Integrated optimal design of structures under multiple loads for topology and shape using genetic algorithm

Purpose - The structural design problem can be viewed as an iterative design loop with each iteration involving two stages for topology and shape designs with genetic algorithm (GA) as the optimization tool for both. Design/methodology/approach - The topology optimization problem, which is ill posed, is regularized using a constraint on perimeter and solved using GA. The problem is formulated as one of compliance minimization subject to volume constraint for the single loading case. A dual formulation Of this has been used for the multiple loading cases resulting in as many behavioral constraints as there are loading cases. The tentative topology given by the topology optimization module is taken and the domain boundary is approximated using straight lines, B-splines and cubic spline curves and design variables are selected among the boundary defining points. Optimum boundary shape of the problem has been obtained using GA in two different ways: without stress constraints; and with stress constraints. Findings - The proposed two stage strategy has been tested on benchmark structural optimization problems and its performance is found to be extremely good. Practical implications - The strategy appears to be eminently suitable for implementation in a general purpose FE software as an add-on module for structural design optimization. Originality/value - It has been observed that the integrated topology and shape design method is robust and easy to implement in comparison with other techniques. The computing time requirements for the GA does not appear daunting in the present scenario of high performance parallel computing and improved GA techniques.