Finite Element Mesh for a Complete Solution of a Problem with a Singularity.
MINNESOTA UNIV MINNEAPOLIS DEPT OF AEROSPACE ENGINEERING AND MECHANICS
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The purpose of this paper has been to show that a finite-element method using only constant-strain triangular elements can be used in a problem with a stress singularity to obtain a complete solution for stress, strain, and displacement at and economical cost in computing. The method does not require and a priori knowledge of the nature of the singularity. The result has been acheived by using and easily-generated mesh scheme which is centered at the point of singularity. The particular problem of a plate with a centered crack in a state of plane stress was chosen because and exact analytical solution was available against which to measure the accuracy of our solution. The finite element solution was obtained by using a mesh yields stress and strain field values which are accurate at distances from the crack tip as small as 0.000001 times the crack length using only reasonable number of degrees of freedom. Additional keywords Computations Supercomputers FORTRAN Computer programs.
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