Optimum design of plate structures using three-point approximation

Abstract

Efficient optimum design of plate structures is achieved with stress, displacement and frequency constraints. To reduce the computational cost of optimum design, attempts have been made to reduce the number of static and dynamic analyses required in the process. To achieve this goal, all the quantities that are the output of analysis are approximated. By substituting these approximate functions into the original design problem, an approximate problem is obtained which can be solved by numerical optimization techniques efficiently. This is one cycle which does not require the analysis of the structure. The resulting solution is used as a starting design point for the next iteration. This process is repeated until the problem converges. The efficiency of the method is based on the creation of high quality approximation of the functions under consideration and thus reducing the number of iterations. A three-point approximation is developed to approximate the forces and the Rayleigh quotient. Numerical examples are offered and the results are compared with previous published work.