hryhorii, Mykola Larionov, and Artem Pazynich. "Mathematical modeling of belt and rigid conveyer’s drum contact with non-affect Coulomb friction." E3S Web of Conferences 109 (2019): 00050. http://dx.doi.org/10.1051/e3sconf/201910900050.

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Conveyor’s belt with the drum contact task is paid a great researcher attention. It had solved in stresses with the mix boundary condition and Coulomb friction low action applies. Obtained solutions, as usual, do not satisfy to the displacement on drum surface boundary condition. The attempt to solve the system of Lamb equations in cylindrical coordinates in condition h/R<<1 values where h the belt thin and R drums radius is done. The Prandtl‘s technique and substitution methods are used to analytical solution obtain. As a result, the displacement expressions for rest and slide drum arcs are obtained. In search of rest arc length, radial and peripheral displacement equalities are used. Applied rest arc efforts are equal in values and have an opposite direction. The equality means the fact that traction efforts do not transfer under rest drum arc. The obtained results are coincided with the ones obtained by Zhukovskiy N.E. for flexible thread model. The fact to simultaneously satisfy to boundary conditions on inner and outer belt sides have to do the conclusion for boundary belt seam existing. Expressions for rest drum arc length without applied friction law are obtained. The displacement and corresponding stresses graphics are demonstrated.

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Chao, Zhiqiang, Fei Wang, Chuanqing Zhang, Huaying Li, and Feng Wang. "Research on the Algorithm of Measurement Path Planning for Inner Wall of Air-Intake Pipe Based on Spraying Robot System." International Journal of Pattern Recognition and Artificial Intelligence 31, no. 09 (February 16, 2017): 1759018. http://dx.doi.org/10.1142/s0218001417590182.

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To solve the problems with spraying over the inner wall of air-intake pipe, this paper introduces an algorithm of measurement path planning based on the spraying robot system and the laser displacement sensor technology. Scanning measurement path planning is the premise and basis of model construction and spray. Traditional methods, such as arc length extrapolation and polynomial are applicable only for the measurement of a plane curve with finite maximum curvature. Drawing references from existing method, this paper focuses on the pre-scanning measurement method for different types of cross-section curves. Algorithm simulation and model reconstruction show that this study solves the problem of collision avoidance for scanning measurement of the inner wall of air-intake pipe.

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Fan, H. G., S.-J. Na, and Y. W. Shi. "Numerical simulation of current density in gas tungsten arc welding including the influence of the cathode." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 211, no. 4 (April 1, 1997): 321–27. http://dx.doi.org/10.1243/0954405971516293.

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A two-dimensional axisymmetric numerical model including the influence of cathode is developed to describe the heat transfer and fluid flow in gas tungsten arc (GTA) welding arcs. The current continuity equation has been solved with the combined arc plasma-cathode system, independent of the assumption of current density distribution on the cathode surface which was essential in the previous studies of the arc plasma. It is indicated that the predicted arc column temperatures agree well with existing experimental data. The effects of current, electrode tip geometry and arc length on the anode current density distributions are analysed using the developed model, and the current density distributions calculated at the anode are compared with the experimental data measured by the probe method.

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Liang, Lie, Shujuan Li, Kehao Lan, Jiabin Wang, and Ruijiang Yu. "Fixed-Diamond Abrasive Wire-Saw Cutting Force Modeling Based on Changes in Contact Arc Lengths." Micromachines 14, no. 6 (June 20, 2023): 1275. http://dx.doi.org/10.3390/mi14061275.

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Monocrystalline silicon is widely used in the semiconductor market, but its hard and brittle physical properties make processing difficult. Fixed-diamond abrasive wire-saw (FAW) cutting is currently the most commonly used cutting method for hard and brittle materials due to advantages such as narrow cutting seams, low pollution, low cutting force and simple cutting process. During the process of cutting a wafer, the contact between the part and the wire is curved, and the arc length changes during the cutting process. This paper establishes a model of contact arc length by analyzing the cutting system. At the same time, a model of the random distribution of abrasive particles is established to solve the cutting force during the cutting process, using iterative algorithms to calculate cutting forces and chip surface saw marks. The error between the experiment and simulation of the average cutting force in the stable stage is less than 6%, and the errors with respect to the central angle and curvature of the saw arc on the wafer surface are less than 5% between the experiment and simulation. The relationship between the bow angle, contact arc length and cutting parameters is studied using simulations. The results show that the variation trend of the bow angle and contact arc length is consistent, increasing with an increase in the part feed rate and decreasing with an increase in the wire velocity.

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Kong, Ling Ye, Qiu Sheng Yan, Xu Guang Zhou, and Jue Dai. "Research of Grinding Revolving Curved Surface with Arc Envelope Grinding Method." Key Engineering Materials 375-376 (March 2008): 201–5. http://dx.doi.org/10.4028/www.scientific.net/kem.375-376.201.

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Revolving curved surface of mould should have low roughness as well as high accuracy of geometry profile. And it is an essential method to meet the accuracy request with grinding process. In order to solve the problem of grinding such revolving curved surface, an Arc Envelope Grinding Method (AEGM) is presented in this paper, which uses a wheel with arc section. By analyzing the movement of the grinding point, the relationship between the length of trajectory that the grinding point moves along and radius of the arc, curvature of workpiece is explained. Meanwhile, the relationship between the radius of arc, the curvature and the grinding area is studied.

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Souzban, Maedeh, Omid Solaymani Fard, and Akbar H. Borzabadi. "A rapid-based improvement on some mesh refinement strategies in solving optimal control problems." IMA Journal of Mathematical Control and Information 37, no. 2 (February 5, 2019): 395–421. http://dx.doi.org/10.1093/imamci/dnz004.

