SEQUENTIAL LINEAR PROGRAMMING ALGORITHM BASED ON THE SAND FORMULA FOR TRUSS OPTIMIZATION

In this paper, a SLP (Sequential linear Programming) algorithm based on SAND (Simultaneous Analysis and Design) formula is proposed. It is different from the traditional practice of a linear expansion of implicit response functions (e.g. displacement, stress etc.) at the designed variable (e.g. cross sectional area of bar members). Taking a truss structure as an example, using SAND formula, with both bar cross sectional areas and node displacements as the design variables, a linear approximation to the compatibility conditions using explicit bilinear function is made and an LP sub-problem is constructed. By solving a series of LP sub-problems, a best approximat solution for this optimization problem can be obtained. Comparing to the SLP algorithm under traditional optimization formula, this method has 2 advantages: The choice of the move limit of the designed variable is easier; the error involved in the linear approximation can be accurately estimated. Worked examples demonstrate that this algorithm is able to obtain the approximate optimized solution to the optimization problem in a fast yet stable manner.