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Structural Engineering and Mechanics Volume 55, Number 6, September25 2015 , pages 1157-1176 DOI: https://doi.org/10.12989/sem.2015.55.6.1157 |
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Optimizing structural topology patterns using regularization of Heaviside function |
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Dongkyu Lee and Soomi Shin
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| Abstract | ||
| 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 | ||
| Address | ||
| 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 | ||