Hamiltonian-Based Derivation of the High-Performance Scaled-Boundary Finite-Element Method Applied to the Complex Multilayered Soil Field in Time Domain

Abstract

Wave propagation in a two-dimensional unbounded domain with rigid bedrock was studied. The study was based on the scaled-boundary finite-element method (SBFEM) combing the continued fraction method. The SBFEM is a novel semianalytical technique, combining the advantages of the finite-element and the boundary-element methods. Meanwhile, SBFEM has unique properties of its own. In this paper, the modified SBFEM was introduced. The original scaling center was replaced by a scaling line, which is more suitable for analyzing the multilayered soil model. As a key point, the modified SBFEM and the dual system, which is used to solve a proposed time domain problem, were combined to derive the governing equations. The derivation process was based on the framework of the Hamiltonian system by introducing dual variables. By using the continued fraction solution and introducing auxiliary variables, the equation of motion was built. More significantly, the efficient, precise time-integration method was first used to solve the global equation of motion. This technology improved the stability of the modified SBFEM greatly. Because the integral interval was divided into very small pieces, five terms of the Taylor expansion were used for each piece. This precision can achieve computer precision. Therefore, an extremely efficient and accurate solution of the SBFEM in time domain was obtained. The substructure method was proposed for solving the multilayered inclined model in engineering practice. Numerical examples demonstrated the accuracy and high efficiency of proposed methods for the complex shape models.