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Abstract Recently, a mesh refinement strategy is presented on pseudospectral methods for solving optimal control problems by using the relative curvature of the state approximation to choose the type of discretization change in each iteration. Nevertheless, this criterion requires a large amount of computational cost in terms of CPU time. The main goal of this paper is to draw attention to select a suitable criterion with fewer computational cost. To this end, we use the arc length of the state approximation in the mesh interval based on the relative error estimate that was recently provided. We also update the number of mesh intervals and the location of mesh points according to the behaviour of the arc length. Indeed, by implementing this criterion, we do not need to solve an optimization problem anymore, and so significantly reduce the computational time as well as CPU times. Finally, we illustrate the accuracy, efficiency and ability of the arc length criterion in comparison with the curvature by offering some numerical examples.

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Baeva, M., E. Siewert, and D. Uhrlandt. "Comparative Studies of Low-Intensity Short-Length Arcs." PLASMA PHYSICS AND TECHNOLOGY 6, no. 1 (2019): 56–59. http://dx.doi.org/10.14311/ppt.2019.1.56.

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We present results obtained by two non-equilibrium modelling approaches and experiments on low-intensity short-length arcs in argon at atmospheric pressure. The first one considers a quasi-neutral arc column combined with boundary conditions on the electrodes based on the energy balance in the space-charge sheaths. The second approach applies a unified description over the entire gap and solves the Poisson equation for the self-consistent electric field. The experiments provide the arc voltage.

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Thongyothee, Chawis, and Somchai Chucheepsakul. "Postbuckling of Unknown-Length Nanobeam Considering the Effects of Nonlocal Elasticity and Surface Stress." International Journal of Applied Mechanics 07, no. 03 (June 2015): 1550042. http://dx.doi.org/10.1142/s1758825115500428.

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The objective of this paper is to study the postbuckling behaviors of an unknown-length nanobeam combined with small-scale effects. The concept of variable-arc-length elastica is firstly applied on the problem of nanobeams. The span length is not changed while the arc length is varied increasingly. The nanobeam is on a clamped support at one end, while the other end is an overhanging part through a frictionless slot subjected to axial compression. At this end, the nanobeam is movable only in a horizontal direction. The governing equation is developed by the moment–curvature relationship based on the classical Euler–Bernoulli beam theory, including the effects of nonlocal elasticity, residual surface stress, and both combined effects. The shooting–optimization technique with two-point boundary condition is employed to solve the differential equations in this problem. The results, including nonlocal elasticity, reveal that nanobeams have decreased structural stiffness; meanwhile, the residual surface tension and both combined effects have increased strength. The postbuckling loads decrease as the arc length of nanobeams is increased. The equilibrium configurations are close to an anti-loop for very large deflections. The friction force at the nanoslot is also considered.

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Kruchinin, Anatoliy M., Mikhail Ya Pogrebisskiy, Elena S. Ryazanova, and Andrey Yu Chursin. "Determining the Rational Electrical Operation Modes of Industrial Electric Arc Furnaces." Vestnik MEI 3, no. 3 (2021): 51–57. http://dx.doi.org/10.24160/1993-6982-2021-3-51-57.

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The choice of a rational electrical mode of existing or newly commissioned electric arc furnaces (EAFs) is a very difficult task for process engineers in view of the influence of external disturbing factors. Based on an electric arc heat-transfer model (EAHTM), a method is proposed, using which the problem of determining the optimal electrical operation mode can be solved with the minimal number of simplifications and assumptions, and with taking into account the specific features of a particular EAF. In solving the problem, the following factors are taken into account: the arc heat transfer conditions in the melting space; the influence of the thermal operation conditions of the electrodes and the arc length on the structure of heat fluxes during the heating by arcs, and the effect the chemical composition of the working medium has on the thermophysical properties of the arc column plasma. The radiation from EAF arcs with taking into account the column temperature profile is calculated using the method of universal arc characteristics based on the solution of a system of nonlinear algebraic equations of the EAHTM column cylindrical model. The arc length calculation is based on the EAHTM structural characteristics method and consists of comparing the arc voltage value calculated using the furnace equivalent circuit equation and the arc voltage calculated using the EAHTM. Knowing the arc length, it is possible to calculate the arc radiation power in the EAF melting space. The choice of an electrical operation mode implies specifying an electrical parameter to be maintained by the controller for a certain period of melting. The value of this parameter (arc current or the EAF phase loop impedance) governs the other electrical parameters of the electric furnace installation, such as arc power, electrical losses, power factors, efficiency, etc. In addition, the correct choice of the electrical operation mode has an influence on other important operational characteristics, such as the specific consumption of electrodes, the duration of the interval between repairs, etc.

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Yu, Meng, Qing Dong Zhang, Bo Wang, Xiao Feng Zhang, and Jian Peng. "Research on Rolling Model Based on Non-Circular Contact Arc for Cold Strip Temper Rolling." Advanced Materials Research 145 (October 2010): 223–29. http://dx.doi.org/10.4028/www.scientific.net/amr.145.223.

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During temper rolling, the reduction is small, the length of contact arc is short, and the elastic deformation of work roll is large. Roll shape is not circular arc, the assumption of circular roll shape is no longer applicable. In this paper, quintic B-spline function is used in interpolation operations with normal pressure distribution so that roll shape can be solved by Gaussian integration. And a rolling model based on non- circular contact arc for cold strip temper rolling is established. The calculated results show good agreement with the actual value. The model can meet manufacturing requirement of the field and receives better control effect of elongation.

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Jayagowri, P., and G. Geetha Ramani. "Using Trapezoidal Intuitionistic Fuzzy Number to Find Optimized Path in a Network." Advances in Fuzzy Systems 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/183607.

