FINITE-ELEMENT ANALYSES OF 3-DIMENSIONAL FULLY PLASTIC SOLUTIONS USING QUASI-NONSTEADY ALGORITHM AND TETRAHEDRAL ELEMENTS

To estimate entire elastic-plastic behaviors of cracked bodies, fully plastic solutions are utilized with linear elastic solutions in the en gineering approach. Some numerical algorithms such as the Selective Re duced Integration/Penalty Function (SRI/PF) method have been developed and utlized to calculate various two-dimensional fully plastic soluti ons. However, only a few three-dimensional solutions have been obtaine d because of their numerical instability caused by the interaction amo ng crack-tip singularity, material nonlinearity and incompressibility. This paper describes a new finite element algorithm for three-dimensi onal fully plastic solutions. The algorithm is basically classified in to the mixed formulations. By introducing an artificial viscosity term to the governing equations, static crack problems are converted into quasi-nonsteady ones, which are solved using the fractional step metho d. The conversion makes the algorithm stable even in the analyses of c omplex crack geometries though it would need a number of iterations. i n the analyses, mixed interpolation tetrahedral elements are also empl oyed from a viewpoint of high quality mesh generation for three-dimens ional cracked geometries. Numerical accuracy of the present algorithm is clearly demonstrated through the analyses of the three-dimensional fully plastic solutions of center cracked plates.