Dissertations / Theses: 'Nonlinear geometrical analysi'

1

Ruggerini, Andrea Walter <1988&gt. "Geometrically nonlinear analysis of thin-walled beams based on the Generalized Beam Theory." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amsdottorato.unibo.it/8497/7/Geometrically-nonlinear-GBT-beam-AndreaW-Ruggerini.pdf.

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The thesis addresses the geometrically nonlinear analysis of thin-walled beams by the Generalized Beam Theory ( GBT ). Starting from the recent literature, the linear theory is illustrated, along with some issues related to GBT finite element formulation. Potential benefits of using the GBT in design are exemplified with reference to the design of roofing systems. To assess the deterioration of member capacity due to cross-section distortion phenomena, the formulation of a geometrically nonlinear GBT is then pursued. The generalization of the GBT to the nonlinear context is performed by using the Implicit Corotational Method ( ICM ), devising a strategy to effectively apply the ICM when considering higher order deformation modes. Once, obtained, the nonlinear model has been implemented using a state-of-the-art mixed-stress finite element. The nonlinear finite element is then implemented starting from the linear GBT one. Extensive numerical results show the performance of the proposed approach in buckling and path-following analyses.

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2

Al-Qarra, H. H. "The geometrically nonlinear analysis of sandwich panels." Thesis, University of Southampton, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.373567.

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3

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.
Ph. D.

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4

Aydin, Ayhan. "Geometric Integrators For Coupled Nonlinear Schrodinger Equation." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12605773/index.pdf.

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Multisymplectic integrators like Preissman and six-point schemes and a semi-explicit symplectic method are applied to the coupled nonlinear Schrö
dinger equations (CNLSE). Energy, momentum and additional conserved quantities are preserved by the multisymplectic integrators, which are shown using modified equations. The multisymplectic schemes are backward stable and non-dissipative. A semi-explicit method which is symplectic in the space variable and based on linear-nonlinear, even-odd splitting in time is derived. These methods are applied to the CNLSE with plane wave and soliton solutions for various combinations of the parameters of the equation. The numerical results confirm the excellent long time behavior of the conserved quantities and preservation of the shape of the soliton solutions in space and time.

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5

Benatti, Luca. "Monotonicity Formulas in Nonlinear Potential Theory and their geometric applications." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/346959.

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In the setting of Riemannian manifolds with nonnegative Ricci curvature, we provide geometric inequalities as consequences of the Monotonicity Formulas holding along the flow of the level sets of the p-capacitary potential. The work is divided into three parts. (1) In the first part, we describe the asymptotic behaviour of the p-capactitary potential in a natural class of Riemannian manifolds. (2) The second part is devoted to the proof of our Monotonicity-Rigidity Theorems. (3) In the last part, we apply the Monotonicity Theorems to obtain geometric inequalities, focusing on the Extended Minkowski Inequality.

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6

Madutujuh, Nathan. "Geometrically nonlinear analysis of plane trusses and plane frames." Master's thesis, This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-01262010-020134/.

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7

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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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.
Master of Science

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8

SOAVE, NICOLA. "Variational and geometric methods for nonlinear differential equations." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/49889.

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This thesis is devoted to the study of several problems arising in the field of nonlinear analysis. The work is divided in two parts: the first one concerns existence of oscillating solutions, in a suitable sense, for some nonlinear ODEs and PDEs, while the second one regards the study of qualitative properties, such as monotonicity and symmetry, for solutions to some elliptic problems in unbounded domains. Although the topics faced in this work can appear far away one from the other, the techniques employed in different chapters share several common features. In the firts part, the variational structure of the considered problems plays an essential role, and in particular we obtain existence of oscillating solutions by means of non-standard versions of the Nehari's method and of the Seifert's broken geodesics argument. In the second part, classical tools of geometric analysis, such as the moving planes method and the application of Liouville-type theorems, are used to prove 1-dimensional symmetry of solutions in different situations.

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Kwan, Herman Ho Ming. "Multilayer beam analysis including shear and geometric nonlinear effects." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26711.

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This thesis presents an analysis and experimental verification for a multilayer beam in bending. The formulation of the theoretical analysis includes the combined effect of shear and geometric nonlinearity. From this formulation, a finite element program (CUBES) is developed. The experimental tests were done on multilayer, corrugated paper beams. Failure deflections and loads are thus obtained. The experimental results are reasonably predicted by the numerical results. Based upon this comparison, a maximum compressive stress is determined for the tested beam. Finally, design curves for the tested beam are drawn using the determined maximum compressive stress and the finite element program.
Applied Science, Faculty of
Civil Engineering, Department of
Graduate

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10

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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12

Makeev, Andrew. "Geometrically nonlinear analysis of laminated composites with extension-twist coupling." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/12028.

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13

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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14

Davalos, Julio F. "Geometrically nonlinear finite element analysis of a glulam timber dome." Diss., Virginia Polytechnic Institute and State University, 1989. http://hdl.handle.net/10919/54509.