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In real life, information available on situations/issues/problems is vague, inexact, or insufficient and so the parameters involved therein are grasped in an uncertain way by the decision maker. But in real life such uncertainty is unavoidable. One possible way out is to consider the knowledge of experts about the parameters involved as fuzzy data. In a network, the arc length may represent time or cost. In Relevant literature reports there are several methods to solve such problems in network-flow. This paper proposes an optimized path for use in networks, using trapezoidal intuitionistic fuzzy numbers, assigned to each arc length in a fuzzy environment. It proposes a new algorithm to find the optimized path and implied distance from source node to destination node.

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Tseng, Wei-Kuo, Wei-Jie Chang, and Chin-Lin Pen. "New Meridian Arc Formulae by the Least Squares Method." Journal of Navigation 67, no. 3 (February 14, 2014): 495–510. http://dx.doi.org/10.1017/s0373463313000817.

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Navigational software often lacks official standardisation of the methods used and their accuracy due to commercial confidentiality. The “black box solutions” used by navigational systems are unknown, thus a logical and simple method to solve navigational problems must be presented. This paper presents new meridian arc formulae by the least squares method. As the traditional meridian arc formulae cannot be expressed as a closed form, they are often truncated to the first few terms for practical use and in doing so neglect the values not used. By forming an overdetermined system with known components of the traditional meridian arc formula and actual length of the meridian arc, the least squares method can be used to approximate the best fitting coefficients for the traditional meridian arc formulae and forms the new compact formulae. The new formulae are based on highly accurate values of the meridian arc for the WGS-84 ellipsoid datum, and are perfect for the computational algorithms implemented in navigational software such as Geographic Information Systems (GIS), Electronic Chart Display and Information Systems (ECDIS) and other Electronic Chart Systems (ECS). Their accuracy is compared with other methods and shows that the new proposed formulae are shorter and accurate with negligible errors. The new formulae can be adapted to the accuracy needed and imply different numbers of coefficients. This can also shorten the calculations in navigation such as rhumb-line or great elliptic sailing on the ellipsoid because the meridian arc length is essential for these calculations.

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Hong, Yu Xiang, Bo Hong, Jian Liu, and Xiang Wen Li. "A Method for Welding Deviation Acquisition Based on Magnetic-Control Arc Sensing for Multi-Pass Welding." Advanced Materials Research 852 (January 2014): 239–43. http://dx.doi.org/10.4028/www.scientific.net/amr.852.239.

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In order to solve the problems of seam tracking for automation welding of large welding structure, this paper has respectively built mathematic model for length of magnetic-control arc according to two typical forms of weld pass in multi-pass welding for V-groove seam. By using Matlab/Simulink to analyze the transformation discipline of welding currents, a method for deviation acquisition based on magnetic-control arc sensing for multi-pass welding is proposed. Welding experiments demonstrates that the method proposed can effectively resolve the dilemma of deviation acquisition during multi-pass welding for thick plates with V-groove seam.

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Zou, Xiang Xiang, Yan Yu Ding, Tai Yong Wang, Zhen Sang, and He Nan Xu. "Research of RTCP Function for Five-Axis Machine Tools Based on Low-Cost Embedded CNC System." Key Engineering Materials 693 (May 2016): 1591–97. http://dx.doi.org/10.4028/www.scientific.net/kem.693.1591.

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To solve the problem which current research of RTCP function is limited to high-grade CNC system. Based on limited computational resources of the embedded CNC system, analyzes and modeling calculates RTCP function of CA double swing structure, and points out the offset distance is only related to the chord length corresponding to the arc length that the rotating radius crosses, and obtains the calculation formula of compensation. Finally, gives the implementing flow chart of the RTCP algorithm for low-cost embedded CNC system.

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Noor, Khalida Inayat. "On subclasses of close-to-convex functions of higher order." International Journal of Mathematics and Mathematical Sciences 15, no. 2 (1992): 279–89. http://dx.doi.org/10.1155/s016117129200036x.

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The classesTk(ρ),0≤ρ<1,k≥2, of analytic functions, using the classVk(ρ)of functions of bounded boundary rotation, are defined and it is shown that the functions in these classes are close-to-convex of higher order. Covering theorem, arc-length result and some radii problems are solved. We also discuss some properties of the classVk(ρ)including distortion and coefficient results.

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Hu, Bin, Xue Dao Shu, and Zhe Hong. "Study on Influence of End Concavity of Rolled Piece by Billet Circular Arc Angle with CWR." Applied Mechanics and Materials 599-601 (August 2014): 478–81. http://dx.doi.org/10.4028/www.scientific.net/amm.599-601.478.

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In order to solve the stub bar defects and improve the material utilization, this paper proposes the method of using billet with circular arc shape on the end face to control the end concavity. It establishes the cross wedge rolling finite element model by DEFORM-3D software, and through the displacement method to analyze the flow law of metal of rolled piece on the end face, and obtains the influence law of end concavity with different circular arc angles by numerical simulation. Finally, it gets the result that the end concavity length decreases with the increase of the circular arc angle. In comparison with the original billet, when the angle is 90°, the end concavity of rolled piece reduces by 69.04%. The results provide a theoretical basis for saving material and achieving the cross wedge rolling production without the stub bar.

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Kadivar, Ali, and Kaveh Niayesh. "Effects of Fast Elongation on Switching Arcs Characteristics in Fast Air Switches." Energies 13, no. 18 (September 16, 2020): 4846. http://dx.doi.org/10.3390/en13184846.

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This paper is devoted to investigating the effects of high-speed elongation of arcs inside ultra-fast switches (ucontact≈ 5–80 m/s), through a 2-D time-dependent model, in Cartesian coordinates. Two air arcs in series, one between a stationary anode and a moving cathode and the other between a stationary cathode and a moving anode in the arc chamber, are considered. A variable speed experimental setup through a Thomson drive actuator is designed to support this study. A computational fluid dynamics (CFD) equations system is solved for fluid velocity, pressure, temperature, and electric potential, as well as the magnetic vector potential. Electron emission mechanisms on the contact surface and induced current density due to magnetic field changes are also considered to describe the arc root formation, arc bending, lengthening, and calculating the arc current density, as well as the contact temperatures, in a better way. Data processing techniques are utilized to derive instantaneous core shape and profiles of the arc to investigate thermo-electrical characteristics during the elongation progress. The results are compared with another experimentally verified magnetohydrodynamics model of a fixed-length, free-burning arc in the air. The simulation and experimental results confirm each other.

