P-adaptive hybrid/mixed finite element method.

摘要

The purpose of this dissertation was to develop an efficient computational program for accurate two- and three-dimensional stress analysis. The p-adaptive hybrid/mixed finite element formulation has been developed for this purpose. The most general Hu-Washizu principle in solid mechanics is used in the hybrid/mixed finite element formulation. The stress, strain and displacement variables are assumed independently. The displacement field is interpolated using hierarchical shape functions for p-adaptive purpose. The stress and strain fields are interpolated using the normalized Legendre polynomials so that the formation of the element stiffness matrix has been greatly simplified. Computations show that the computing time for the hybrid/mixed p-method is less than that for the displacement based p-method for 3-D problem. Higher accuracy can be achieved by increasing polynomial order p.; For element with curved boundaries and surfaces, new p-order geometric mappings are developed from blending functions using Lagrange hierarchical shape functions. This mapping technique can be easily incorporated into most finite element programs and works very well as seen by numerical test.; A novel Lagrange approach was developed for the 1-D hierarchical shape functions, from which the 2-D and 3-D hierarchical shape functions were constructed. This approach started directly from the second order shape functions plus higher-order hierarchical shape functions.; Several 2-D and 3-D numerical examples are given to test the convergence and accuracy of the p-version hybrid/mixed finite element programs. Numerical examples have shown the successful use of the p-version hybrid/mixed finite element method.