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Dissertations / Theses on the topic 'Nonlinear finite element method'

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Published: 4 June 2021
Last updated: 14 June 2025

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1

Yao, Zhong, and 姚钟. "Nonlinear finite element analysis of reinforced concrete beams." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B5090002X.

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A nonlinear finite element program to simulate the behavior of reinforced concrete (RC) members under the action of monotonic increasing loading has been developed. The nonlinear response of the RC members is mainly due to the nonlinear material characteristics including nonlinear biaxial stress-strain relations and cracking of concrete and yielding of steel reinforcement. A constitutive model of concrete under biaxial stress state is adopted in this thesis. In this model, concrete fails and critical cracks occur when the tensile strain of concrete exceeds the limiting tensile strain. The complete stress-strain relationship of concrete under compression and tension are employed in the study to investigate the post-peak behavior of reinforced concrete members. An elaborate cracking model has been implemented which allows concrete to crack in one or two directions. The tension stiffening effect of cracked concrete is also incorporated into this model by including a descending branch in the stress-strain curve of concrete under tension. Other nonlinear effects such as crushing of concrete in compression and yielding or strain hardening of steel reinforcement are also taken into account. A nonlinear finite element program was developed, in which the abovementioned nonlinear effects have all been included in modeling the reinforced concrete structures. The nonlinear equations of equilibrium are solved using an incremental-iterative technique performed under displacement control. The validity of the model including the confinement effect of secondary reinforcements has been examined by analyzing three reinforced concrete beams. The performance of the numerical model was assessed by comparing results with those from available experimental data.<br>published_or_final_version<br>Civil Engineering<br>Master<br>Master of Philosophy
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Suriyachat, Phanuwat. "Modelling of mine openings using nonlinear finite element method." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=39380.

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A nonlinear finite element model, called MINE-PAL, has been developed for elasto-plastic, large deformation analysis of underground and surface mining excavations. The model accounts for both material nonlinearity due to yielding and strain-hardening and strain-softening effects and geometric nonlinearity due to large deformations. The finite element equations are formulated using incremental plasticity theory with Total Lagrangian approach where the Kirchhoff stress tensor and Green strain increment tensor are used. The model is developed for use on microcomputer system and is designed to perform 2-D nonlinear analysis of mine excavations in multiple-material domain, thus predicting the distribution of elastic, strain-softening, strain-hardening and residual strength zones. The model accommodates any arbitrary stope geometry and it allows for a variety of mining-type loading conditions in situ stresses, gravity loading and boundary tractions. Special provision has been made to permit the simulation of backfill as in situ stress-free material. Stress-space strain-softening is invoked into model using the concept of damage parameter in the incremental stress-strain relation.<br>In addition to model verification and sensitivity analysis, two numerical modelling case studies have been undertaken. The first case study is of a narrow vein mine with backfill which is located in the province of Karnchanaburi, Thailand. The second case study is about a room-and-pillar design of a potash deposit in the province of Chaiyaphum, Thailand.
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Jau, Jih Jih. "Geometrically nonlinear finite element analysis of space frames." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/54302.

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The displacement method of the finite element is adopted. Both the updated Lagrangian formulation and total Lagrangian formulation of a three-dimensional beam element is employed for large displacement and large rotation, but small strain analysis. A beam-column element or finite element can be used to model geometrically nonlinear behavior of space frames. The two element models are compared on the basis of their efficiency, accuracy, economy and limitations. An iterative approach, either Newton-Raphson iteration or modified Riks/Wempner iteration, is employed to trace the nonlinear equilibrium path. The latter can be used to perform postbuckling analysis.<br>Ph. D.
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4

Huang, Chiung-Yu. "Geometrically nonlinear finite element analysis of a lattice dome." Thesis, Virginia Tech, 1989. http://hdl.handle.net/10919/44650.

