Study Of Two-dimensional Adaptive Finite Element Static Analysis Method

Adaptive finite element analysis is a numerical solution process to automatically adjust its algorithms to improve the accuracy, including adaptive mesh, error estimation and other technologies. To carry out basic research on relevant technologies is of great significance for dealing with increasingly sophisticated engineering.An improved two-dimensional adaptive triangle and quadrilateral mesh generator has been developed, which includes two-dimension-al triangular mesh generation algorithms based on Delaunay algorithm and the principle of static equilibrium, full quadrilateral mesh generating algorithm based on the whole triangular grid and the center of gravity search method, grid smoothing algorithm and grid refinement algorithm, for solving the problem of adaptive meshing, regeneration and refinement for two-dimensional geometric model. Storage space is significantly reduced using the methods of assembling only non-zero cells in element stiffness matrix and keeping only non-zero elements in structural stiffness matrix. Direct solution of finite element equation based on reverse Cuthill-McKee ordering algorithms and Cholesky decomposition method was studied in combination with the sparsely characteristic of structural stiffness matrix. Besides, a finite element analysis program was developed for the continuum plane problem as well, checked by the commercial software ANSYS. Based on elements’solution accuracy, Stress results and polished program, a posteriori error estimates method was implemented. Three adaptive methods was studied and implemented, including h method, p method and h—p method. The h adaptive method based on mesh regeneration has a higher convergence rate in a detailed comparison with the h adaptive method based on mesh enrichment. A new element type conversion strategy was proposed by introducing the scale factor λ, controlling when switch h adaptive method to p adaptive method. That meant the element order will increase one and recalculated when the current accuracy of finite element analysis achieves λ times the target analytical precision. Numerical results show that this method can achieve the target accuracy with faster convergence rate.