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Journal articles on the topic 'Nonlinear element'

Author: Grafiati

Published: 28 May 2022

Last updated: 31 July 2025

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1

Shirazi-Adl, A. "Nonlinear finite element analysis of wrapping uniaxial elements." Computers & Structures 32, no. 1 (1989): 119–23. http://dx.doi.org/10.1016/0045-7949(89)90076-x.

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2

De Gersem, Herbert, Vaishnavi Srinivasan, and Carsten Muehle. "Nonlinear three-port magnetic-circuit elements for simulating bending magnets." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 1 (2018): 266–79. http://dx.doi.org/10.1108/compel-12-2016-0526.

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Purpose The purpose of this paper is to show that constructing magnetic equivalent circuits (MECs) for simulating accelerator magnets is possible by defining a three-port magnetic element for modelling the T-shape field distribution, where the flux leaves the yoke and enters the aperture. Design/methodology/approach A linear three-port magnetic element is extracted from an analytical field solution and can be represented by a number of two-port elements. Its nonlinear counterpart is obtained as a combination of the corresponding nonlinear two-port elements. An improved nonlinear three-port ele

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3

Xu, Qiang, Jian Yun Chen, Jing Li, Gui Bing Zhang, Hong Yuan Yue, and Xian Zheng Yu. "Nonlinear analysis for the polygonal element." MATEC Web of Conferences 272 (2019): 01020. http://dx.doi.org/10.1051/matecconf/201927201020.

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As an important method for solving boundary value problems of differential equations, the finite element method (FEM) has been widely used in the fields of engineering and academic research. For two dimensional problems, the traditional finite element method mainly adopts triangular and quadrilateral elements, but the triangular element is constant strain element, its accuracy is low, the poor adaptability of quadrilateral element with complex geometry. The polygon element is more flexible and convenient in the discrete complex geometric model. Some interpolation functions of the polygon eleme

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4

Dao, Nguyen Van. "Nonlinear oscillations in systems with large static deflection of elastic elements." Vietnam Journal of Mechanics 15, no. 4 (1993): 7–16. http://dx.doi.org/10.15625/0866-7136/10214.

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In mechanical systems the static deflection of the elastic elements is usual not appeared in the equations of motion. The reason is that either a linear model of the elastic elements or their too small static deflection assumption was accepted. In the present paper both nonlinear model of elastic elements and their large static deflection are considered, so that the nonlinear terms in the equation of motion appear with different degrees of smallness. In this case the nonlinearity of the system depends not only on the nonlinear characteristic of the elastic element but on its static deflection.

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5

Carey, Graham F., and Bo-Nan Jiang. "Element-by-element linear and nonlinear solution schemes." Communications in Applied Numerical Methods 2, no. 2 (1986): 145–53. http://dx.doi.org/10.1002/cnm.1630020205.

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6

Sun, Guanhua, Yongtao Yang, and Hong Zheng. "A Three-Node Triangular Element with Continuous Nodal Stress (Trig3-CNS) for Geometry Nonlinear Solid Mechanics Problems." International Journal of Computational Methods 15, no. 04 (2018): 1850022. http://dx.doi.org/10.1142/s0219876218500226.

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This paper investigates the performance of the three-node triangular element with continuous nodal stress (Trig3-CNS) for geometry nonlinear solid mechanic problems. This Trig3-CNS element was recently proposed to improve accuracy of the finite element method (FEM). By synergizing the individual strengths of meshfree method and FEM, the Trig3-CNS element achieves higher accuracy and convergence rate. Furthermore, Trig3-CNS presents high tolerance to mesh distortion. Therefore, it is potentially useful for geometry nonlinear solid mechanics problems in which mesh distortion takes place. Compare

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7

Balagangadhar, Ramesh, and Joseph C. Slater. "On the Convergence of Nonlinear Modes of a Finite Element Model." Shock and Vibration 15, no. 6 (2008): 655–64. http://dx.doi.org/10.1155/2008/645014.