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PHUNGPAINGAM, BOONCHAI, LAWRENCE N. VIRGIN, and SOMCHAI CHUCHEEPSAKUL. "STABILITY OF SPATIAL ELASTICA IN A GRAVITATIONAL FIELD." International Journal of Structural Stability and Dynamics 12, no. 02 (March 2012): 403–21. http://dx.doi.org/10.1142/s0219455412500101.

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This paper considers the behavior of a spatial elastica in a gravitational field. The slenderness of the system considered is such that the weight becomes an important consideration in determining elastic equilibrium configurations. Both ends of the elastica are clamped in an initially (planar) horizontal orientation at a fixed distance apart. However, one of the ends allows an increase in arc-length, that is, it is a sleeve joint. Thus, the total arc-length is the primary control parameter. This kind of elastica typically loses stability, resulting in out-of-plane deflections, when the total arc-length is increased beyond a critical value. A small mid-length torque can used to perturb a planar equilibrium configuration in order to test for stability. The aim of this study is to assess the effect of self-weight of the elastica (which is typically ignored) on promoting or delaying the loss of stability. To this end, it is useful to compare and contrast the results of orientation, that is, the system is configured in both an initial "upright" orientation and then in an "upside-down" orientation to highlight the influence of gravity. The results of the weightless elastica are used as a reference. Analysis is based on Kirchhoff's rod theory and Euler parameters, and the resulting set of governing differential equations are solved using a shooting method. The results from an experimental system using a slender superelastic wire made from Nitinol (Nickel Titanium Naval Ordnance Laboratory) exhibit close agreement with the analytical results.

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Jabbari, Marouane, Christophe Volat, and Issouf Fofana. "Development of a New Bi-Arc Dynamic Numerical Model for Modeling AC Flashover Processes of EHV Ice-Covered Insulators." Energies 11, no. 10 (October 17, 2018): 2792. http://dx.doi.org/10.3390/en11102792.

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This paper presents the development of a new bi-arc dynamic numerical model for predicting AC critical flashover voltage (FOV) of ice-covered extra-high voltage (EHV) insulators. The proposed model is based on a generic calculation algorithm coupled with commercial finite element method software designed to solve the Obenaus/Rizk model. The proposed model allows one to implement the Nottingham and Mayr approaches and compare the results obtained as a function of the arcing distance, the freezing water conductivity, and the initial arc length. The validation of the model demonstrated high accuracy in predicting the FOV of ice-covered post-type insulators and its capability to simulate the interaction of the two partial arcs during the flashover process. In particular, the results showed that the Nottingham approach is sensibly more accurate than the Mayr one, especially in simulating the dynamic behavior of the partial arcs during the flashover process. Based on the encouraging results obtained, a multi-arc calculation algorithm was proposed using the bi-arc dynamic numerical model as a basis. The basic idea, which consists in dividing the multi-arc model in several bi-arc modules, was not implemented and validated but will serve as a promising concept for future work.

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Ulya, Ulvi, Dede Suratman, and Asep Nursangaji. "PENGEMBANGAN BAHAN AJAR INTERAKTIF UNTUK PEROLEHAN KETERAMPILAN PADA MATERI LINGKARAN." Jurnal AlphaEuclidEdu 1, no. 2 (December 8, 2020): 162. http://dx.doi.org/10.26418/ja.v1i2.42874.

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This research aims to determine the feasibility of interactive teaching materials that are developed, and how intellectual skills of students after using teaching materials that are developed. The research method used is descriptive. The subjects of this research were 24 students from class XI SMP Islam Bawari Pontianak. The data source of this research were the student test answers sheet, and the validation sheet for the feasibility of interactive teaching materials. The results showed that interactive teaching materials were declared to be very valid, refer to material experts and media experts. The students' intellectual skills of relationship the central angle with length of arc is 58.33% in the sufficient category. The students' intellectual skills of relationship the central angle with area of circle sector is 50% in the sufficient category. The students' intellectual skills of solve problems related to the central angle, inscribed angle, length of arc, and area of circle sector, and its relationship is 20.83% in the low category.Keywords: Circles, Intellectual Skills, Interactive Teaching Materials

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Rustamova, Mexseti A. "Unloading wave in the cylindrical network from nonlinear elastic fibers." Structural Mechanics of Engineering Constructions and Buildings 15, no. 2 (December 15, 2019): 149–57. http://dx.doi.org/10.22363/1815-5235-2019-15-2-149-157.

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Aims of research. Investigation of a wave of unloading in a cylindrical network of nonlinear elastic fibers. Given the many options for wave propagation in cylindrical networks, an attempt is made to solve the problem of continuous waves. Methods. The movement of the network in the axial direction is cornsidered. nonlinear elastic fibers; To a basis of a cylindrical system are accepted: an individual vector i r parallel wave of unloading; cylindrical network; to a cylinder axis, j r · an individual vector of a tangent to cross-section section continuous waves of the cylinder, k · an individual vector perpendicular to the previous ones, x - is the coordinate in the direction of the axis of the cylinder, y - is the length of an arc of the circumference of the cylinder. The problem reduces to a hyperbolic system of equations under appropriate conditions. Since the wave speed increases when the net is stretched, the stretch wave will obviously be discontinuous. In order to study continuous waves, the problem of wave propagation is solved when unloading a pre-stretched cylinder from a nonlinear basis. The problem is solved by the method of characteristics. Results. The results are illustrated with calculations and can be used at calculations of various flexible pipes, including flexible drilling.

