Advanced development of boundary element methods in material nonlinear analysis

The principal focus of this thesis is the advanced development of the Boundary Element Method (BEM) for nonlinear analysis of elastoplastic, nonlinear contact, thermoplastic and soil consolidation problems.;Analytical integrations of boundary and volume kernels integrals are performed for both two-dimensional and three-dimensional problems. Whenever the geometry of the problem meets the straight line or flat surface requirement, the analytical integration is faster and more accurate than numerical integration.;A new form of the Newton-Raphson algorithm in nonlinear BEM is established in the present work. The formation of right hand side terms in each iteration is simplified. The procedures of the algorithm is fully illustrated graphically. Extensive comparisons are made between the present nonlinear algorithm and those developed earlier. In the new algorithm, only the equations related to the yielded nodes need Gaussian elimination after the first iteration of the first load step. This advantage combined with the sub-region technique makes BEM a viable alternative to FEM for the material nonlinear analysis.;The nonlinear contact algorithm for elastic analysis is combined with the Newton-Raphson algorithm. The result is the developed capability of plastic analysis of bodies in contact by BEM. To the best of the author's knowledge, such analysis have not been performed before in BEM.;The complete set of new kernel functions of linear time variation approach is obtained for thermoplasticity and nonlinear soil consolidation problems. Compared to the constant time approach, the linear time variation approach enables the use of relatively large time steps.;All of the formulations cited above have been implemented in a general purpose boundary element software. This now enables a suite of new engineering problems to be solved by this method of analysis.