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Convergence of finite element models is generally realized via observation of mesh independence. In linear systems invariance of linear modes to further mesh refinement is often used to assess mesh independence. These linear models are, however, often coupled with nonlinear elements such as CFD models, nonlinear control systems, or joint dynamics. The introduction of a single nonlinear element can significantly alter the degree of mesh refinement necessary for sufficient model accuracy. Application of nonlinear modal analysis [1,2] illustrates that using linear modal convergence as a measure o

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8

Yang, Yongtao, Xuhai Tang, Hong Zheng, and Quansheng Liu. "Four-Node Quadrilateral Element with Continuous Nodal Stress for Geometrical Nonlinear Analysis." International Journal of Computational Methods 15, no. 02 (2017): 1850005. http://dx.doi.org/10.1142/s0219876218500056.

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In this paper, the performance of a hybrid ‘FE-Meshfree’ quadrilateral element with continuous nodal stress (Quad4-CNS) is investigated for geometrical nonlinear solid mechanic problems. By combining finite element method (FEM) and meshfree method, this Quad4-CNS synergizes the individual strengths of these two methods, which leads to higher accuracy, better convergence rate, as well as high tolerance to mesh distortion. Therefore, Quad4-CNS is attractive for geometrical nonlinear solid mechanic problems where excessive distorted meshes occur. For geometrical nonlinear analysis, numerical resu

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9

Xu, Shu Feng, Huai Fa Ma, and Yong Fa Zhou. "Moving Grid Method for Simulating Crack Propagation." Applied Mechanics and Materials 405-408 (September 2013): 3173–77. http://dx.doi.org/10.4028/www.scientific.net/amm.405-408.3173.

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A moving grid nonlinear finite element method was used in this study to simulate crack propagation. The relevant elements were split along the direction of principal stress within the element and thus automatic optimization processing of local mesh was realized. We discussed the moving grid nonlinear finite element algorithm was proposed, compiled the corresponding script files based on the dedicated finite element language of Finite Element Program Generator (FEPG), and generate finite element source code programs according to the script files. Analyses show that the proposed moving grid fini

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10

Osman, Ashwaq, Mohamed Aboshok, Gehan Hamdy, and Osama El-Mahdy. "Nonlinear Finite Element Modeling of Wooden Elements Strengthened by FRP." Engineering Research Journal (Shoubra) 53, no. 2 (2024): 110–18. http://dx.doi.org/10.21608/erjsh.2023.242398.1230.

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11

Mikhailov, S. G., and O. V. Rudenko. "A simple nonlinear element model." Acoustical Physics 63, no. 3 (2017): 270–74. http://dx.doi.org/10.1134/s1063771017030101.

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12

Mikhailov, S. G., and O. V. Rudenko. "A Simple Bimodular Nonlinear Element." Acoustical Physics 64, no. 3 (2018): 293–98. http://dx.doi.org/10.1134/s1063771018020112.

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13

Hai, Chi-Ming. "Prestrain and cholinergic receptor-dependent differential recruitment of mechanosensitive energy loss and energy release elements in airway smooth muscle." Journal of Applied Physiology 126, no. 4 (2019): 823–31. http://dx.doi.org/10.1152/japplphysiol.01008.2018.

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We tested the hypothesis that oscillatory airway smooth muscle (ASM) mechanics is governed by mechanosensitive energy loss and energy release elements that can be recruited by prestrain and cholinergic stimulation. We measured mechanical energy loss and mechanical energy release in unstimulated and carbachol-stimulated bovine ASM held at prestrains ranging from 0.3 to 1.0 Lo (reference length) and subjected to sinusoidal length oscillation at 1 hz with oscillatory strain amplitudes ranging from 0.1 to 1.5% Lo. We found that oscillatory ASM mechanics during sinusoidal length oscillation is gove

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14

Li, Zhi, Song Cen, and Chenfeng Li. "Extension of the unsymmetric 8-node hexahedral solid element US-ATFH8 to geometrically nonlinear analysis." Engineering Computations 38, no. 8 (2021): 3219–53. http://dx.doi.org/10.1108/ec-04-2020-0203.

