Optimal design of structural support positions for minimizing maximal bending moment

The design of the structural supports has always been practically important in engineering applications. In addition to holding a structure properly, supports can also be utilized to improve the structural performances. For this purpose, this paper presents an appropriate optimization scheme of minimization of the maximal absolute bending moment in a planar frame by means of the optimal design of the support positions. First, the sensitivity analysis of the bending moment is investigated with regard to the movement of a simple support position by using the adjoint variable method. In this procedure, both elastic and rigid supports are taken into account, and a closed-form expression for the moment derivative is generated. Next, on the basis of the design sensitivity, a heuristic optimization algorithm, called the evolutionary shift method, is applied to minimize the maximal bending moment under multiple load cases. At each design iteration, the support with the highest sensitivity is shifted in priority. As a consequence, the optimal solution is achieved gradually. Finally, three numerical examples are given to demonstrate the validity of the design sensitivity analysis and the capability of the proposed optimization procedure for solving the maximal-moment minimization problem. Results show that support position optimization can reduce the maximal moment significantly, and deserves more investigation.