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Structural Engineering and Mechanics
  Volume 55, Number 6, September25 2015, pages 1157-1176

Optimizing structural topology patterns using regularization of Heaviside function
Dongkyu Lee and Soomi Shin

    This study presents optimizing structural topology patterns using regularization of Heaviside function. The present method needs not filtering process to typical SIMP method. Using the penalty formulation of the SIMP approach, a topology optimization problem is formulated in co-operation, i.e., couple-signals, with design variable values of discrete elements and a regularized Heaviside step function. The regularization of discontinuous material distributions is a key scheme in order to improve the numerical problems of material topology optimization with 0 (void)-1 (solid) solutions. The weak forms of an equilibrium equation are expressed using a coupled regularized Heaviside function to evaluate sensitivity analysis. Numerical results show that the incorporation of the regularized Heaviside function and the SIMP leads to convergent solutions. This method is tested using several examples of a linear elastostatic structure. It demonstrates that improved optimal solutions can be obtained without the additional use of sensitivity filtering to improve the discontinuous 0-1 solutions, which have generally been used in material topology optimization problems.
Key Words
    optimization; topology patterns; SIMP; filtering process, regularized Heaviside function
Dongkyu Lee, Department of Architectural Engineering, College of Engineering, Sejong University, 143-747, Seoul, Korea
Soomi Shin, Research Institute of Industrial Technology, Pusan National University, 609-735, Busan, Korea

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