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<p>The geometry and the finite element method modelling of a lattice dome is presented. Linear analyses and geometrically nonlinear analyses of the dome are performed. In addition, a buckling load prediction method is studied and extended to the multiple load distributions. The results obtained from linear analyses are checked against the requirements of NDS, National Design Standard.<br>Master of Science
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5

He, Xiaogang. "Constitutive modeling of reinforced concrete for nonlinear finite element analysis /." Hong Kong : University of Hong Kong, 1999. http://sunzi.lib.hku.hk/hkuto/record.jsp?B21607473.

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6

Zhang, Yixia. "Refined non-conforming linear and nonlinear finte [sic] element analysis." Hong Kong : University of Hong Kong, 2001. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22753060.

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7

Earls, Christopher J. "Comparison of nonlinear finite element formulations: application to trusses." Thesis, Virginia Polytechnic Institute and State University, 1992. http://hdl.handle.net/10919/50104.

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Two prominent continuum mechanics based incremental nonlinear finite element formulations are reviewed. An introduction to different material response measures suitable for nonlinear analysis, in addition to an overview of the Total and Updated Lagrangian reference frames, serve as the starting point for this review. The two nonlinear formulations are specialized for use with a geometrically nonlinear plane truss finite element. The truss formulations are then implemented into separate geometrically nonlinear finite element codes. Numerical comparisons of five test structures are carried out using ABAQUS and both programs. ABAQUS serves as the bench-mark by which the solution accuracy of the two programs is judged.<br>Master of Science<br>incomplete_metadata
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8

賀小崗 and Xiaogang He. "Constitutive modeling of reinforced concrete for nonlinear finite element analysis." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31240264.

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9

Lai, Zhi Cheng. "Finite element analysis of electrostatic coupled systems using geometrically nonlinear mixed assumed stress finite elements." Diss., Pretoria : [s.n.], 2007. http://upetd.up.ac.za/thesis/available/etd-05052008-101337/.

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10

Chan, Mun Fong. "Nonlinear finite element analysis of sheet pile interlocks." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/54482.

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A finite element program is developed to depict the behavior of a sheet pile interlock connection in an axial pull test. Two types of sheet piles, PS32 and PSX32, are considered. The thumb and finger in the interlock of a sheet pile will provide three contact points for connection with another sheet pile. The problem is highly nonlinear in nature which involves large deflections and rotations, elastic-plastic material response, and a nonlinear boundary effect due to multi-contact surfaces. The Updated Lagrangian formulation is adopted in this study. When the response is in elastic range the Updated Lagrangian with Transformation is used while the Updated Lagrangian with Jaumann stress rate is employed when the element starts to yield. An elastic-plastic with isotropic strain hardening material model is used. The yielding of an element is detected by the Von Mises yield criterion. The finite element formulation also includes a moving contact algorithm to incorporate with both geometric and material nonlinearities. Incremental potential of contact forces for a discretized system is constructed such that geometric compatibilities are maintained between contacting bodies. A method to calculate contact tractions from residual load of internal element stresses is employed. The incremental equilibrium equation is solved by a Newton-Raphson technique. Convergence criteria based on incremental displacement, incremental internal energy of the system, and the changes in contact forces can be chosen to advance or terminate the iteration process.<br>Ph. D.
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11

Buah, Patrick Asebiah. "Finite element methods for computational nonlinear optics." Thesis, City University London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319669.

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12

Huh, Jungwon. "Dynamic reliability analysis for nonlinear structures using stochastic finite element method." Diss., The University of Arizona, 1999. http://hdl.handle.net/10150/289087.

