Two-Point Piecewise Adaptive Approximation for Structural Optimization

This study proposes a new two-point approximation method called two-point piecewise adaptive approximation (TPPAA) for structural optimization. For applying the mathematical optimization to structural design, several kinds of structural behavior, including stress, displacement and natural frequency, are represented as explicit functions of design variables by approximation technique. The optimum design can be found with sequential sub-problems solved, which is known as sequential approximate optimization (SAO). To ensure the approximation quality, structural behavior is approximated with considering the monotonicity. Monotonic functions are available in TPPAA when the first order derivatives of two successive design points have the same signs since many kinds of structural behavior vary quasi-monotonically with respect to design variables. Non-monotonic form can also be obtained when the two derivatives of two successive design points have different signs. TPPAA adopts the piecewise approximate functions to avoid inappropriate approximation that existing approximation schemes would encounter. In this study, a program integrating ANSYS, AutoCAD and Microsoft Visual C++ is developed for automated structural optimization. The practicability of TPPAA is examined in several structural optimization problems and the comparison of several approximation methods are also presented. Furthermore, TPPAA is applied to optimum design of large structures, such as effective FE model construction of PCB and design of high-accuracy measuring stage structure.