Thesis--Auburn University, 2009. / Abstract. Includes bibliographic references (p.74-75).

Thesis (M.A.)--California State University Channel Islands, 2009. / Submitted in partial fulfillment of the requirements for the degree of Masters Of Science in Mathematics. Title from PDF t.p. (viewed February 22, 2010).

No description available.

An analysis of the finite deformation of an elastic body using the finite element method is investigated. The governing nonlinear equations of equilibrium are derived through the principle of virtual work using a Lagrangian description. A general incremental virtual work equation is obtained, and then linearized to permit the use of direct solution techniques. A residual loading term is defined which represents the nonsatisfaction of equilibrium of the solution obtained at the end of an increment using the linear incremental virtual work equation. The residual loading term is used to control the divergence of the linearized incremental solution from the exact equilibrium solution, through the self-correcting solution technique. The finite element method is introduced in general for three dimensional analysis, and is then specialized for two dimensional, plane elasticity analysis. Two eight degree of freedom rectangular finite elements are developed using a bilinear assumed displacement field. The first element is numerically integrated using Gaussian quadrature, while the second employs a nonuniform integration scheme in order to improve this element's performance. Four finite deformation problems are analysed using the procedure presented in this thesis, and the results are compared with available closed form solutions. The problems analysed are those of a uniformly loaded infinite plate strip having either simply supported longitudinal edges or fixed longitudinal edges, a cantilever beam under a uniformly distributed load, and lastly a cantilever beam with a para-bolically distributed end load. Excellent agreement was obtained between the finite element analysis results and the closed form solutions. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

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published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

The study examines the behavior of pinned-end, centrally loaded columns of monosymmetric and asymmetric cross sections, with emphasis on angle shapes. The investigation covers flexural and flexural-torsional buckling in the elastic and inelastic ranges, which the aim of developing a rational method of predicting the buckling load for cross sections with low torsional rigidity and single or no axes of symmetry. The computer program that was developed takes into account the effect of residual stresses. The properties of the cross section were determined in the laboratory and utilized in the computer model. Full-scale column tests were run to verify the theoretical model. The results shows that equal-legged angles with low width-to-thickness ratio have flexural and flexural-torsional buckling loads that are less than 2% different. It is therefore suitable to continue using a flexural buckling solution for such shapes. This is also true for equal-legged angles with a high width-to-thickness ratio that fail in the elastic range, but in the inelastic range the flexural-torsional buckling load was about 11% less than the flexural buckling load. When the angle is unequal-legged, the flexural-torsional buckling load is always smaller than the corresponding flexural buckling load, in both the elastic and the inelastic ranges. The average difference between the flexural and flexural-torsional load for unequal-legged angle ranges from 3% in the elastic range to 10% in the inelastic range. The average ratio of the experimental results to the minimum of the theoretical results was 0.95 and the coefficient of variation was 0.053. Comparison with the results of other researchers show that it is possible to formulate an empirical formula that can be used in designing columns that are made of monosymmetric or asymmetric cross sections. However, due to the scarcity of data at this stage, it is recommended that the development of such a formula be postponed until additional test data are available. Moreover, in designing any cross section that does not have two axes of symmetry, it is advisable to check the possibility of flexural and flexural-torsional buckling.

No description available.

No description available.

Lai Chi-fai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 98-99). / Abstracts in English and Chinese. / Chapter 1. --- INTRODUCTION --- p.7 / Chapter 1.1 --- Motivations and objectives --- p.7 / Chapter 1.2 --- Thesis Organization --- p.10 / Chapter 2. --- related works --- p.11 / Chapter 2.1 --- Deformation Techniques --- p.11 / Chapter 2.1.1 --- Deformation techniques requiring a deformation tool --- p.11 / Chapter 2.1.2 --- Directly specified deformation techniques --- p.14 / Chapter 2.1.3 --- Comparison on Different Deformation Technique --- p.15 / Chapter 2.2 --- Application of Deformation --- p.16 / Chapter 2.2.1 --- Deforming superquadrics --- p.16 / Chapter 2.2.2 --- Volume wraping --- p.16 / Chapter 2.2.3 --- Deforming linear object --- p.17 / Chapter 2.2.4 --- FFD for animation synthesis --- p.17 / Chapter 2.2.5 --- Using FFD on feature-based Surface --- p.18 / Chapter 2.2.6 --- NURBS-BASED Free-Form Deformation (NFFD) --- p.18 / Chapter 2.3 --- Algebraic Patch Techniques --- p.20 / Chapter 2.3.1 --- Dahmen's scheme --- p.20 / Chapter 2.3.2 --- Lodha and Warren's technique --- p.20 / Chapter 2.3.3 --- Guo's method --- p.21 / Chapter 3. --- BACKGROUND THEORIES --- p.22 / Chapter 3.1 --- Algebraic Patches --- p.22 / Chapter 3.1.1 --- Bernstein-Bezier representation of a single patch --- p.22 / Chapter 3.1.2 --- Constructing free-form objects --- p.29 / Chapter 3.1.2.1 --- Bounding volumes for quadric patches --- p.29 / Chapter 3.1.2.2 --- Filling two-sided gaps --- p.31 / Chapter 3.2 --- Constructive Shell Representation --- p.35 / Chapter 3.2.1 --- Properties of quadric patches and its construction tetrahedron and trunctets --- p.38 / Chapter 3.3 --- Free-Form Deformation --- p.40 / Chapter 3.3.1 --- Formulating free-form deformation --- p.40 / Chapter 4. --- FREE-FORM DEFORMATION OF CSR SOLID MODELS --- p.43 / Chapter 4.1 --- Determination of Lattice Structure --- p.43 / Chapter 4.2 --- "Relation between weights, normals and shape of a trunctet" --- p.46 / Chapter 4.3 --- Applying FFD on CSR solid models --- p.49 / Chapter 4.3.1 --- Deforming normal at vertices --- p.52 / Chapter 4.3.2 --- Using vertices' neighborhoods --- p.54 / Chapter 4.4 --- Free-Form Deformation of CSR objects by Surface Fitting --- p.57 / Chapter 4.4.1 --- Deforming a single surface patch --- p.57 / Chapter 4.4.1.1 --- Locating surface points --- p.59 / Chapter 4.4.1.2 --- Conversion between barycentric and Cartesian coordinates --- p.61 / Chapter 4.4.1.3 --- Evaluating the deformed surface patch --- p.62 / Chapter 4.4.1.4 --- Saddle shape trunctet --- p.64 / Chapter 4.4.1.5 --- Using double tetrahedrons --- p.66 / Chapter 4.4.1.6 --- Surface subdivision --- p.69 / Chapter 4.4.2 --- Deforming Entire Solid Model --- p.72 / Chapter 4.4.3 --- Comparison on different approaches --- p.75 / Chapter 4.5 --- Conversion of CSG solid Models into CSR --- p.76 / Chapter 4.5.1 --- Converting halfspaces into CSR objects --- p.77 / Chapter 5. --- IMPLEMENTATION AND RESULTS --- p.82 / Chapter 5.1 --- Implementation --- p.82 / Chapter 5.2 --- Experimental Results --- p.84 / Chapter 6. --- CONCLUSION AND SUGGESTIONS FOR FURTHER WORK --- p.93 / Chapter 6.1 --- Conclusion --- p.93 / Chapter 6.2 --- Suggestions for further work --- p.96