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Lemos, Randerson, Olmer Garcia, and Janito Vaqueiro Ferreira. "Local and Global Path Generation for Autonomous Vehicles Using Splines." Ingeniería 21, no. 2 (May 26, 2016): 188–200. http://dx.doi.org/10.14483/udistrital.jour.reving.2016.2.a05.

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Context: Before autonomous vehicles being a reality in daily situations, outstanding issues regarding the techniques of autonomous mobility must be solved. Hence, relevant aspects of a path planning for terrestrial vehicles are shown.Method: The approached path planning technique uses splines to generate the global route. For this goal, waypoints obtained from online map services are used. With the global route parametrized in the arc-length, candidate local paths are computed and the optimal one is selected by cost functions.Results: Different routes are used to show that the number and distribution of waypoints are highly correlated to a satisfactory arc-length parameterization of the global route, which is essential to the proper behavior of the path planning technique.Conclusions: The cubic splines approach to the path planning problem successfully generates the global and local paths. Nevertheless, the use of raw data from the online map services showed to be unfeasible due the consistency of the data. Hence, a preprocessing stage of the raw data is proposed to guarantee the well behavior and robustness of the technique.

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Tayyebi, Javad, and Massoud Aman. "Efficient algorithms for the reverse shortest path problem on trees under the hamming distance." Yugoslav Journal of Operations Research 27, no. 1 (2017): 46–60. http://dx.doi.org/10.2298/yjor150624009t.

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Given a network G(V,A,c) and a collection of origin-destination pairs with prescribed values, the reverse shortest path problem is to modify the arc length vector c as little as possible under some bound constraints such that the shortest distance between each origin-destination pair is upper bounded by the corresponding prescribed value. It is known that the reverse shortest path problem is NP-hard even on trees when the arc length modifications are measured by the weighted sum-type Hamming distance. In this paper, we consider two special cases of this problem which are polynomially solvable. The first is the case with uniform lengths. It is shown that this case transforms to a minimum cost flow problem on an auxiliary network. An efficient algorithm is also proposed for solving this case under the unit sum-type Hamming distance. The second case considered is the problem without bound constraints. It is shown that this case is reduced to a minimum cut problem on a tree-like network. Therefore, both cases studied can be solved in strongly polynomial time.

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Li, Xiao Li, and Jing Ji. "Nonlinear Stability Analysis for Schwedler Reticulated Dome." Applied Mechanics and Materials 182-183 (June 2012): 1609–12. http://dx.doi.org/10.4028/www.scientific.net/amm.182-183.1609.

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On the base of finite element linear Eigen value analysis, overall stability analysis of Schwedler reticulated dome has been conducted by means of the nonlinear finite element method. The arc-length method was utilized to solve the nonlinear equation systems, and the load-displacement curves of the spatial latticed shell structure were obtained. It is safer to adopt the nonlinear buckling analysis for structure. These can provide a valuable reference for the design and analysis of the similar special latticed shell.

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Strasser, Ben, Daniel Harabor, and Adi Botea. "Fast First-Move Queries through Run-Length Encoding." Proceedings of the International Symposium on Combinatorial Search 5, no. 1 (September 1, 2021): 157–65. http://dx.doi.org/10.1609/socs.v5i1.18311.

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We introduce a novel preprocessing-based algorithm to solve the problem of determining the first arc of a shortest path in sparse graphs. Our algorithm achieves query running times on the 100 nanosecond scale, being significantly faster than state-of-the-art first-move oracles from the literature. Space consumption is competitive, due to a compression approach that rearranges rows and columns in a first-move matrix and then performs run length encoding (RLE) on the contents of the matrix.

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Hansknecht, Christoph, Imke Joormann, and Sebastian Stiller. "Dynamic Shortest Paths Methods for the Time-Dependent TSP." Algorithms 14, no. 1 (January 12, 2021): 21. http://dx.doi.org/10.3390/a14010021.

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The time-dependent traveling salesman problem (TDTSP) asks for a shortest Hamiltonian tour in a directed graph where (asymmetric) arc-costs depend on the time the arc is entered. With traffic data abundantly available, methods to optimize routes with respect to time-dependent travel times are widely desired. This holds in particular for the traveling salesman problem, which is a corner stone of logistic planning. In this paper, we devise column-generation-based IP methods to solve the TDTSP in full generality, both for arc- and path-based formulations. The algorithmic key is a time-dependent shortest path problem, which arises from the pricing problem of the column generation and is of independent interest—namely, to find paths in a time-expanded graph that are acyclic in the underlying (non-expanded) graph. As this problem is computationally too costly, we price over the set of paths that contain no cycles of length k. In addition, we devise—tailored for the TDTSP—several families of valid inequalities, primal heuristics, a propagation method, and a branching rule. Combining these with the time-dependent shortest path pricing we provide—to our knowledge—the first elaborate method to solve the TDTSP in general and with fully general time-dependence. We also provide for results on complexity and approximability of the TDTSP. In computational experiments on randomly generated instances, we are able to solve the large majority of small instances (20 nodes) to optimality, while closing about two thirds of the remaining gap of the large instances (40 nodes) after one hour of computation.

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Pulngern, T., S. Chucheepsakul, and M. W. Halling. "Analytical and Experimental Studies on the Large Amplitude Free Vibrations of Variable-Arc-Length Beams." Journal of Vibration and Control 11, no. 7 (July 2005): 923–47. http://dx.doi.org/10.1177/1077546305054858.