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An efficient and accurate algorithm is developed to evaluate reliability in the time domain for nonlinear structures subjected to short duration dynamic loadings, including earthquake loading. The algorithm is based on the nonlinear stochastic finite element method (SFEM). Uncertainties in the dynamic and seismic excitation, and resistance-related parameters are incorporated by modeling them as realistically as possible. The uncertainty in them is explicitly addressed. The proposed algorithm intelligently integrates the concepts of response surface method (RSM), finite element method (FEM), first-order reliability method (FORM), and an iterative linear interpolation scheme. This leads to the stochastic finite element concept. It has the potential to estimate the risk associated with any linear or nonlinear structure that can be represented by a finite element algorithm subjected to seismic loading or any short duration dynamic loadings. In the context of the finite element method, the assumed stress-based finite element algorithm is used to increase its efficiency. Two iterative response surface schemes consisting of second order polynomials (with and without cross terms) are proposed. A mixture of saturated and central composite designs is used to assure both efficiency and accuracy of the algorithm. Sensitivity analysis is used to improve the efficiency further. The unique feature of the algorithm is that it is capable of calculating risk using both serviceability and strength limit states and actual earthquake loading time histories can be used to excite structures, enabling a realistic representation of the loading condition. The uncertainty in the amplitude of the earthquake is successfully considered in the context of RSM. Uncertainty in the frequency content of an earthquake is considered indirectly by conducting a parametric study to quantify the effect of uncertainty in the frequency content of earthquakes on the overall reliability of structures. The algorithm has been extensively verified using the Monte Carlo simulation technique. The verified algorithm is used to study the reliability of structures excited by actual earthquake time histories. The results of the numerical examples show that the proposed algorithm can be used accurately and efficiently to estimate the risk for nonlinear structures subjected to short duration time-variant loadings including seismic loading.
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13

Kim, Wooram. "Unconventional finite element method for nonlinear analysis of beams and plates." [College Station, Tex. : Texas A&M University, 2008. http://hdl.handle.net/1969.1/ETD-TAMU-3003.

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14

Neto, Dorival Piedade. "On the Generalized Finite Element Method in nonlinear solid mechanics analyses." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-20012014-094606/.

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The Generalized Finite Element Method (GFEM) is a numerical method based on the Partition of Unity (PU) concept and inspired on both the Partition of Unity Method (PUM) and the hp-Cloud method. According to the GFEM, the PU is provided by first-degree Lagragian interpolation functions, defined over a mesh of elements similar to the Finite Element Method (FEM) meshes. In fact, the GFEM can be considered an extension of the FEM to which enrichment functions can be applied in specific regions of the problem domain to improve the solution. This technique has been successfully employed to solve problems presenting discontinuities and singularities, like those that arise in Fracture Mechanics. However, most publications on the method are related to linear analyses. The present thesis is a contribution to the few studies of nonlinear analyses of Solid Mechanics by means of the GFEM. One of its main topics is the derivation of a segment-to-segment generalized contact element based on the mortar method. Material and kinematic nonlinear phenomena are also considered in the numerical models. An Object-Oriented design was developed for the implementation of a GFEM nonlinear analyses framework written in Python programming language. The results validated the formulation and demonstrate the gains and possible drawbacks observed for the GFEM nonlinear approach.<br>O Método dos Elementos Finitos Generalizados (MEFG) é um método numérico baseado no conceito de partição da unidade (PU) e inspirado no Método da Partição da Unidade (MPU) e o método das Nuvens-hp. De acordo com o MEFG, a PU é obtida por meio de funções de interpolação Lagragianas de primeiro grau, definidas sobre uma rede de elementos similar àquela do Método dos Elementos Finitos (MEF). De fato, o MEFG pode ser considerado uma extensão do MEF para a qual se pode aplicar enriquecimentos em regiões específicas do domínio, buscando melhorias na solução. Esta técnica já foi aplicada com sucesso em problemas com descontinuidades e singularidades, como os originários da Mecânica da Fratura. Apesar disso, a maioria das publicações sobre o método está relacionada a análises lineares. A presente tese é uma contribuição aos poucos estudos relacionados a análises não-lineares de Mecânica dos Sólidos por meio do MEFG. Um de seus principais tópicos é o desenvolvimento de um elemento de contato generalizado do tipo segmento a segmento baseado no método mortar. Fenômenos não lineares devidos ao material e à cinemática também são considerados nos modelos numéricos. Um projeto de orientação a objetos para a implementação de uma plataforma de análises não-lineares foi desenvolvido, escrito em linguagem de programação Python. Os resultados validam a formulação e demonstram os ganhos e possíveis desvantagens da abordagem a problemas não lineares por meio do MEFG.
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15

Iu, Vai-pan. "Nonlinear vibration analysis of multilayer sandwich structure by incremental finite elements /." [Hong Kong : University of Hong Kong], 1985. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12322945.