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A finite element modeling and geometrically nonlinear static analysis of glued-laminated timber domes is presented. The modeling and analysis guidelines include: the generation of the geometry, the selection of finite elements to model the components of a dome (beams, purlins, connections, and tension ring), the specification of boundary conditions, the specification of material properties, the determination of a sufficiently accurate mesh, the determination of design loads and the specification of load combinations, the application of analysis procedures to trace the complete response of the structure, and the evaluation of the response. The modeling assumptions and analysis procedures are applied to a dome model whose geometry is based on an existing glulam timber dome of 133 ft span and 18 ft rise above the tension ring. This dome consists of triangulated networks of curved southern pine glulam members connected by steel hubs. The members lie on great circles of a spherical surface of 133.3 ft radius. The dome is covered with a tongue-and-groove wood decking, which is not considered in this study. Therefore, the surface pressures are converted into member loads and then discretized into nodal concentrated loads. A geometrically nonlinear, 3-d, 3-node, isoparametric beam element for glulam beams is formulated, and a program is developed for the analysis of rigid-jointed space frames that can trace the response of the structure by the modified Newton-Ralphson and the modified Risk-Wempner methods. The material is assumed to be continuous, homogeneous, and transversely isotropic. The material properties are assumed to be constant through the volume of the element. The transverse isotropy assumption is validated for southern pine by testing small samples in torsion. The accuracy of the modeling assumptions for southern pine glulam beams is experimentally verified by testing full-size, curved and straight, glulam beams under combined loads. The results show that the isobeam element can accurately represent the overall linear response of the beams. However, to analyze glulam domes with the program, connector elements to model the joints and a truss element to model the tension ring must be added. Therefore, the finite element program ABAQUS is used for the analysis of the dome model. Three dead-load/snow-load combinations are considered in the analysis of the dome model. The space frame joints and the purlin-to-beam connections are modeled with 2-node isobeam elements. A 3-d, 2-node, truss element is used to model the tension ring. Three distinct analyses are considered for rigid and flexible joints: a linear analysis to check the design adequacy of the members. A linearized eigenvalue buckling prediction analysis to estimate the buckling load, which provided accurate estimates of the critical loads when rigid joints were specified. Finally, an incremental, iterative, geometrically nonlinear analysis to trace the complete response of the structure up to failure. It is shown that elastic instability, which is governed by geometric nonlinearities, is the dominant failure mode of the test dome. At the critical load, the induced element stresses remained below the proportional limit of the material. A discussion of the results is presented, and recommendations for future extensions are included.
Ph. D.

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15

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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Sherzad, Rafiullah, and Awrangzib Imamzada. "Buckling and Geometric Nonlinear Stress Analysis : Circular glulam arched structures." Thesis, Linnéuniversitetet, Institutionen för byggteknik (BY), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-54569.

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An arched structure provides an effective load carrying system for large span structures. When it comes to long span roof structures, timber arches are one of the best solutions from both structural and aesthetical point of view. Glulam arched structures are often designed using slender elements due to economic consideration. Such slender cross-section shape increases the risk of instability. Instability analysis of straight members such as beam and column are explicitly defined in Eurocode. However, for instability of curved members no analytical approach is provided in the code, thus some numerical method is required. Nonetheless, an approximation is frequently used to obtain the effective buckling length for the arched structures in the plane of arches. In this master thesis a linear buckling analysis is carried out in Abaqus to obtain an optimal effective buckling length both in-plane and out-of-plane for circular glulam arched structures. The elastic springs are used to simulate the overall stiffness of the bracing system. The results obtained by the FE simulations are compared with a simple approximation method. Besides, the forces acting on the bracings system is obtained based on 3D geometric nonlinear stress analysis of the timber trusses. Our findings conclude that the approximation method overestimates the effective buckling length for the circular glulam arched structures. In addition, the study indicates that the position of the lateral supports along the length of the arch is an important design aspect for buckling behaviour of the arched structures. Moreover, in order to acquire an effective structure lateral supports are needed both in extrados and intrados. Furthermore, instead of using elastic spring elements to simulate the overall stiffness of the bracing system, a full 3D simulation of two parallel arches was performed. It was shown that the springs are stronger than the real bracing system for the studied arch.

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17

Silwal, Baikuntha. "An Investigation of the Beam-Column and the Finite-Element Formulations for Analyzing Geometrically Nonlinear Thermal Response of Plane Frames." OpenSIUC, 2013. https://opensiuc.lib.siu.edu/theses/1160.

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The objective of this study is to investigate the accuracy and computational efficiency of two commonly used formulations for performing the geometrically nonlinear thermal analysis of plane framed structures. The formulations considered are the followings: the Beam-Column formulation and the updated Lagrangian version of the finite element formulation that has been adopted in the commercially well-known software SAP2000. These two formulations are used to generate extensive numerical data for three plane frame configurations, which are then compared to evaluate the performance of the two formulations. The Beam-Column method is based on an Eulerian formulation that incorporates the effects of large joint displacements. In addition, local member force-deformation relationships are based on the Beam-Column approach that includes the axial strain, flexural bowing, and thermal strain. The other formulation, the SAP2000, is based on the updated Lagrangian finite element formulation. The results for nonlinear thermal responses were generated for three plane structures by these formulations. Then, the data were compared for accuracy of deflection responses and for computational efficiency of the Newton-Raphson iteration cycles required for the thermal analysis. The results of this study indicate that the Beam-Column method is quite efficient and powerful for the thermal analysis of plane frames since the method is based on the exact solution of the differential equations. In comparison to the SAP2000 software, the Beam-Column method requires fewer iteration cycles and fewer elements per natural member, even when the structures are subjected to significant curvature effects and to restrained support conditions. The accuracy of the SAP2000 generally depends on the number of steps and/or the number of elements per natural member (especially four or more elements per member may be needed when structure member encounters a significant curvature effect). Succinctly, the Beam-Column formulation requires considerably fewer elements per member, fewer iteration cycles, and less time for thermal analysis than the SAP2000 when the structures are subjected to significant bending effects.