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Purpose The purpose of this paper is to extend a recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with high distortion tolerance, which uses the analytical solutions of linear elasticity governing equations as the trial functions (analytical trial function) to geometrically nonlinear analysis. Design/methodology/approach Based on the assumption that these analytical trial functions can still properly work in each increment step during the nonlinear analysis, the present work concentrates on the construction of incremental nonlinear formulations of the unsymmetric element US-

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15

Pryadkin, Vladimir, and Aleksandr Zavyalov. "SIMULATION OF TRUCKING MODE CARS WITH A COMBINED ELASTIC ELEMENT IN THE REAR AXLE SUSPENSION." Voronezh Scientific-Technical Bulletin 4, no. 4 (2021): 114–19. http://dx.doi.org/10.34220/2311-8873-2021-4-4-114-119.

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The article analyzes elastic elements with a nonlinear characteristic. To improve the smoothness of a truck, a combined elastic element is proposed, including a semi-eleptic spring and an air cylinder, for installation in the rear axle suspension of a car. In order to assess the effect of a combined elastic element with a nonlinear characteristic on the smoothness of the ride, a mathematical model has been developed. The mathematical model allows for a numerical experiment taking into account the nature of the interaction of tires with unevenness of the roadway and the nonlinear characteristic

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16

Pham, Vu Nam, and Cong Ich Le. "Nonlinear bending of FGP beams and frames based on a third-order shear deformable theory." Journal of Physics: Conference Series 2949, no. 1 (2025): 012040. https://doi.org/10.1088/1742-6596/2949/1/012040.

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Abstract The nonlinear bending of beams and frames made of functionally graded porous (FGP) material under mechanical loading is presented based on a third-order shear deformable theory. The beams and frames consist of an FGP core and two faces of isotropic material. The porosities of the core are considered to be symmetric distributions in the direction of thickness. The von Kármán nonlinear assumption is adopted to formulate a nonlinear beam element, and then to construct the nonlinear equilibrium equation. Different from the existing third-order shear deformable elements, the present elemen

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17

Xu, Binlin, Zhongchu Tian, Jihua Deng, and Zujun Zhang. "Geometric Nonlinear Analysis of the Catenary Cable Element Based on UPFs of ANSYS." Applied Sciences 12, no. 19 (2022): 9971. http://dx.doi.org/10.3390/app12199971.

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The catenary cable element has more advantages than other nonlinear truss elements but is less used in commercial programs. In this paper, the initial geometric configuration of the element is solved iteratively by the dichotomous method. Then the Updated Lagrangian (UL) Formulation for the two-node catenary cable element is combined with the element secondary development tool provided by ANSYS platform-User Programmable Features (UPFs) to develop a three- dimensional cable element—user101. The algorithm and procedure of this paper are verified through examples and a real bridge. The study sho

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18

Apiwattanalunggarn, Polarit, Steven W. Shaw, Christophe Pierre, and Dongying Jiang. "Finite-Element-Based Nonlinear Modal Reduction of a Rotating Beam with Large-Amplitude Motion." Journal of Vibration and Control 9, no. 3-4 (2003): 235–63. http://dx.doi.org/10.1177/107754603030751.

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A nonlinear one-dimensional finite-element model representing the axial and transverse motions of a cantilevered rotating beam is reduced to a single nonlinear normal mode using invariant manifold techniques. This system is an idealized representation for large-amplitude vibrations of a rotorcraft blade. Although this model is relatively simple, it possesses the essential nonlinear coupling effects between the axial and transverse degrees of freedom. The nature of this coupling leads to the fact that we must use many degrees of freedom, whether based on finite elements or modal expansions, in

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19

Ng, S. F., M. S. Cheung, and J. Q. Zhao. "A materially nonlinear finite element model for the analysis of curved reinforced concrete box-girder bridges." Canadian Journal of Civil Engineering 20, no. 5 (1993): 754–59. http://dx.doi.org/10.1139/l93-100.

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A layered finite element model with material nonlinearity is developed to trace the nonlinear response of horizontally curved reinforced concrete box-girder bridges. Concrete is treated as an orthotropic nonlinear material and reinforcement is modeled as an elastoplastic strain-hardening material. Due to the fact that the flanges and webs of the structure are much different both in configuration and in the state of stresses, two types of facet shell elements, namely, the triangular generalized conforming element and the rectangular nonconforming element, are adopted to model them separately. A

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20

Mahmoud, Khalid S., and Mohannad H. Al-Sherrawi. "NONLINEAR FINITE ELEMENT ANALYSIS OF COMPOSITE CONCRETE BEAMS." Journal of Engineering 8, no. 03 (2024): 273–88. http://dx.doi.org/10.31026/j.eng.2002.03.11.