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16

Zhang, Yixia, and 張義霞. "Refined non-conforming linear and nonlinear finte [sic] element analysis." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31242704.

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17

Sedaghati, Ramin. "Investigations in structural optimization of nonlinear problems using the finite element method." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape4/PQDD_0010/NQ52772.pdf.

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18

Gaballa, Mohamed Abdelrhman Ahmed. "Nonlinear multiphasic mechanics of soft tissue using finite element methods." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184837.

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The purpose of the research was to develop a quantitative method which could be used to obtain a clearer understanding of the time-dependent fluid filteration and load-deformation behavior of soft, porous, fluid filled materials (e.g. biological tissues, soil). The focus of the study was on the development of a finite strain theory for multiphasic media and associated computer models capable of predicting the mechanical stresses and the fluid transport processes in porous structures (e.g. across the large blood vessels walls). The finite element (FE) formulation of the nonlinear governing equations of motion was the method of solution for a poroelastic (PE) media. This theory and the FE formulations included the anisotropic, nonlinear material; geometric nonlinearity; compressibility and incompressibility conditions; static and dynamic analysis; and the effect of chemical potential difference across the boundaries (known as swelling effect in biological tissues). The theory takes into account the presence and motion of free water within the biological tissue as the structure undergoes finite straining. Since it is well known that biological tissues are capable of undergoing large deformations, the linear theories are unsatisfactory in describing the mechanical response of these tissues. However, some linear analyses are done in this work to help understand the more involved nonlinear behavior. The PE view allows a quantitative prediction of the mechanical response and specifically the pore pressure fluid flow which may be related to the transport of the macromolecules and other solutes in the biological tissues. A special mechanical analysis was performed on a representative arterial walls in order to investigate the effects of nonlinearity on the fluid flow across the walls. Based on a finite strain poroelastic theory developed in this work; axisymmetric, plane strain FE models were developed to study the quasi-static behavior of large arteries. The accuracy of the FE models was verified by comparison with analytical solutions wherever is possible. These numerical models were used to evaluate variables and parameters, that are difficult or may be impossible to measure experimentally. For instance, pore pressure distribution within the tissue, relative fluid flow; deformation of the wall; and stress distribution across the wall were obtained using the poroelastic FE models. The effect of hypertension on the mechanical response of the arterial wall was studied using the nonlinear finite element models. This study demonstrated that the finite element models are powerful tools for the study of the mechanics of complicated structures such as biological tissue. It is also shown that the nonlinear multiphasic theory, developed in this thesis, is valid for describing the mechanical response of biological tissue structures under mechanical loadings.
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19

Choe, Kyu Y. "The discontinuous finite element method with the Taylor-Galerkin approach for nonlinear hyperbolic conservation laws /." Thesis, Connect to this title online; UW restricted, 1991. http://hdl.handle.net/1773/9977.

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20

Kreuzer, Christian. "A convergent adaptive Uzawa finite element method for the nonlinear Stokes problem." kostenfrei, 2008. http://d-nb.info/991291271/34.

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21

Iu, Vai-pan, and 姚偉彬. "Nonlinear vibration analysis of multilayer sandwich structure by incremental finite elements." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1985. http://hub.hku.hk/bib/B31230623.

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22

Kavi, Sandeep A. "Nonlinear 3-D beam/connector finite element with warping for a glulam dome." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-07102009-040624/.

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23

Li, Jian. "Three dimensional isoparametric finite element analysis with geometric and material nonlinearities." Thesis, Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/12165.

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24

Darong, Jin. "An hp-finite element computational framework for nonlinear magneto-fluid problems including magnetostriction." Thesis, Swansea University, 2015. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.678368.

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25

鍾偉昌 and Wai-cheong Chung. "Geometrically nonlinear analysis of plates using higher order finite elements." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1986. http://hub.hku.hk/bib/B31207601.

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Chung, Wai-cheong. "Geometrically nonlinear analysis of plates using higher order finite elements /." [Hong Kong : University of Hong Kong], 1986. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12225022.

