An efficient implementation of BEM for transient analyses of thermomechanics and soil consolidation
The focus of this dissertation is on the efficient implementation of BEM for transient analyses of linear and nonlinear thermomechanics and soil consolidation. Based on the integration based boundary convolution method, a fast boundary convolution method is presented, which only uses an equivalent set of variables of each element for convolution. As demonstrated in the examples analyzed, this method greatly saves computation burden while giving the same good solutions as the traditional convolution method. In order to address the existing difficulty in solving nonlinear transient thermomechanics and soil consolidation effectively, this idea is expanded to the boundary convolution of nonlinear analysis. The volume integration is also implemented effectively by representing the nodal variables with the equivalent volume element variables. All existing nonlinear BEM algorithms are difficult to converge when it nears collapse, when the results become unstable. The Newton-Raphson solution algorithm presented in this dissertation improved both the accuracy and the stability. All formulations are implemented for 2D, 3D and axisymmetry in a general purpose, multi-region computer code with the capability of local definition of boundary conditions. Several examples of practical interests are shown to demonstrate the practical utilities of the developed analyses.