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To study the nonlinear response of composite concrete beams, a finite element analysis is presented. Material nonlinearities as a result of nonlinear response of concrete in compression, crushing and cracking of concrete, strain softening and stiffening after cracking, yielding of reinforcement, bond- slip, shear-slip, and dowel action between the precast concrete beams and the cast-in-situ slabs are considered.A biaxial concrete model is adopted. Concrete is treated as an orthotropic material with smeared rotating crack model. The steel reinforcement is assumed to be in a uniaxial stress stat

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21

Kien, Nguyen Dinh, Trinh Thanh Huong, and Le Thi Ha. "A co-rotational beam element for geometrically nonlinear analysis of plane frames." Vietnam Journal of Mechanics 35, no. 1 (2013): 51–65. http://dx.doi.org/10.15625/0866-7136/35/1/2892.

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A co-rotational beam element for geometrically nonlinear analysis of plane frames is presented. On the base of the shallow arch expression for local strain, the element is formulated by using exact polynomials to interpolate the transversal displacement and rotation. Using the formulated element, the critical load and equilibrium path are computed with the aid of the bracketing procedure and the arc-length control method, respectively. Numerical examples show that the proposed element is capable to give accurate results with a smaller number of elements comparing to the elements previously use

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22

Mohamed, Aizuddin, and Razi Abdul-Rahman. "Computation of Nonlinear Thermoelectric Effects with Adaptive Methods." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 76, no. 3 (2020): 75–84. http://dx.doi.org/10.37934/arfmts.76.3.7584.

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An implementation for a fully automatic adaptive finite element method (AFEM) for computation of nonlinear thermoelectric problems in three dimensions is presented. Adaptivity of the nonlinear solvers is based on the well-established hp-adaptivity where the mesh refinement and the polynomial order of elements are methodically controlled to reduce the discretization errors of the coupled field variables temperature and electric potential. A single mesh is used for both fields and the nonlinear coupling of temperature and electric potential is accounted in the computation of a posteriori error e

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23

Zhou, Yi, Yuan-Qi Li, Zu-Yan Shen, and Ying-Ying Zhang. "Corotational Formulation for Geometric Nonlinear Analysis of Shell Structures by ANDES Elements." International Journal of Structural Stability and Dynamics 16, no. 03 (2016): 1450103. http://dx.doi.org/10.1142/s021945541450103x.

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The corotational (CR) kinematic description was a recent method for formulation of geometric nonlinear structural problems. Based on the consistent symmetrizable equilibrated (CSE) CR formulation, a linear triangular flat shell element with three translational and three rotational degrees of freedom (DOFs) at each of the three nodes was derived by the assumed natural deviatoric strain (ANDES) formulation, which can be used to the geometric nonlinear analysis of shell structures with large rotations and small strains. By taking variations of the internal energy with respect to nodal freedoms, t

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24

Wang, Rui Fang. "Nonlinear Coupling Analysis on Working Behaviour of Pile Group." Advanced Materials Research 168-170 (December 2010): 2259–62. http://dx.doi.org/10.4028/www.scientific.net/amr.168-170.2259.

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The numerical analysis of finite element coupling infinite element is recently used to simulate the effects of unbounded foundation of stresses and displacements. In this thesis, the finite element analysis is adopted to simulate the piles and the near soil; between the pile and the soil a joint element is designed to imitate the relative settlement while the infinite element is used to imitate the distant soil. elastic analysis way for concret elements and infinite elements are used, K-G model and E-U model for near soil.Calculation results show that using Goodman contact element to simulate

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25

Fernández Ruiz, M., G. Argirova, and A. Muttoni. "How simple can nonlinear finite element modelling be for structural concrete?" Informes de la Construcción 66, Extra-1 (2014): m013. http://dx.doi.org/10.3989/ic.13.085.