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Gonzalez, Csaszar Eduardo. "Analysis of optical propagation in isotropic nonlinear devices by the finite element method." Thesis, University College London (University of London), 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244741.

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28

Zhou, Yiguang. "Efficient stochastic finite element method for the reliability analysis of nonlinear frame structures." Diss., The University of Arizona, 1992. http://hdl.handle.net/10150/185746.

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An efficient stochastic finite element-based procedure is proposed for the reliability analysis of frame and truss structures with geometrical and material nonlinearities under static loading condition. The material properties, geometry and external loads of the structure are considered as random variables. The failure criteria of the structure are expressed in terms of limit-state functions. The method is based on the advanced first order second moment reliability analysis procedure. The assumed stress field approach is used in the finite element formulation to compute nonlinear structural responses and the corresponding response gradients. The proposed method is suitable for the reliability analysis of geometrically nonlinear frame structures with flexible connections. The mechanical properties of the nonlinear flexible connections can be deterministic or random. A random index parameter is introduced as a basic random variable to consider the uncertainties in the modeling of the connections. Structures with different types of connections can be handled by this method. An efficient method is also proposed for the reliability analysis of highly redundant elastic-perfectly-plastic frame structures with large deformations under proportional loading. The proposed method avoids dealing with the complicated failure mechanisms and stable configurations in the structure system reliability analysis, and has several advantages over the other available methods.
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29

Ribeiro, Pedro Manuel Leal. "Geometrical nonlinear vibration of beams and plates by the hierarchical finite element method." Thesis, University of Southampton, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.264388.

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Ribeiro, Pedro Manuel Leal. "Geometrical nonlinear vibration of beams and plates by the hierarchical finite element method." Doctoral thesis, University of Southampton, 1998. http://hdl.handle.net/10216/12056.

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31

Giffin, Brian Doran. "Partitioned Polytopal Finite-Element Methods for Nonlinear Solid Mechanics." Thesis, University of California, Davis, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10752138.

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<p> This work presents a novel polytopal finite-element framework that addresses the collective issues of discretization sensitivity and mesh generation for computational solid mechanics problems. The use of arbitrary polygonal and polyhedral shapes in place of canonical isoparametric elements seeks to remediate issues pertaining to meshing and mesh quality (particularly for irregularly shaped elements), while maintaining many of the desirable features of a traditional finite element method. </p><p> A general class of <i>partitioned element methods</i> (PEM) is proposed and analyzed, constituting a family of approaches for constructing piecewise polynomial approximations to harmonic shape functions on arbitrary polytopes. Such methods require a geometric partition of each element, and under certain conditions will directly yield integration consistency. Two partitioned element methods are explored in detail, including a novel approach herein referred to as the <i>discontinuous Galerkin partitioned-element method</i> (DG-PEM). An implementational framework for the DG-PEM is presented, along with a discussion of its associated numerical challenges. </p><p> The numerical precision of the PEM is explored via classical patch tests and single element tests for a representative sampling of polygonal element shapes. Solution sensitivity with respect to element shape is examined for a handful of problems, including a mesh convergence study in the nearly incompressible regime. Finally, the efficacy of the DG-PEM is assessed for a number of benchmark problems involving large deformations and nonlinear material behavior.</p><p>
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Zhang, Zhengru. "Moving mesh methods for convection-dominated equations and nonlinear conservation laws." HKBU Institutional Repository, 2003. http://repository.hkbu.edu.hk/etd_ra/512.

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Wu, Yi. "Post-crack and post-peak behavior of reinforced concrete members by nonlinear finite element analysis." Click to view the E-thesis via HKUTO, 2006. http://sunzi.lib.hku.hk/hkuto/record/B37006447.

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Kalpundi, Ganesh R. "Nonlinear mixed finite element analysis for contact problems by a penalty constraint technique." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-06302009-040252/.

