Quasi-quadratic Two-point Exponential Approximation Method for Structural Optimization

This thesis presents a quasi-quadratic two-point exponential approximation method for structural optimization. Originally structural behaviors, such as stresses, displacements, natural frequencies, and dynamic responses, cannot be expressed by explicit functions of design variables. In order to save the computer time of the optimization process, these complex structural behaviors are approximated by explicit approximation functions in terms of design variables. The proposed two-point approximation method satisfies functional values and first-order sensitivity values at both the current point and the previous point. Through this kind of approximation, structural optimization problems can be solved easily by using the general numerical optimization method. A computer program was also developed by combining this approximation method and the finite element software ANSYS. With the developed program, several constrained structural optimization problems are investigated. The search results demonstrate that the proposed method is stable, reliable and produces fast and satisfactory convergent solutions for general structural optimization problems.