Nguyen, Vu Thua (1999) Finite element simulation of Durelli's photoelastic stress minimization method for shape optimization. Research Master thesis, Victoria University of Technology.

Abstract

Finite Element Method (FEM) was used to simulate the Photoelastic Stress Minimization (PSM) method developed by Durelli to solve the problem of finding the optimal stress raiser profiles in isotropic and advanced composite structures. In Durelli's method, material in lowly stressed regions of the design domain is removed so as to make the sections of the discontinuity boundary become isochromatics of the same Tresca stress. The process of material removal was simulated by iterative deleting of elements lying on the stress raiser boundary, followed by smoothing and remeshing subroutines. The criterion proposed for element "removal" was to select only a number of elements having lower stresses among those that are in the design domain and on the current boundary. This number was set by a removal rate and controlled to get smaller as the optimization proceeds. The process was terminated when the stress distribution on the boundary became uniform or the number of elements to be removed reached the predefined minimum value. It was shown that the proposed FEM simulation could be applied to solve various stress minimization problems involving isotropic materials. Investigations of the effects of parameters controlling the optimization process on the convergence and the final results were carried out. By taking into account the existence of isotropic points stress, which could lead to the divergence from the optimal profile, the proposed FEM simulation proved to be capable of handling more general classes of stress minimization problems. The FEM simulation was further extended to search for optimal stress raiser profiles for structures made of advanced composite materials.

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