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Shi, Haijian. "Nonlinear finite element modeling and characterization of guyed towers under severe loading." Diss., Columbia, Mo. : University of Missouri-Columbia, 2007. http://hdl.handle.net/10355/4703.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2007.<br>The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on February 29, 2008) Vita. Includes bibliographical references.
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Hammerand, Daniel C. "Geometrically-Linear and Nonlinear Analysis of Linear Viscoelastic Composites Using the Finite Element Method." Diss., Virginia Tech, 1999. http://hdl.handle.net/10919/28893.

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Over the past several decades, the use of composite materials has grown considerably. Typically, fiber-reinforced polymer-matrix composites are modeled as being linear elastic. However, it is well-known that polymers are viscoelastic in nature. Furthermore, the analysis of complex structures requires a numerical approach such as the finite element method. In the present work, a triangular flat shell element for linear elastic composites is extended to model linear viscoelastic composites. Although polymers are usually modeled as being incompressible, here they are modeled as compressible. Furthermore, the macroscopic constitutive properties for fiber-reinforced composites are assumed to be known and are not determined using the matrix and fiber properties along with the fiber volume fraction. Hygrothermo-rheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale, in addition to the usual hygrothermal loads. Both the temperature and moisture are taken to be prescribed. Hence, the heat energy generated by the viscoelastic deformations is not considered. When the deformations and rotations are small under an applied load history, the usual engineering stress and strain measures can be used and the time history of a viscoelastic deformation process is determined using the original geometry of the structure. If, however, sufficiently large loads are applied, the deflections and rotations will be large leading to changes in the structural stiffness characteristics and possibly the internal loads carried throughout the structure. Hence, in such a case, nonlinear effects must be taken into account and the appropriate stress and strain measures must be used. Although a geometrically-nonlinear finite element code could always be used to compute geometrically-linear deformation processes, it is inefficient to use such a code for small deformations, due to the continual generation of the assembled internal load vector, tangent stiffness matrix, and deformation-dependent external load vectors. Rather, for small deformations, the appropriate deformation-independent stiffness matrices and load vectors to be used for all times can be determined once at the start of the analysis. Of course, the time-dependent viscoelastic effects need to be correctly taken into account in both types of analyses. The present work details both geometrically-linear and nonlinear triangular flat shell formulations for linear viscoelastic composites. The accuracy and capability of the formulations are shown through a range of numerical examples involving beams, rings, plates, and shells.<br>Ph. D.
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Dinh, Anh thi. "Finite Element Methods for nonlinear interface problems. Application to a biofilm growth model". Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCD083.

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Un biofilm est un ensemble de micro-organismes tels que les bactéries, les champignons ou encore les algues qui vivent en communauté. Les biofilms ont la capacité d’être présents en tout lieu. Ils sont observés dans les milieux aqueux ou humides. Ils peuvent se développer sur n’importe quel type de surface naturelle ou artificielle,qu’elle soit minérale (roche, interfaces air-liquide...) ou organique (peau, tube digestif,racines et feuilles des plantes), industrielle (canalisations, coques des navires) ou médicale comme les prothèses et les cathéters. Cette ubiquité est à l’origine de nombreuses infections bactériennes. Les infections nosocomiales contractées dans les hôpitaux sont un exemple majeur. Certaines de ces infections pouvant être mortelles.Le traitement médical des biofilms est souvent inefficace pour lutter contre ce type d’infection. Il est donc important de comprendre les mécanismes de croissance d’un biofilm. Telle est la motivation de la présente thèse. Afin de réaliser des simulations numériques d’un modèle décrivant la croissance d’un biofilm, nous combinons différentes méthodes de calcul basées sur la méthode Nitsche-Extended Finite Element Method (NXFEM) ainsi que sur la méthode des lignes de niveau. Ces méthodes nous permettent d’étudier des modèles complexes dans lesquels l’interface entre le biofilm et son environnement est capable de se déformer tout en dépendant du temps. Ceci permet de considérer une discrétisation à l’aide d’un maillage ne coïncidant pas avec l’interface biofilm/environnement.Nous présentons également une technique de découplage d’un système d’équations aux dérivées partielles semi-linéaires et la fac¸on dont nous appliquons la méthode NXFEM pour résoudre un tel problème. Ce système est en relation avec le modèle de croissance du biofilm qui est traité dans cette thèse. Pour l’implémentation, une boite à outils NXFEM, développée en Matlab, a été entièrement conçue pour résoudre un tel problème. Nous donnons dans ce document les détails des algorithmes et techniques numériques utilisés afin que chacun puisse utiliser cette boite à outils pour ses propres projets<br>A biofilm is a collective of living, reproducing microorganisms, such as bacteria, that stick together as a colony or community. They appear everywhere in human life and have impacts on our environment. Biofilm modeling, together with laboratory experiments,has risen toproduce quantitative tools for scientists to better understand the biofilm’s growth. This thesis is motivated to research on this subject.A combination of computational methods which are based on Nitsche-Extended Finite Element Method (NXFEM), Level Set Method and some other stabilized techniques is used to solve and simulate a biofilm growth model. These methods allow us to work with a complex scheme in which the interface between the biofilm and its environment may change with time and on an unfitted mesh. We also present a technique of decoupling a system of semilinear differential equations and how we apply the NXFEM method to solve such a problem. This system has a relation to a model of biofilm’s growth which will be examined carefully in the work.For the implementations, NXFEM toolbox which is a Matlab based toolbox is built for solving such a problem. We also give the details of all algorithms and numerical techniques so that everyone can use this toolbox for their own projects
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LIN, JEEN. "SHAPE OPTIMIZATION OF NONLINEAR STRUCTURES UNDER FATIGUE LOADING." University of Cincinnati / OhioLINK, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=ucin982764930.