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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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19

Li, Lingchuan. "Geometrically nonlinear analysis of discretized structures by the group theoretic approach." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0011/NQ40271.pdf.

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20

Cassani, D. "Nonlinear elliptic systems with critical growth." Doctoral thesis, Università degli Studi di Milano, 2005. http://hdl.handle.net/2434/23899.

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In the first part we study a class of semi-linear and quasi-linear systems which describe the interaction between charged fields or quantum particles with an unknown external gauge. We consider the limiting case when the nonlinearity exhibits the maximal growth which allows us to treat such problems by a variational approach. In particular we obtain non-existence results by Pohozaev-type techniques and then, adding lower-order perturbations we recover existence of mountain pass type solutions. In the second part, we consider semi-linear Hamiltonian systems where the nonlinearities enjoy a suitable coupled critical growth and in bounded domains. We provide a direct variational approach to construct a min-max level of linking type, involving explicit concentrating directions which affect the problem with a lack of compactness. Finally, we look at the systems considered in the second part but with inequalities instead of equalities and in the whole space. Exploiting non-linear capacity arguments introduced by S. Pohozaev we give a new proof and a generalization of a non-existence result by E.Mitidieri. In particular we show that the system of differential inequalities has no nontrivial solutions, in an optimal weak sense, for the nonlinearities satisfying a sharp growth condition. Here the case of dimension two is also covered.

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21

Chandrashekhara, K. "Geometric and material nonlinear analysis of laminated composite plates and shells." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/54739.

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An inelastic material model for laminated composite plates and shells is formulated and incorporated into a finite element model that accounts for both geometric nonlinearity and transverse shear stresses. The elasto-plastic material behavior is incorporated using the flow theory of plasticity. In particular, the modified version of Hill's initial yield criterion is used in which anisotropic parameters of plasticity are introduced with isotropic strain hardening. The shear deformation is accounted for using an extension of the Sanders shell theory and the geometric nonlinearity is considered in the sense of the von Karman strains. A doubly curved isoparametric rectangular element is used to model the shell equations. The layered element approach is adopted for the treatment of plastic behavior through the thickness. A wide range of numerical examples is presented for both static and dynamic analysis to demonstrate the validity and efficiency of the present approach. The results for combined nonlinearity are also presented. The results for isotropic results are in good agreement with those available in the literature. The variety of results presented here based on realistic material properties of more commonly used advanced laminated composite plates and shells should serve as references for future investigations.
Ph. D.

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22

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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23

陳永堅 and Wing-kin Chan. "Formulation of solid elements for linear and geometric nonlinear analysis of shells." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B30252842.

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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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25

Steinbrink, Scott Edward. "Geometrically Nonlinear Analysis of Axially Symmetric, Composite Pressure Domes Using the Method of Multiple Shooting." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/26099.

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An analysis is presented of the linear and geometrically nonlinear static response of "thin" doubly-curved shells of revolution, under internal pressure loading. The analysis is based upon direct numerical integration of the governing differential equations, written in first-order state vector form. It is assumed that the loading and response of the shell are both axially symmetric; the governing equations are thus ordinary differential equations. The geometry of the shell is limited in the analysis by the assumptions of axisymmetry and constant thickness. The shell is allowed to have general composite laminate construc- tion, elastic supports at the edges and internal ring stiffeners. In addition, the analysis allows for the possibility of circumferential line loads at discrete locations along the dome meridian. The problem is a numerically unstable two-point boundary value problem; inte- grations are performed using the technique of multiple shooting. A development of the multiple shooting technique known as stabilized marching is given. Results achieved by use of the multiple shooting technique are verified by comparison to results of finite ele- ment analysis using the finite element analysis codes STAGS and ABAQUS. Parametric studies are performed for ellipsoidal domes constructed of symmetric, 8-ply laminates. The parametric studies examine the effects of dome geometry for a quasi-isotropic lami- nate first, then examine whether material properties may be adjusted to create a "better" design. Conclusions and recommendations for future work follow.
Ph. D.

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26

Tongtoe, Samruam. "Failure Prediction of Spatial Wood Structures: Geometric and Material Nonlinear Finite Element Analysis." Diss., Virginia Tech, 1997. http://hdl.handle.net/10919/30557.

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The purpose of this study is to investigate spatial wood structures, trace their response on equilibrium paths, identify failure modes, and predict the ultimate load. The finite element models of this study are based on the Crafts Pavilion dome (Triax) in Raleigh, North Carolina, and the Church of the Nazarene dome (Varax) in Corvallis, Oregon. Modeling considerations include 3-d beam finite elements, transverse isotropy, torsional warping, beam-decking connectors, beam-beam connectors, geometric and material nonlinearities, and the discretization of pressure loads. The primary objective of this study is to test the hypothesis that the beam-decking connectors (B-D connectors) form the weakest link of the dome. The beam-decking connectors are represented by nonlinear springs which model the load slip behavior of nails between the beam and the decking. The secondary objective of this study is to develop models that are sufficiently simple to use in engineering practice.
Ph. D.

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27

Harrell, Timothy M. "Application of Groebner bases to geometrically nonlinear analysis of axisymmetric circular isotropic plates." Thesis, Tennessee Technological University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=1567200.