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Using the finite element method, we investigate large amplitude vibrations of horizontal variable-arc-length beams, considering the effect of large initial static sag deflections due to self-weight. The variability in beam arc-length arises from one end being pinned, and the other end being supported by a frictionless roller at a fixed distance from the pinned end. Using Lagrange’s equation of motion, the large amplitude free vibration equation of motion is derived based on the variational formulation. Included in the formulation are the energy dissipation due to large bending using the exact non-linear expression of curvature and the non-linearity arising from axial force. The non-linear eigenvalue problem is solved by the direct iteration method to obtain the beam’s non-linear frequencies and corresponding mode shapes for specified vibration amplitudes. We also present changes in the frequency of vibration as a function of amplitude, demonstrating the beam non-linearity. A more accurate solution analyzed in the frequency domain of the direct numerical integration method is adopted as an alternative solution. Large amplitude vibration experimental modal analysis was also conducted to complement the analytical results. The measured results were found to be in good agreement with those obtained from two analytical solutions.

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Ansari, Reza, Mostafa Faghih Shojaei, Vahid Mohammadi, and Hessam Rouhi. "Free vibration and postbuckling of laminated composite Timoshenko beams." Science and Engineering of Composite Materials 23, no. 1 (January 1, 2016): 107–21. http://dx.doi.org/10.1515/secm-2013-0237.

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AbstractA numerical solution method was developed to investigate the postbuckling behavior and vibrations around the buckled configurations of symmetrically and unsymmetrically laminated composite Timoshenko beams subject to different boundary conditions. The Hamilton principle was employed to derive the governing equations and corresponding boundary conditions which are then discretized by introducing a set of matrix differential operators. The pseudo-arc-length continuation method was used to solve the postbuckling problem. To study the free vibration that takes place around the buckled configurations, the corresponding eigenvalue problem was solved by means of the postbuckling configuration modes obtained in the previous step. The static bifurcation diagrams for composite beams with different lay-up laminates are given, and it is shown that the lay-up configuration considerably affects the magnitude of critical buckling load and postbuckling behavior. The study of the vibrations of composite beams with different laminations around the buckled configurations indicates that the natural frequency in the prebuckling domain increases as the stiffness of a beam increases, while there is no specific relation between the lay-up lamination and natural frequency in the postbuckling domain which necessitates conducting an accurate analysis in this area.

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Zheng, Zhaoli, Yonghui Xie, Di Zhang, and Xiaolong Ye. "Effects of Stator Stiffness, Gap Size, Unbalance, and Shaft’s Asymmetry on the Steady-State Response and Stability Range of an Asymmetric Rotor with Rub-Impact." Shock and Vibration 2019 (August 27, 2019): 1–11. http://dx.doi.org/10.1155/2019/6162910.

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The asymmetric rotor and the rub-impact behavior are important sources of instability and may cause severe vibrations. However, the dynamics of the rotor-bearing system simultaneously considering the two factors has not gained sufficient attention in available investigations. In this paper, the steady-state response and stability of an asymmetric rotor with rub-impact were evaluated. The asymmetric rotor was modeled by beam elements with asymmetric cross section, and the nonlinear equations of motion were established in the rotating frame. The multiharmonic balance (MHB) method was employed to obtain the linearized form of the nonlinear equations of motion. Either the asymmetry of rotor or rub-impact can result in instability and make the problem difficult to solve. Thus, the arc-length method was utilized to trace the branch of the solutions. In order to improve the calculation speed and accurately predict the solution, the alternating frequency/time domain (AFT) was adopted to calculate the iteration of the arc-length method. Based on the proposed method, the effects of stator stiffness, gap size, unbalance, and asymmetric in shaft on the steady-state response and stability were obtained.

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Evstigneev, Nikolay M. "Disconnected stationary solutions for 3D Kolmogorov flow problem: preliminary results." Journal of Physics: Conference Series 2090, no. 1 (November 1, 2021): 012046. http://dx.doi.org/10.1088/1742-6596/2090/1/012046.

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Abstract The extension of the classical A.N. Kolmogorov’s flow problem for the stationary 3D Navier-Stokes equations on a stretched torus for velocity vector function is considered. A spectral Fourier method with the Leray projection is used to solve the problem numerically. The resulting system of nonlinear equations is used to perform numerical bifurcation analysis. The problem is analyzed by constructing solution curves in the parameter-phase space using previously developed deflated pseudo arc-length continuation method. Disconnected solutions from the main solution branch are found. These results are preliminary and shall be generalized elsewhere.

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Shanmugavel, Madhavan, Antonios Tsourdos, Brian A. White, and Rafaeł Żbikowski. "Differential Geometric Path Planning of Multiple UAVs." Journal of Dynamic Systems, Measurement, and Control 129, no. 5 (January 16, 2007): 620–32. http://dx.doi.org/10.1115/1.2767657.

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Safe and simultaneous arrival of constant speed, constant altitude unmanned air vehicles (UAVs) on target is solved by design of paths of equal lengths. The starting point for our solution is the well-known Dubins path, which is composed of circular arc and line segments, thus requiring only one simple maneuver—constant rate turn. An explicit bound can be imposed on the rate during the design and the resulting paths are the minimum time solution of the problem. However, transition between arc and line segments entails discontinuous changes in lateral acceleration (latax), making this approach impractical for real fixed wing UAVs. Therefore, we replace the Dubins solution with a novel one, based on quintic Pythagorean hodograph (PH) curves, whose latax demand is continuous. The PH paths are designed to have lengths close to the lengths of the Dubins paths to stay close to the minimum time solution. To derive the PH paths, the Dubins solution is first interpreted in terms of differential geometry of curves using the path length and curvature as the key parameters. The curvature of a Dubins path is a piecewise constant and discontinuous function of its path length, which is a differential geometric expression of the discontinuous latax demand involved in transitions between the arc and the line segment. By contrast, the curvature of the PH path is a fifth order polynomial of its path length. This is not only continuous but also has enough design parameters (polynomial coefficients) to meet the latax (curvature) constraints (bounds) and make the PH solution close to the minimum time one. The solution involves the design of paths meeting the curvature constraint and is followed by producing multiple paths of equal length by increasing the lengths of the shorter paths to match the longest one. The safety constraint, intercollision avoidance is achieved by satisfying two conditions: minimum separation distance and nonintersection at equal distance. The offset curves of the PH path are used to design a safety region along each path.