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39

Spiess, Holger. "Reduction methods in finite element analysis of nonlinear structural dynamics /." Hannover : IBNM, 2006. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=015469897&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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40

Villeneuve, Donald. "A p-type finite element method for devices with nonlinear materials and curved boundaries." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0025/NQ50324.pdf.

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41

Gao, Liwei. "Stochastic finite element method for the reliability analysis of nonlinear frames with PR connections." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186898.

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A nonlinear stochastic finite element-based procedure is developed for reliability analyses of structures. The procedure is based on the First Order Reliability Method. The failure criteria of structures are expressed in terms of the ultimate and serviceability state functions. The adjoint variable method is used to formulate the computation of the gradient vector. The assumed stress-based finite element method is used to compute nonlinear structural responses and the corresponding response gradients for steel frames. Nonlinearities due to geometry, material and partially restrained connections are considered in the procedure. A computational model based on the Richard model is developed to address the uncertain properties of partially restrained connections. The material properties, geometric properties, connections parameters and external loads are considered as random variables. Several observations with design implications are made from numerical examples. Frames designed considering strength may not be acceptable when serviceability is considered. The presence of partially restrained connections changes the stress distribution in frames and makes frames more flexible so that serviceability could become the governing limit state. It is essential to properly consider the presence of partially restrained connections in the analysis and design of frames. The proposed method can be used as an alternative to the currently available methods to design a structure and evaluate the corresponding reliability. As an extended study, an efficient finite element-based procedure is also developed for estimating nonlinear responses of complex two or three dimensional steel frames with partially restrained connections under dynamic and seismic excitations. The hysteretic behavior of partially restrained connections are modeled by using the Masing rule combined with the Richard model to describe the loading, unloading and reverse loading paths for connections. Numerical examples show that this procedure is accurate and efficient compared with other existing nonlinear methods.
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42

Skoglund, Oskar, and Daniel Samvin. "Design of slender steel members : A comparison between the reduced stress method and the effective width method." Thesis, KTH, Bro- och stålbyggnad, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-189029.