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This thesis demonstrates a new application of Groebner basis by finding an analytical solution to geometrically nonlinear axisymmetric isotropic circular plates. Because technology is becoming capable of creating materials that can perform materially in the linear elastic range while experiencing large deformation geometrically, more accurate models must be used to ensure the model will result in realistic representations of the structure. As a result, the governing equations have a highly nonlinear and coupled nature. Many of these nonlinear problems are solved numerically. Since analytic solutions are unavailable or limited to only a few simplified cases, their analysis has remained a challenging problem in the engineering community.

On the other hand, with the increasing computing capability in recent years, the application of Groebner basis can be seen in many areas of mathematics and science. However, its use in engineering mechanics has not been utilized to its full potential. The focus of this thesis is to introduce this methodology as a powerful and feasible tool in the analysis of geometrically nonlinear plate problems to find the closed form solutions for displacement, stress, moment, and transverse shearing force in the three cases defined in Chapter 4.

The procedure to determine the closed form solutions developed in the current study can be summarized as follows: 1) the von Kármán plate theory is used to generate nonlinear governing equations, 2) the method of minimum total potential energy combined with the Ritz methodology converts the governing equations into a system of nonlinear and coupled algebraic equations, 3) and Groebner Basis is employed to decouple the algebraic equations to find analytic solutions in terms of the material and geometric parameters of the plate. Maple 13 is used to compute the Groebner basis. Some examples of Maple worksheets and ANSYS log files for the current study are documented in the thesis.

The results of the present analysis indicate that nonlinear effects for the plates subjected to larger deformation are significant for predicting the deflections and stresses in the plates and necessary compared to those based on the linear assumptions. The analysis presented in the thesis further shows the potential of the Groebner basis methodology combined with the methods of Ritz, Galerkin, and similar approximation methods of weighted residuals which may provide a useful procedure of analysis to other nonlinear problems and a basis of preliminary design in engineering practice.

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Yao, Ming-Sheng. "Linear and geometrically nonlinear structural dynamic analysis using reduced basis finite element technique." Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/46620.

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Stoll, Frederick. "A method for the geometrically nonlinear analysis of compressively loaded prismatic composite structures." Diss., Virginia Tech, 1991. http://hdl.handle.net/10919/39814.

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30

Liu, Chorng-Fuh. "Geometrically nonlinear analysis of composite laminates using a refined shear deformation shell theory." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/54453.

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The theory is based on an assumed displacement field, in which the surface displacements are expanded in powers of the thickness coordinate up to the third order. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory accounts for small strains but moderately large displacements (i.e., von Karman strains). Exact solutions for certain cross-ply shells and finite-element models of the theory are also developed. The finite-element model is based on independent approximations of the displacements and bending moments (i.e., mixed formulation), and therefore only C°-approximations are required. Further, the mixed variational formulations developed herein suggest that the bending moments can be interpolated using discontinuous approximations (across inter-element boundaries). The finite element is used to analyze cross-ply and angle-ply laminated shells for bending, vibration, and transient response. Numerical results are presented to show the effects of boundary conditions, lamination scheme (i.e., bending-stretching coupling and material anisotropy) shear deformation, and geometric nonlinearity on deflections and frequencies. Many of the numerical results presented here for laminated shells should serve as references for future investigations.
Ph. D.

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31

Sampathkumar, Narasimhan. "Three dimensional geometrical and material nonlinear finite element analysis of adhesively bonded joints for marine structures." Thesis, University of Southampton, 2005. https://eprints.soton.ac.uk/142767/.

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The use of adhesive bonding as a structural joining method has been gaining recognition in marine industry in recent years, though it has been widely adopted in other fields such as aerospace, automobiles, trains and in civil constructions. The type of materials used and design practices followed in marine structures are different from what is applied in other disciplines. Therefore new research approaches are required and recent novel ideas are ex- plored in the context of application of bonded joint configurations in marine environment. The research is directed at developing analysis tools for predicting the displacement, stress and strain fields in adhesively bonded joints between dissimilar adherends. In the finite element formulation, the adherends may be isotropic or orthotropic layered materi- als, which are assumed to behave linear elastically. The adhesive material is assumed to behave as elasto-plastic continuum, where the nonlinear behaviour is modelled as either a rigid or a semi-rigid adhesive solid that can be represented by the Ramberg-Osgood ma- terial model. The yield behaviour of the polymeric adhesive is modelled using a modified von Mises criterion, which accounts for the fact that plastic yielding of polymer materials may occur under the action of hydrostatic as well as deviatoric stresses. The geometric nonlinearity is based on the assumption of large displacement, large rotation but small strain, and it is implemented in the code using the total Lagrangian approach. The scheme is applied on three case studies viz.: a study of adherend imbalances in a single lap joint, stress analysis of a butt-strap joint system and a hybrid joint are un- dertaken. The influence of geometric and material nonlinearity on joint deformations and adhesive stresses, are studied for a single lap joint with dissimilar adherends, aluminium and a Fibre Reinforced plastic composite material, with varying adhrend thickness ratios. The adhesive stress-strain data obtained from the model are compared with the exper- imental stress-strain curve and the numerical results are validated with the analytical solution. Three dimensional effects like ’anticlastic’ and bending-twisting’ are shown in the joint with a dissimilar adherends. Key results are obtained that explains the state of nonlinear adhesive stress state in the joint. Analysis of butt-strap joint focussed on nonlinear modelling of a semi-rigid adhesive ma- terial that is used to bond two dissimilar adherends, steel and aluminium. The analysis demonstrate that the influence of geometric and material nonlinearity on the joint de- formations as well as the adhesive stresses is significant. Nonlinear adhesive stresses are compared with the actual strength of the highly flexible adhesive, highlighting the need for the consideration of material nonlinearity in the bonded joints. Failure modes for the joint are inferred from the observations made on the adhesive stress state in the butt-strap joint. Last study, deals with three dimensional analysis of a GRP-Steel hybrid joint carried out to model the initiation and propagation of crack under a set of static loading cases. Earlier studies were restricted only to two dimensional analysis. This three dimensional analysis showed that the adhesive normal stress is not constant across the width of the joint. Critical locations of stress concentrations are identified and the failure mechanisms are compared with the experimental specimens. The observations made from this research study using a three dimensional finite element program, compliments the present knowledge in the field of adhesively bonded joints.

