Adaptive Scaled Boundaru Finite Element Method And Its Application In Elastomechanics

The equilibrium equations and their solutions of scaled boundary finite element method (SBFEM) are derived based on the virtual work principle in this thesis, not only for elastostatics but also for elastodynamics. Energy error estimator based on stress recovery technique is extended from elastostatics to elastodyanmics, and an efficient remeshing strategy is given out with a simple but accurate mesh mapping procedure. Furthermore, the error caused by time discretisation is also taken into account, leading to a datively complete adaptive SBFEM for general elstodynamic problems. Additionally, a polygon scaled boundary finite element method is developed based on Delauney Triangulation, making the discritisation in SBFEM fully-automatic.The equilibrium equations of SBFEM are derived based on virtual work for elastostatics. Two different stress recovery teniques, including superconvergent patch recovery (SPR) and node average technique, are compared. Total energy, energy error and error estimator are given out in semi-analytical formula. An h-type remeshing procedure and a follow chart of the adaptive approach are described in detail. The changes of adaptive meshes, accuracy and computational time are investigated through a numerical experiment. The stress filed calculated by adaptive SBFEM is also compared with that of FEM.The equilibrium equations of SBFEM are extended to elastodynamics also based on virtual work principle. Newmark intergration scheme is employed to solve the equations. Kenetic energy, strain energy, total energy and energy error are calculated semi-analytically, followed by an energy error estimator developed for elastodynamic cases. A simple but accurate meshing mapping method is derived semi-analytically as well. The follow chart of adaptive SBFEM is described for elasodynamic problems. This method is used to calculate the structures’responses under blast/impact loading, and the results are compared with traditional SBFEM, FEM and adaptive FEM in order to verify the effectiveness of the present method.The conception of "super element" is introduced and the semi-analytical calculations of kinetic energy, strain energy, total energy and energy error are extended to subdomain level, and a distinguish approach of the subdomain energy error is proposed. A simple subdomain subdivision procedure, combined with the developed mesh mapping method, leads to a new adaptive SBFEM. A simply-supported beam and a cantilever under an impact loading are calculated by this method respectively.The acceleration field is rebuilt based on the assumption of linear distributed acceleration for Newmark integration scheme. The calculation of the time discretisation error, followed by a local error estimator, is given out. Based on the adjustment of time incresement, an adaptive time-stepping procedure of SBFEM is developed with its follow chart. Several numerical examples are examined based on this method.A polygon SBFEM is developed based on the Delauney Triangulation. Nodes shared by different triangles or the gravity centres of polygons are taken as the scaling centre of subdomains, a polygon mesh of SBFEM is constructed directly and automaticly. The influence of element size on calculation accuracy is investigated by several numerical examples; meanwhile the total energy is calculated.This thesis aims at extending the theory of adaptive SBFEM and making a good prepare for its applications in engineering, especially for crack propagation modeling.