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As of now, the most common way in Sweden, to address the issue of local buckling of steelstructures is through the procedure called the effective width method. A less commonprocedure for dealing with local buckling is the reduced stress method. The benefit of thelatter method is that, when combined with finite element analysis, results in a less tediousdesign process. However, this method is often labelled as a method that results in anoverconservative design. Therefore, the purpose of this report is to compare and evaluate thereduced stress method against the effective width method and nonlinear finite elementmethod. The nonlinear FE-analyses are performed with intention of simulating the realbehaviour of the structure and serve as a reference for the other two methods. The comparisonis conducted through a series of analyses, on different steel members with various loadconfigurations and slenderness in order to include the most common cases in the constructionindustry. This report resulted in recommendations for when the reduced stress method couldbe a relevant design procedure, with emphasis on providing reliable and accurate resultscompared to FE-analyses. Furthermore, the report resulted in proposed further studies, bothregarding the improvement of the reduced stress method and other structural elements thatshould be studied. The result from the report indicates that the reduced stress method can beused when the effect of patch loading is small. Furthermore, it is recommended to obtain thecritical stresses from a linear finite element analysis rather than from hand calculations, as tonot end up with over-conservative results.<br>I Sverige behandlas problemet med lokal buckling av stålkonstruktioner vanligtvis med hjälpav den effektiva bredd metoden, vilket är en dimensionergsmetod som återfinns i Eurocode.En ytterligare dimensionerings metod för lokal buckling som presenteras i Eurocode är denreducerade spänningsmetoden. Den senare nämnda metoden är fördelaktig då den kombinerasmed linjära finita element analyser, vilket resulterar i en mindre tidskrävandedimensioneringsprocess. Dock är metoden känd för att ofta resultera i överdimensioneradekonstruktioner, vilket bidragit till att mindre antal konstruktörer använder sig av denna metod.Syftet med denna rapport blir därmed att jämföra och utvärdera den reduceradespänningsmetoden gentemot den effektiva bredd metoden och olinjär finita element metoden.De olinjära finita element analyserna genomfördes med syfte att simulera det verkligabeteendet och för att sedan jämföra dessa resultat med de två andra metoderna. Analyser harutförts på flera stålbalkar med olika lastkombinationer och slankhet för att inkludera devanligaste fallen inom byggindustrin. Dessutom har det tagits fram några rekommendationerför användningen av metoderna och dessa är presenterade med avseende på de erhållnaresultaten. Rekommendationer för den reducerade spänningsmetoden har presenterats ochytterligare studier gällande dessa metoder och andra konstruktionselement har föreslagits. Deslutsatser som kunde dras är att den reducerade spänningsmetoden kan användas förkonstruktioner som inte påverkas i allt för stor grad av intryckning. För att ge tillförliterligaresultat så rekommenderas att kritiska spänningar erhålles från linjära finita element analyser.
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43

Yang, Victor P. "Finite element methods for the nonlinear motion of flexible aircraft." Diss., Connect to online resource, 2006. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3219052.

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44

Kurniawan, Antonius S. "Generalized Eulerian-Lagrangian finite element methods for nonlinear dynamic problems." Case Western Reserve University School of Graduate Studies / OhioLINK, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=case1054912471.

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45

Wu, Yi, and 吳奕. "Post-crack and post-peak behavior of reinforced concrete members by nonlinear finite element analysis." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37006447.

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Wong, Chun-kuen, and 黃春權. "Symmetry reduction for geometric nonlinear analysis of space structures." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31214721.

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Wong, Chun-kuen. "Symmetry reduction for geometric nonlinear analysis of space structures /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B18379734.

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48

Guo, Xiu Xiu. "Finite element analysis of nonlinear stochastic oscillators with Poisson white noise excitation." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2182943.

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49

Lasis, Andris. "hp-version discontinuous Galerkin finite element methods for nonlinear parabolic problems." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.426392.

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50

Ritter, Baird S. "Solution strategies for second order, nonlinear, one dimensional, two point boundary value problems by FEM analysis." Thesis, Monterey, California : Naval Postgraduate School, 1990. http://handle.dtic.mil/100.2/ADA246063.

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Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, December 1990.<br>Thesis Advisor: Salinas, D. "December 1990." Description based on title screen as viewed on April 1, 2010. DTIC Identifier(s): Boundary value problems, finite element analysis, differential equations, problem solving, theses, interpolation, iterations, one dimensional, computer programs, approximation/mathematics, linearity. Author(s) subject terms: Galerkin FEM, nonlinear, quasilinearization, linearization, interpolation, iteration, differential equation, convergence. Includes bibliographical references (p. 164). Also available in print.
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