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32

Garcilazo, Juan Jose. "Nonlinear Analysis of Plane Frames Subjected to Temperature Changes." OpenSIUC, 2015. https://opensiuc.lib.siu.edu/dissertations/1009.

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In this study, methods for the geometric nonlinear analysis and the material nonlinear analysis of plane frames subjected to elevated temperatures are presented. The method of analysis is based on a Eulerian (co-rotational) formulation, which was developed initially for static loads, and is extended herein to include geometric and material nonlinearities. Local element force-deformation relationships are derived using the beam-column theory, taking into consideration the effect of curvature due to temperature gradient across the element cross-section. The changes in element chord lengths due to thermal axial strain and bowing due to the temperature gradient are also taken into account. This "beam-column" approach, using stability and bowing functions, requires significantly fewer elements per member (i.e. beam/column) for the analysis of a framed structure than the "finite-element" approach. A computational technique, utilizing Newton-Raphson iterations, is developed to determine the nonlinear response of structures. The inclusion of the reduction factors for the coefficient of thermal expansion, modulus of elasticity and yield strength is introduced and implemented with the use of temperature-dependent formulas. A comparison of the AISC reduction factor equations to the Eurocode reduction factor equations were found to be in close agreement. Numerical solutions derived from geometric and material analyses are presented for a number of benchmark structures to demonstrate the feasibility of the proposed method of analysis. The solutions generated for the geometrical analysis of a cantilever beam and an axially restrained column yield results that were close in proximity to the exact, theoretical solution. The geometric nonlinear analysis of the one-story frame exhibited typical behavior that was relatively close to the experimental results, thereby indicating that the proposed method is accurate. The feasibility of extending the method of analysis to include the effects of material nonlinearity is also explored, and some preliminary results are presented for an experimentally tested simply supported beam and the aforementioned one-story frame. The solutions generated for these structures indicate that the present analysis accurately predicts the deflections at lower temperatures but overestimates the failure temperature and final deflection. This may be in part due to a post-buckling reaction after the first plastic hinge is formed. Additional research is, therefore, needed before this method can be used to analyze the materially nonlinear response of structures.

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33

Providas, Efthimios. "On the geometrically nonlinear constant moment triangle (with a note on drilling rotations)." Thesis, Brunel University, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.277518.

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34

Abu, Kassim Abdul Majid. "Theorems of structural and geometric variation for linear and nonlinear finite element analysis." Thesis, University of Edinburgh, 1985. http://hdl.handle.net/1842/10710.

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Chen, Yahao. "Geometric analysis of differential-algebraic equations and control systems : linear, nonlinear and linearizable." Thesis, Normandie, 2019. http://www.theses.fr/2019NORMIR04.