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26

Tang, Y. Q., Y. P. Liu, and S. L. Chan. "Element-Independent Pure Deformational and Co-Rotational Methods for Triangular Shell Elements in Geometrically Nonlinear Analysis." International Journal of Structural Stability and Dynamics 18, no. 05 (2018): 1850065. http://dx.doi.org/10.1142/s0219455418500657.

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Proposed herein is a novel pure deformational method for triangular shell elements that can decrease the element quantities and simplify the element formulation. This approach has computational advantages over the conventional finite element method for linear and nonlinear problems. In the element level, this method saves time for computing stresses, internal forces and stiffness matrices. A flat shell element is formed by a membrane element and a plate element, so that the pure deformational membrane and plate elements are derived and discussed separately in this paper. Also, it is very conve

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27

Nagappan, Kumar, and Ganesh Raja. "Evaluation of Linear and Nonlinear Gap Elements Using Finite Element Method." SAE International Journal of Aerospace 2, no. 1 (2009): 159–64. http://dx.doi.org/10.4271/2009-01-3181.

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28

Bai, Run Bo, Fu Sheng Liu, and Zong Mei Xu. "Element Selection and Meshing in Finite Element Contact Analysis." Advanced Materials Research 152-153 (October 2010): 279–83. http://dx.doi.org/10.4028/www.scientific.net/amr.152-153.279.

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Contact problem, which exists widely in mechanical engineering, civil engineering, manufacturing engineering, etc., is an extremely complicated nonlinear problem. It is usually solved by the finite element method. Unlike with the traditional finite element method, it is necessary to set up contact elements for the contact analysis. In the different types of contact elements, the Goodman joint elements, which cover the surface of contacted bodies with zero thickness, are widely used. However, there are some debates on the characteristics of the attached elements of the Goodman joint elements. F

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29

Karad, P. B., and P. V. Patel. "Geometric Nonlinear Analysis of RC Frame structure using Applied Element Method (AEM)." Proceedings of the 12th Structural Engineering Convention, SEC 2022: Themes 1-2 1, no. 1 (2022): 245–50. http://dx.doi.org/10.38208/acp.v1.504.

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Reinforced Concrete (RC) structural elements having vast varieties of applications. Understanding the failure mechanism, deflection capacity beyond elastic limit is very important from the structural engineering point of view. Various RC structures are slender in nature which produces large deformations due to geometric nonlinearity. Nonlinear analysis of RC structures is very complex in nature and hence there is need of highly efficient numerical method. Applied Element Method (AEM) is a displacement-based method which can track highly nonlinear behavior of the structure i.e. crack initiation

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30

Subhashini, K. R., and A. T. Praveen Kumar. "Comparative Analysis of Linear and Nonlinear Pattern Synthesis of Hemispherical Antenna Array Using Adaptive Evolutionary Techniques." International Journal of Antennas and Propagation 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/987140.

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Hemispherical antenna arrays are subjected to linear and nonlinear synthesis and are optimized using adaptive based differential evolution (ADE) and fire fly (AFA) algorithm. The hemispherical shaped array with isotropic elements is considered. Antenna element parameters that are used for synthesis are excitation amplitude and angular position. Linear synthesis is termed as the variation in the element excitation amplitude and nonlinear synthesis is process of variation in element angular position. Both ADE and AFA are a high-performance stochastic evolutionary algorithm used to solveN-dimensi

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31

Selvadurai, A. P. "Nonlinear mechanics of cracks subjected to indentation." Canadian Journal of Civil Engineering 33, no. 6 (2006): 766–75. http://dx.doi.org/10.1139/l06-019.

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The paper presents the application of a boundary element technique to study the behaviour of plane cracks that are located at corner regions of an elastic solid and open during indentation. In particular, the surfaces of the planes on which indentation takes place also exhibit Coulomb frictional responses and degradation in the friction angle with plastic energy dissipation. An incremental boundary element formulation, in which special singularity elements model the behaviour at the crack tip, is used to examine the crack problems. The methodology is applied to investigate the mode I stress in

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32

Chang, Bilin, and A. A. Shabana. "Nonlinear Finite Element Formulation for the Large Displacement Analysis of Plates." Journal of Applied Mechanics 57, no. 3 (1990): 707–18. http://dx.doi.org/10.1115/1.2897081.

