SINGULARITY ELEMENTS FOR THE P-VERSION OF THE FINITE ELEMENT METHOD (HIGHLY CONFORMING FORMULATION, H-VERSION)
Abstract
The purpose of this dissertation is to develop an appropriate element model with a general but simple formulation in FEM for improvement of the accuracy and the rate of convergence in computing the strain energy (or stress intensity) for linear elastic mechanics problems. Firstly, the FEM with the highly conforming formulations between elements for the p-version is studied. It is demonstrated that this strategy is only a valid and effective method for one-dimensional problems. Then the square root triangular singularity elements with C(DEGREES) formulations for the p-version are investigated. A general but simple rule for placing all the boundary and interior nodal locations for these singularity elements is developed. Based on the numerical analysis of the experimental results obtained from simple practical problems, these singularity elements are not only useful for the inverse square root stress singularity problems, but are also applicable to the other linear elastic problems, such as absence of singularity, nearly incompressible materials and variation of strength of singularity problems. The computer programs using these singularity elements in the FEM are moderately efficient and cost of computer time is reasonable.
Degree
Ph.D.
Subject Area
Civil engineering
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