Quasi-Quadratic Method of Moving Asymptotes Approximation for Structural Optimization

This thesis presents a new approximation method for structural optimization called quasi-quadratic method of moving asymptotes approximation (QMMA), which is derived from method of moving asymptotes approximation (MMA). By adding a nonspherical second order term, the approximate function can be constructed with respect to the function value of current design point and sensitivities of two successive design points. With the use of this new approximation method, the structural behavior functions, such as stress, natural frequency or displacement functions, can be converted to explicit functions of design variables. Therefore, structural optimization problem can be solved efficiently by applying conventional optimization techniques. Moreover, a new computer program is developed by integrating CAD software, FEM analysis software and optimization theorem to solve structural optimization problems. The result indicates that the proposed approximation method can quickly find the convergence and accurate solutions for some typical structural optimization problems, and it also verified that this new method is practical and efficient in structural optimization.