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Yaghoubshahi, M., E. Asadi, and S. J. Fariborz. "A higher-order shell model applied to shells with mixed boundary conditions." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 2 (June 20, 2010): 292–303. http://dx.doi.org/10.1243/09544062jmes2050.

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By means of the principle of virtual work, the governing equations together with the required boundary conditions of a higher-order shear deformation theory are formulated for the analysis of laminated shells under static loads. A system of 31 first-order partial differential equations is performed for the determination of stress resultants and displacement components. These equations are then solved numerically, utilizing the generalized differential quadrature method for two isotropic cylindrical panels with equal arc length but different radii having S2-type simply supported boundary conditions. The results matched those of other theories. Another analysis is carried out for composite cylindrical panels with two lamination schemes, five different mixed boundary conditions, and two length-to-thickness ratios. The results are compared against solutions obtained from ANSYS finite-element software.

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Saood, Ahmad, Zain A. Khan, Mohd T. Parvez, and Arshad H. Khan. "On the Large Amplitude Forced Vibration Analysis of Composite Sectorial Plates." Journal of Composites Science 5, no. 3 (March 15, 2021): 83. http://dx.doi.org/10.3390/jcs5030083.

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The nonlinear steady state large amplitude forced vibration response of a laminated composite annular sector plate is presented. The nonlinear governing equation of motion of the laminated composite annular sector plate has been obtained using kinematics of first-order shear deformation theory (FSDT) and employing Hamilton’s principle. The governing equations of motion have been solved in a time domain using a modified shooting method and arc-length/pseudo-arc length continuation technique. The influence of the boundary condition, sector angle, and annularity ratio on the linear as well as nonlinear steady state forced vibration response has been investigated. The strain/stress variation across the thickness of the annular sector plate is presented to explain the reason for a decrease/increase in hardening nonlinear behaviour. The periodic variation of the non-linear steady state stress has also been obtained to throw light into the factors influencing the unequal stress half cycles and multiple cyclic stress reversals, which is detrimental to the fatigue design of laminated composite annular sectorial plates. The frequency spectra of the steady state stress reveals large even and odd higher harmonic contributions for different cases due to changes in the restoring force dynamics. The modal interaction/exchange during a cycle is demonstrated using a deformed configuration of the laminated annular sector plate.

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Xu, Zhenyu. "Research on kinematics and attitude control model of a surgical interventional catheter." International Journal of Advanced Robotic Systems 16, no. 5 (September 1, 2019): 172988141987463. http://dx.doi.org/10.1177/1729881419874639.

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To solve the problems of poor versatility and inactivity of the traditional interventional catheters, a forward kinematic model of multi-segment catheters in series is established by using D-H parameter method, which is based on the geometrical structure of the designed catheters. In order to ensure the decoupling control of the driver’s length, we look into the relationship between the driver’s length and the posture of the catheter unit. The control model of the catheter’s posture is further presented, in which the characteristics of driver is equivalent to the arc shape. Finally, the fuzzy Proportional-Integral-Differential Control (PID) control is designed to control the catheter unit which greatly improves the precision of the control model. The results show that the relationship between the predicted driver length and the catheter attitude angle is basically consistent with the experimental results, which verifies the effectiveness of the variable universe fuzzy PID control.

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Bich, Quyen Vu Thi, Tien Dao Ngoc, and Van Tran Thi Thuy. "Geometrically nonlinear buckling analysis of truss with length imperfection subjected to mechanical and thermal load using hybrid FEM." E3S Web of Conferences 410 (2023): 03003. http://dx.doi.org/10.1051/e3sconf/202341003003.

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This paper presents a novel hybrid FEM-based approach to establish the mathematical model for solving the nonlinear buckling problem of truss systems with length imperfection under mechanical and thermal load. due to constant temperature change-based hybrid FEM. The proposed approach deals with establishing hybrid types of truss elements, including perfect truss elements without thermal deformation and truss elements with length imperfection and thermal deformation. The equilibrium equation of both truss elements is established based on compatibility relationships considering geometric nonlinearity. The hybrid global equilibrium equations of truss systems are developed by assembling constructed perfect truss elements without thermal deformation and truss elements with length imperfection and thermal deformation. The incremental-iterative algorithm based on the arc-length method is used to establish calculation programs to solve the hybrid global equilibrium equation for investigating the geometrically nonlinear buckling behavior of the truss system. The numerical test is presented to investigate the buckling and post-buckling behavior of truss systems having some elements with length imperfection under thermal and mechanical load.

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Khaled, AbdulRahim Assaad. "Thermal performance of six different types of wavy-fins." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 4 (May 5, 2015): 892–911. http://dx.doi.org/10.1108/hff-06-2014-0174.

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Purpose – Heat transfer inside wavy fins is analyzed in this work. The paper aim to discuss this issue. Design/methodology/approach – Six different types of wavy fins are considered. The fin equation for each fin type is solved using a high accurate finite difference method. Excellent agreement is obtained between the numerical solution under zero wave amplitude and the exact solution of the plain fin. Findings – The following wavy fin types and conditions are found to produce larger heat transfer rate and its volumetric value than those for the plain fin and other wavy fins: short fins with parallel wavy profiles and large surface-wave frequency; long fins with symmetric wavy surface around the length axis, positive cross-sectional area gradient at the base, and large surface-wave frequency; and long fins with symmetric wavy profiles around the length axis, positive cross-sectional area gradient at the base, and small surface-wave frequency. Research limitations/implications – In addition, both fins with symmetric wavy surface around the width axis and parallel wavy surfaces along the width axis have same performance indicators. Also, these wavy fins possess higher fin efficiency than either that of the plain fin or those of the other types of wavy fins. Originality/value – Finally, heat transfer enhancements in the studied wavy fins are increased by increases in the excess of the surface area, cross-sectional area gradient at the base, arc length and arc width relative to those of the plain fin.

