Shape optimization with the biological growth method: a parameter study

Abstract

Studies the effect of parameters controlling the biological growth method by applying it to the classical optimization problem of a plate with a central hole under biaxial stress state. It has been found that the optimization character of the method depends strongly on the so‐called reference stress. Depending on the magnitude of this parameter either a local or global optimum is approached. A global optimum corresponds to the minimum possible v. Mises stress along the hole boundary (and hence in the plate), whereas a local optimum presents the modified shape of the hole yielding an uniform stress distribution whose magnitude is larger than the minimum possible value and which is equal to the specified reference stress. The magnification factor applied to the iterative displacement results influences the optimization speed. Too large factors lead to divergence of the solution. Furthermore, it has been found that the dimension of the optimization domain has a critical effect on the optimization result.

Citation

Erman Tekkaya, A. and Güneri, A. (1996), "Shape optimization with the biological growth method: a parameter study", Engineering Computations, Vol. 13 No. 8, pp. 4-18. https://doi.org/10.1108/02644409610152989