Earticle

This study shows a variance regularization method in order to obtain the stable optimal solutions, when a numerical method accelerating design variables is used for material topology optimization algorithm. Since a moved and regularized Heaviside function used in the accelerated method is composed of nonlinear concave and convex functions in a given design domain between 0 and 1, design variables below 0.5 can move fast toward the value of 0 and those over 0.5 are rapidly located to the value of 1. However optimal solutions may be not stable due to singularity of element stiffness, while the accelerated design variables are too closed to value 0. In particular this instability may occur to the accelerated method-based material topology optimization algorithms much repeating the moved and regularized Heaviside function. In order to resolve the problem, in this study, a variance regularization is formulated within a linear governing equation for structural analyses of optimization procedures. Numerical examples for topologically optimally modeling a linear elastostatic MBB-beam verify that the accelerated method of design variables take numerical stability of topological optimal solutions by being associated with the variance regularization method.