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CHEN, Y. Z., X. Y. LIN, Z. X. WANG, and N. M. A. NIK LONG. "SOLUTION OF CONTACT PROBLEM FOR AN ARC CRACK USING HYPERSINGULAR INTEGRAL EQUATION." International Journal of Computational Methods 05, no. 01 (March 2008): 119–33. http://dx.doi.org/10.1142/s0219876208001418.

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This paper investigates the contact problem for an arc crack, for example, under a remote compression. A hypersingular integral equation (HSIE) for curved cracks in plane elasticity is suggested. It is found that the direct usage of HSIE cannot solve the mentioned contact problem. For the contact problem, one must take necessary modifications for solving the HSIE. The main modified points are as follows. First, one should assume some portion along the crack under contact. The margin or the end of the contacted portion is determined by the vanishing normal contact stress at the margin point. In addition, it is found that a suggested quadrature rule in conjunction with the curve length method provides a very effective way to solve the HSIE. Finally, several numerical examples are given.

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Rezaiee-Pajand, Mohammad, and Hossein Estiri. "Geometrically nonlinear analysis of shells by various dynamic relaxation methods." World Journal of Engineering 14, no. 5 (October 2, 2017): 381–405. http://dx.doi.org/10.1108/wje-10-2016-0109.

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Purpose Numerical experiences reveal that the performances of the dynamic relaxation (DR) method are related to the structural types. This paper is devoted to compare the DR schemes for geometric nonlinear analysis of shells. To achieve this task, 12 famous approaches are briefly introduced. The differences among these schemes are between the estimation of the time step, the mass and the damping matrices. In this study, several benchmark structures are analyzed by using these 12 techniques. Based on the number of iterations and the analysis duration, their performances are graded. Numerical findings reveal the high efficiency of the kinetic DR (kdDR) approach and Underwood’s strategy. Design/methodology/approach Up to now, the performances of various DR algorithms for geometric nonlinear analysis of thin shells have not been investigated. In this paper, 12 famous DR methods have been used for solving these structures. It should be noted that the difference between these approaches is in the estimation of the fictitious parameters. The aforementioned techniques are used to solve several numerical samples. Then, the performances of all schemes are graded based on the number of iterations and the analysis duration. Findings The final ranking of each strategy will be obtained after studying all numerical examples. It is worth emphasizing that the number of iterations and that of convergence points of the arc length algorithms are dependent on the value of the initial arc length. In other words, a slight change in the magnitude of the arc length may lead to the wrong responses. Contrary to this behavior, the analyzer’s role in the dynamic relaxation techniques is considerably less than the arc length method. In the DR strategies when the answer approaches the limit points, the iteration number increases automatically. As a result, this algorithm can be used to analyze the structures with complex equilibrium paths. Research limitations/implications Numerical experiences reveal that the DR method performances are related to the structural types. This paper is devoted to compare the DR schemes for geometric nonlinear analysis of shells. Practical implications Geometric nonlinear analysis of shells is a sophisticated procedure. Consequently, extensive research studies have been conducted to analyze the shells efficiently. The most important characteristic of these structures is their high resistance against pressure. This study demonstrates the performances of various DR methods in solving shell structures. Originality/value Up to now, the performances of various DR algorithms for geometric nonlinear analysis of thin shells are not investigated.

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Agüero-Rubio, José, Javier López-Martínez, Marta Gómez-Galán, and Ángel-Jesús Callejón-Ferre. "A Didactic Procedure to Solve the Equation of Steady-Static Response in Suspended Cables." Mathematics 8, no. 9 (September 1, 2020): 1468. http://dx.doi.org/10.3390/math8091468.

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Students in the electrical branch of the short-cycle tertiary education program acquire developmental and design skills for low voltage transmission power lines. Aerial power line design requires mathematical tools not covered well enough in the curricula. Designing suspension cables requires the use of a Taylor series and integral calculation to obtain the parabola’s arc length. Moreover, it requires iterative procedures, such as the Newton–Raphson method, to solve the third-order equation of the steady-static response. The aim of this work is to solve the steady-static response equation for suspended cables using simple calculation tools. For this purpose, the influence of the horizontal component of the cable tension on its curvature was decoupled from the cable’s self-weight, which was responsible for the tension’s vertical component. To this end, we analyzed the laying and operation of the suspended cables by defining three phases (i.e., stressing, lifting, and operation). The phenomena that occurred in each phase were analyzed, as was their manifestation in the cable model. Herein, we developed and validated the solution of the steady-static response equation in suspended cables using simple equations supported with intuitive graphics. The best results of the proposed calculation procedure were obtained in conditions of large temperature variations.

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Taczała, Maciej, Ryszard Buczkowski, and Michal Kleiber. "Elastic-Plastic Buckling and Postbuckling Finite Element Analysis of Plates Using Higher-Order Theory." International Journal of Structural Stability and Dynamics 21, no. 07 (April 7, 2021): 2150095. http://dx.doi.org/10.1142/s0219455421500954.

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In this paper, some of the displacement-based plate theories are used to investigate the elastic-plastic analysis of plates in the framework of the finite element method including the buckling and postbuckling effects with the focus on the general third-order plate theory (GTPT). The plate calculation results were compared with the results obtained using 64-nodes solid elements involving Lobatto integration scheme. The problem is solved using the Newton–Raphson method applying modified Crisfield constant arc-length procedure. The results show good agreement of results and the GTPT can be acknowledged to fulfill essential criteria for application to the elastic-plastic analysis of thin and thick plates.

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Journal articles on the topic 'Arc-Length Solver'

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