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Dans la première partie de cette thèse, nous étudions les équations différentielles algébriques (en abrégé EDA) linéaires et les systèmes de contrôles linéaires associés (en abrégé SCEDA). Les problèmes traités et les résultats obtenus sont résumés comme suit : 1. Relations géométriques entre les EDA linéaires et les systèmes de contrôles génériques SCEDO. Nous introduisons une méthode, appelée explicitation, pour associer un SCEDO à n'importe quel EDA linéaire. L'explicitation d'une EDA est une classe des SCEDO, précisément un SCEDO défini, à un changement de coordonnées près, une transformation de bouclage près et une injection de sortie près. Puis nous comparons les « suites de Wong » d'une EDA avec les espaces invariants de son explicitation. Nous prouvons que la forme canonique de Kronecker FCK d'une EDA linéaire et la forme canonique de Morse FCM d'un SCEDO, ont une correspondance une à une et que leurs invariants sont liés. De plus, nous définissons l'équivalence interne de deux EDA et montrons sa particularité par rapport à l'équivalence externe en examinant les relations avec la régularité interne, i.e., l'existence et l'unicité de solutions. 2. Transformation d'un SCEDA linéaire vers sa forme canonique via la méthode d'explicitation avec des variables de driving. Nous étudions les relations entre la forme canonique par bouclage FCFB d'un SCEDA proposée dans la littérature et la forme canonique de Morse pour les SCEDO. Premièrement, dans le but de relier SCEDA avec les SCEDO, nous utilisons une méthode appelée explicitation (avec des variables de driving). Cette méthode attache à une classe de SCEDO avec deux types d'entrées (le contrôle original et le vecteur des variables de driving) à un SCEDA donné. D'autre part, pour un SCEDO linéaire classique (sans variable de driving) nous proposons une forme de Morse triangulaire FMT pour modifier la construction de la FCM. Basé sur la FMT nous proposons une forme étendue FMT et une forme étendue de FCM pour les SCEDO avec deux types d'entrées. Finalement, un algorithme est donné pour transformer un SCEDA dans sa FCFB. Cet algorithme est construit sur la FCM d'un SCEDO donné par la procédure d'explicitation. Un exemple numérique illustre la structure et l'efficacité de l'algorithme. Pour les EDA non linéaires et les SCEDA (quasi linéaires) nous étudions les problèmes suivants : 3. Explicitations, analyse externe et interne et formes normales des EDA non linéaires. Nous généralisons les deux procédures d'explicitation (avec ou sans variables de driving) dans le cas des EDA non linéaires. L'objectif de ces deux méthodes est d'associer un SCEDO non linéaire à une EDA non linéaire telle que nous puissions l'analyser à l'aide de la théorie des EDO non linéaires. Nous comparons les différences de l'équivalence interne et externe des EDA non linéaires en étudiant leurs relations avec l'existence et l'unicité d'une solution (régularité interne). Puis nous montrons que l'analyse interne des EDA non linéaire est liée à la dynamique nulle en théorie classique du contrôle non linéaire. De plus, nous montrons les relations des EDAS de forme purement semi-explicite avec les 2 procédures d'explicitations. Finalement, une généralisation de la forme de Weierstrass non linéaire FW basée sur la dynamique nulle d'un SCEDO non linéaire donné par la méthode d'explicitation est proposée
In the first part of this thesis, we study linear differential-algebraic equations (shortly, DAEs) and linear control systems given by DAEs (shortly, DAECSs). The discussed problems and obtained results are summarized as follows. 1. Geometric connections between linear DAEs and linear ODE control systems ODECSs. We propose a procedure, named explicitation, to associate a linear ODECS to any linear DAE. The explicitation of a DAE is a class of ODECSs, or more precisely, an ODECS defined up to a coordinates change, a feedback transformation and an output injection. Then we compare the Wong sequences of a DAE with invariant subspaces of its explicitation. We prove that the basic canonical forms, the Kronecker canonical form KCF of linear DAEs and the Morse canonical form MCF of ODECSs, have a perfect correspondence and their invariants (indices and subspaces) are related. Furthermore, we define the internal equivalence of two DAEs and show its difference with the external equivalence by discussing their relations with internal regularity, i.e., the existence and uniqueness of solutions. 2. Transform a linear DAECS into its feedback canonical form via the explicitation with driving variables. We study connections between the feedback canonical form FBCF of DAE control systems DAECSs proposed in the literature and the famous Morse canonical form MCF of ODECSs. In order to connect DAECSs with ODECSs, we use a procedure named explicitation (with driving variables). This procedure attaches a class of ODECSs with two kinds of inputs (the original control input and the vector of driving variables) to a given DAECS. On the other hand, for classical linear ODECSs (without driving variables), we propose a Morse triangular form MTF to modify the construction of the classical MCF. Based on the MTF, we propose an extended MTF and an extended MCF for ODECSs with two kinds of inputs. Finally, an algorithm is proposed to transform a given DAECS into its FBCF. This algorithm is based on the extended MCF of an ODECS given by the explication procedure. Finally, a numerical example is given to show the structure and efficiency of the proposed algorithm. For nonlinear DAEs and DAECSs (of quasi-linear form), we study the following problems: 3. Explicitations, external and internal analysis, and normal forms of nonlinear DAEs. We generalize the two explicitation procedures (with or without driving variable) proposed in the linear case for nonlinear DAEs of quasi-linear form. The purpose of these two explicitation procedures is to associate a nonlinear ODECS to any nonlinear DAE such that we can use the classical nonlinear ODE control theory to analyze nonlinear DAEs. We discuss differences of internal and external equivalence of nonlinear DAEs by showing their relations with the existence and uniqueness of solutions (internal regularity). Then we show that the internal analysis of nonlinear DAEs is closely related to the zero dynamics in the classical nonlinear control theory. Moreover, we show relations of DAEs of pure semi-explicit form with the two explicitation procedures. Furthermore, a nonlinear generalization of the Weierstrass form WE is proposed based on the zero dynamics of a nonlinear ODECS given by the explicitation procedure

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Filchev, Ivan. "Buckling and geometric nonlinear FE analysis of pitched large-spanroof structure of wood." Thesis, Linnéuniversitetet, Institutionen för byggteknik (BY), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-54324.

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An arched structure provides an effective load carrying system for large span structures. When it comes to long span roof structures, timber arches are one of the best solutions from both structural and aesthetical point of view. Glulam arched structures are often designed using slender elements due to economic consideration. Such slender cross-section shape increases the risk of instability. Instability analysis of straight members such as beam and column are explicitly defined in Eurocode. However, for instability of curved members no analytical approach is provided in the code, thus some numerical method is required. Nonetheless, an approximation is frequently used to obtain the effective buckling length for the arched structures in the plane of arches. In this master thesis a linear buckling analysis is carried out in Abaqus to obtain an optimal effective buckling length both in-plane and out-of-plane for circular glulam arched structures. The elastic springs are used to simulate the overall stiffness of the bracing system. The results obtained by the FE simulations are compared with a simple approximation method. Besides, the forces acting on the bracings system is obtained based on 3D geometric nonlinear stress analysis of the timber trusses. Our findings conclude that the approximation method overestimates the effective buckling length for the circular glulam arched structures. In addition, the study indicates that the position of the lateral supports along the length of the arch is an important design aspect for buckling behaviour of the arched structures. Moreover, in order to acquire an effective structure lateral supports are needed both in extrados and intrados. Furthermore, instead of using elastic spring elements to simulate the overall stiffness of the bracing system, a full 3D simulation of two parallel arches was performed. It was shown that the springs are stronger than the real bracing system for the studied arch.