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In this investigation a nonlinear total Lagrangian finite element formulation is developed for the dynamic analysis of plates that undergo large rigid body displacements. In this formulation shape functions are required to include rigid body modes that describe only large translational displacements. This does not represent any limitation on the technique presented in this study, since most of commonly used shape functions satisfy this requirement. For each finite plate element an intermediate element coordinate system, whose axes are initially parallel to the axes of the element coordinate sy

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33

Trlep, M., L. Skerget, B. Kreca, and B. Hribernik. "Hybrid finite element-boundary element method for nonlinear electromagnetic problems." IEEE Transactions on Magnetics 31, no. 3 (1995): 1380–83. http://dx.doi.org/10.1109/20.376284.

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34

LAULUSA, A., and J. N. REDDY. "A CRITICAL EVALUATION OF VARIOUS NONLINEAR BEAM FINITE ELEMENTS." International Journal of Computational Methods 09, no. 04 (2012): 1250045. http://dx.doi.org/10.1142/s0219876212500454.

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The characteristics of interdependent interpolation and mixed interpolation nonlinear beam finite elements are investigated in comparison with the equal-order interpolation element with uniform reduced integration. The stiffness matrix of the 3-noded and 4-noded equal order interpolation elements is identical to that of the 2-noded interdependent interpolation element if the internal nodal degrees-of-freedom are eliminated. The extension of the latter to include nonlinear kinematics by approximating the extensional displacement and the twist rotation with quadratic and cubic Lagrange polynomia

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35

Barour, Sabiha, Farid Bouziadi, and Waleed. "Analyse the effect of carbon fiber reinforced polymer (CFRP) strengthening of beams using ANSYS." Journal of Building Materials and Structures 11, no. 2 (2024): 115–21. https://doi.org/10.34118/jbms.v11i2.4115.

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This paper presents a nonlinear finite element model analysis to effect of carbon fiber reinforced polymer (CFRP) strengthening of beams using ANSYS, Finite element software ANSYS 12.0 has been used for modeling the beams by conducting nonlinear static analysis. The SOLID 65 and SHELL 181, LINK180 elements have been used to, respectively; model the 3D concrete beams and the composite layer, steel rebars. The results of the finite element were compared with the experimental data The results showed that the general behavior of the finite element models represented by the load-deflection curves s

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36

Zhao, Feng Hua, Yong Sheng Qi, and Y. Y. Zhou. "Nonlinear Finite Element Analysis of FQQB." Applied Mechanics and Materials 438-439 (October 2013): 639–43. http://dx.doi.org/10.4028/www.scientific.net/amm.438-439.639.

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The mechanical properties of the whole wall and the wall with openings under vertical loads are analyzed by nonlinearity finite element method (NFEM). The results show that the stress of steel wire has a direct relationship with the load form. The inclined plug wire mainly carries the stress caused by load differences between the two sides of concrete, it makes both sides of concrete work together better. As the diameter of the inclined plug wire increased, the effects on the FQQB mechanical properties become greater, wire mesh stress on both sides decrease, and the vertical displacement of FQ

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37

Kuczmann, Miklos. "Nonlinear finite element method in magnetism." Pollack Periodica 4, no. 2 (2009): 13–24. http://dx.doi.org/10.1556/pollack.4.2009.2.2.

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38

Andreev, Y. A., O. V. Bubnov, and Y. A. Shyrygin. "Nonlinear element for solar cell simulator." Proceedings of Tomsk State University of Control Systems and Radioelectronics 21, no. 1 (2018): 135–38. http://dx.doi.org/10.21293/1818-0442-2018-21-1-135-138.

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39

Kolukula, Siva Srinivas, and P. Chellapandi. "Nonlinear Finite Element Analysis of Sloshing." Advances in Numerical Analysis 2013 (February 27, 2013): 1–10. http://dx.doi.org/10.1155/2013/571528.