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37

Guo, Sheng. "On Neumann Problems for Fully Nonlinear Elliptic and Parabolic Equations on Manifolds." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1571696906482925.

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SUBRAMANIAN, BALAKRISHNAN. "GEOMETRICALLY NONLINEAR ANALYSIS OF THIN ARBITRARY SHELLS USING DISCRETE-KIRCHHOFF CURVED TRIANGULAR ELEMENTS (FINITE)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/188101.

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The research work presented here deals with the problems of geometrically nonlinear analysis of thin shell structures. The specific objective was to develop geometrically nonlinear formulations, using Discrete-Kirchhoff Curved Triangular (DKCT) thin shell elements. The DKCT elements, formulated in the natural curvilinear coordinates, based on arbitrary deep shell theory and representing explicit rigid body modes, were successfully applied to linear elastic analysis of composite shells in an earlier research work. A detailed discussion on the developments of classical linear and nonlinear shell theories and the Finite Element applications to linear and nonlinear analysis of shells has been presented. The difficulties of developing converging shell elements due to Kirchhoff's hypothesis have been discussed. The importance of formulating shell elements based on deep shell theory has also been pointed out. The development of shell elements based on Discrete-Kirchhoff's theory has been discussed. The development of a simple 3-noded curved triangular thin shell element with 27 degrees-of-freedom in the tangent and normal displacements and their first-order derivatives, formulated in the natural curvilinear coordinates and based on arbitrary deep shell theory, has been described. This DKCT element has been used to develop geometrically nonlinear formulation for the nonlinear analysis of thin shells. A detailed derivation of the geometrically nonlinear (GNL) formulation, using the DKCT element based on the Total Lagrangian approach and the principles of virtual work has been presented. The techniques of solving the nonlinear equilibrium equations, using the incremental methods has been described. This includes the derivation of the Tangent Stiffness matrix. Various Newton-Raphson solution algorithms and the associated convergence criteria have been discussed in detail. Difficulties of tracing the post buckling behavior using these algorithms and hence the necessity of using alternative techniques have been mentioned. A detailed numerical evaluation of the GNL formulation has been carried out by solving a number of standard problems in the linear buckling and GNL analysis. The results compare well with the standard solutions in linear buckling cases and are in general satisfactory for the GNL analysis in the region of large displacements and small rotations. It is concluded that this simple and economical element will be an ideal choice for the expensive nonlinear analysis of shells. However, it is suggested that the element formulation should include large rotations for the element to perform accurately in the region of large rotations.

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39

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.
Ph. D.

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40

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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Vu, Duy Thang [Verfasser]. "Geometrically nonlinear higher-order shear deformation FE analysis of thin-walled smart structures / Duy Thang Vu." Aachen : Hochschulbibliothek der Rheinisch-Westfälischen Technischen Hochschule Aachen, 2011. http://d-nb.info/1018190376/34.

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Vasilescu, Adrian. "Analysis of geometrically nonlinear and softening response of thin structures by a new facet shell element." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape4/PQDD_0018/MQ57743.pdf.

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Lam, Siu-Shu Eddie. "Linear and geometrically nonlinear analysis of shell structures by a shear flexible finite element shell formulation." Thesis, University of Southampton, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328340.

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Andruet, Raul Horacio. "Special 2-D and 3-D Geometrically Nonlinear Finite Elements for Analysis of Adhesively Bonded Joints." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/30450.

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Finite element models have been successfully used to analyze adhesive bonds in actual structures, but this takes a considerable amount of time and a high computational cost. The objective of this study is to develop a simple and cost-effective finite element model for adhesively bonded joints which could be used in industry. Stress and durability analyses of crack patch geometries are possible applications of this finite element model. For example, the lifetime of aging aircraft can be economically extended by the application of patches bonded over the flaws located in the wings or the fuselage. Special two and three- dimensional adhesive elements have been developed for stress and displacement analyses in adhesively bonded joints. Both the 2-D and 3-D elements are used to model the whole adhesive system: adherends and adhesive layer. In the 2-D elements, adherends are represented by Bernoulli beam elements with axial deformation and the adhesive layer by plane stress or plane strain elements. The nodes of the plane stress-strain elements that lie in the adherend-adhesive interface are rigidly linked with the nodes of the beam elements. The 3-D elements consist of shell elements that represent the adherends and solid brick elements to model the adhesive. This technique results in smaller models with faster convergence than ordinary finite element models. The resulting mesh can represent arbitrary geometries of the adhesive layer and include cracks. Since large displacements are often observed in adhesively bonded joints, geometric nonlinearity is modeled. 2-D and 3-D stress analyses of single lap joints are presented. Important 3-D effects can be appreciated. Fracture mechanics parameters are computed for both cases. A stress analysis of a crack patch geometry is presented. A numerical simulation of the debonding of the patch is also included.
Ph. D.

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45

Vasilescu, Adrian Carleton University Dissertation Engineering Civil and Environmental. "Analysis of geometrically nonlinear and softening response of thin structures by a new Facet Shell Element." Ottawa, 2000.

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46

Ramachandran, Maya. "Nonlinear finite element analysis of TWEEL geometric parameter modifications on spoke dynamics during high speed rolling." Connect to this title online, 2008. http://etd.lib.clemson.edu/documents/1239896731/.

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Junca, Stéphane. "Oscillating waves for nonlinear conservation laws." Habilitation à diriger des recherches, Université Nice Sophia Antipolis, 2013. http://tel.archives-ouvertes.fr/tel-00845827.

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The manuscript presents my research on hyperbolic Partial Differential Equations (PDE), especially on conservation laws. My works began with this thought in my mind: ''Existence and uniqueness of solutions is not the end but merely the beginning of a theory of differential equations. The really interesting questions concern the behavior of solutions.'' (P.D. Lax, The formation and decay of shock waves 1974). To study or highlight some behaviors, I started by working on geometric optics expansions (WKB) for hyperbolic PDEs. For conservation laws, existence of solutions is still a problem (for large data, $L^\infty$ data), so I early learned method of characteristics, Riemann problem, $BV$ spaces, Glimm and Godunov schemes, \ldots In this report I emphasize my last works since 2006 when I became assistant professor. I use geometric optics method to investigate a conjecture of Lions-Perthame-Tadmor on the maximal smoothing effect for scalar multidimensional conservation laws. With Christian Bourdarias and Marguerite Gisclon from the LAMA (Laboratoire de \\ Mathématiques de l'Université de Savoie), we have obtained the first mathematical results on a $2\times2$ system of conservation laws arising in gas chromatography. Of course, I tried to put high oscillations in this system. We have obtained a propagation result exhibiting a stratified structure of the velocity, and we have shown that a blow up occurs when there are too high oscillations on the hyperbolic boundary. I finish this subject with some works on kinetic équations. In particular, a kinetic formulation of the gas chromatography system, some averaging lemmas for Vlasov equation, and a recent model of a continuous rating system with large interactions are discussed. Bernard Rousselet (Laboratoire JAD Université de Nice Sophia-Antipolis) introduced me to some periodic solutions related to crak problems and the so called nonlinear normal modes (NNM). Then I became a member of the European GDR: ''Wave Propagation in Complex Media for Quantitative and non Destructive Evaluation.'' In 2008, I started a collaboration with Bruno Lombard, LMA (Laboratoire de Mécanique et d'Acoustique, Marseille). We details mathematical results and challenges we have identified for a linear elasticity model with nonlinear interfaces. It leads to consider original neutral delay differential systems.

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Burchnall, David. "Formulation and Validation of a Nonlinear Shell Element for the Analysis of Reinforced Concrete and Masonry Structures." Thesis, Virginia Tech, 2014. http://hdl.handle.net/10919/48597.

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Reinforced concrete (RC) shear wall buildings constitute a significant portion of the building inventory in many earthquake-prone regions. A similar type of structural system is fully-grouted reinforced masonry (RM) shear wall structures. The accurate determination of the nonlinear response of reinforced concrete and reinforced masonry (RC/RM) walls subjected to lateral loading is of uttermost importance for ensuring the safety of the built environment. Analytical models provide a cost efficient and comprehensive tool to study the nonlinear response of RC/RM structures, as compared to experimental tests. Predictive models should capture nonlinear material behavior as well as the geometrically nonlinear response of RC/RM shear wall structures during major seismic events. This thesis outlines the formulation and validation of a nonlinear shell element for the simulation of RC/RM structures. The proposed shell element enhances an existing formulation of a four-node Discrete Kirchhoff shell element through the inclusion of a corotational approach to account for geometric nonlinearities and of nonlinear material models to capture the effect of cracking and crushing in concrete or masonry and the nonlinear hysteretic behavior of reinforcing steel. The analytical results obtained from multiple linear and nonlinear analyses are compared against theoretical solutions and experimental test data. These comparative validation studies show the enhanced shell element can satisfactorily capture the salient features of the response of nonlinear reinforced concrete/masonry shear wall structures including axial-shear-flexure interaction, damage patterns, and in-plane and out-of-plane loading.
Master of Science

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Warren, J. E. Jr. "Nonlinear Stability Analysis of Frame-Type Structures with Random Geometric Imperfections Using a Total-Lagrangian Finite Element Formulation." Diss., Virginia Tech, 1997. http://hdl.handle.net/10919/30338.

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With the increasing use of lightweight frame-type structures that span long distances, there is a need for a method to determine the probability that a structure having random initial geometric imperfections will become unstable at a load less than a spe cified fraction of the perfect critical load. The overall objective of this dissertation is to present such a method for frame-type structures that become unstable at limit points. The overall objective may be broken into three parts. The first part concerns the development of a three-dimensional total Lagrangian beam finite element that is used to determine the critical load for the structure. The second part deals with a least squares method for modeling the random initial imperfections using the mo de shapes from a linear buckling analysis, and a specified maximum allowable magnitude for the imperfection at any imperfect node in the structure. The third part deals with the calculation of the probability of failure using a combined response surface/ first-order second-moment method. Numerical results are presented for two example problems, and indicate that the proposed method is reasonably accurate. Several problems with the proposed method were noted during the course of this work and are discussed in the final chapter.
Ph. D.

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NARAYANAN, VIJAY. "STRUCTURAL ANALYSIS OF REINFORCED SHELL WING MODEL FOR JOINED-WING CONFIGURATION." University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1116214221.

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Dissertations / Theses on the topic 'Nonlinear geometrical analysi'

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