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The disturbance on the free surface of the liquid when the liquid-filled tanks are excited is called sloshing. This paper examines the nonlinear sloshing response of the liquid free surface in partially filled two-dimensional rectangular tanks using finite element method. The liquid is assumed to be inviscid, irrotational, and incompressible; fully nonlinear potential wave theory is considered and mixed Eulerian-Lagrangian scheme is adopted. The velocities are obtained from potential using least square method for accurate evaluation. The fourth-order Runge-Kutta method is employed to advance t

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40

Elias, Z. M., and K. ‐L Chen. "Nonlinear Shallow Curved‐Beam Finite Element." Journal of Engineering Mechanics 114, no. 6 (1988): 1076–87. http://dx.doi.org/10.1061/(asce)0733-9399(1988)114:6(1076).

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41

Tadeu, Antonio, Leopold Škerget, and Jure Ravnik. "Boundary element method for nonlinear problems." Engineering Analysis with Boundary Elements 119 (October 2020): 189. http://dx.doi.org/10.1016/j.enganabound.2020.06.012.

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42

Selmin, V., J. Donea, and L. Quartapelle. "Finite element methods for nonlinear advection." Computer Methods in Applied Mechanics and Engineering 52, no. 1-3 (1985): 817–45. http://dx.doi.org/10.1016/0045-7825(85)90016-7.

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43

Bathe, K. J. "Nonlinear finite element analysis and ADINA." Mechanics Research Communications 12, no. 6 (1985): 346. http://dx.doi.org/10.1016/0093-6413(85)90008-4.

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44

Pöttler, R., and G. A. Swoboda. "Nonlinear beam element forr/c structures." Communications in Applied Numerical Methods 3, no. 5 (1987): 397–406. http://dx.doi.org/10.1002/cnm.1630030507.

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45

Krishnamurthy, K., Thomas D. Burton, and Lavern D. Zeller. "Finite element analysis of nonlinear oscillators." International Journal for Numerical Methods in Engineering 21, no. 3 (1985): 409–20. http://dx.doi.org/10.1002/nme.1620210303.

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46

Yupu, Guan, and Tang Limin. "Nonlinear quasi-conforming finite element method." Acta Mechanica Sinica 9, no. 3 (1993): 269–76. http://dx.doi.org/10.1007/bf02486804.

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47

Gülümser, Emir, Uğur Güdükbay, and Sinan Filiz. "Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method." Journal of Applied Mathematics 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/932314.

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We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM). Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a stat

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48

Lan, Shengrui, and Jusheng Yang. "Nonlinear finite element analysis of arch dam — II. Nonlinear analysis." Advances in Engineering Software 28, no. 7 (1997): 409–15. http://dx.doi.org/10.1016/s0965-9978(97)00012-4.

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49

Papakonstantinou, K. G., P. C. Dimizas, and V. K. Koumousis. "An Inelastic Beam Element with Hysteretic Damping." Shock and Vibration 15, no. 3-4 (2008): 273–90. http://dx.doi.org/10.1155/2008/707419.

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In this work, an inelastic beam macro-element that incorporates hysteretic damping is presented. Based on classical theory of plasticity, a Bouc-Wen type model is utilized that simulates the hysteretic behavior of an inelastic spring element. Using this model, an inelastic nonlinear beam element is formulated based on the appropriate combination of two coupled nonlinear spring elements. The equations of motion are determined and are cast in a state-space form for the vector of the end displacements, velocities and hysteretic forces. The system is solved by employing a Runge-Kutta type of algor

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50

Mao, S. G., and A. Y. T. Leung. "Symplectic Integration and Nonlinear Dynamic Symmetry Breaking of Frames." Shock and Vibration 2, no. 6 (1995): 481–92. http://dx.doi.org/10.1155/1995/671835.

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Abstract:

An accurate beam finite element is used to solve nonlinear vibration of arched beams and framed structures. The nonlinear governing equations of a skeletal structure are integrated numerically using symplectic integration schemes so that the Poincaré integral invariant of a Hamiltonian flow are preserved during the evolution. The element stiffness matrices are not required to be assembled into global form, because the integration is completed on an element level so that many elements can be handled in core by a small computer. Testing examples include arched beams and frames with and without d

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