NONLINEAR EXIST-NULL COMBINED BODIES METHOD FOR FRAME TOPOLOGICAL OPTIMIZATION WITH DISPLACEMENTS CONSTRAINTS

A nonlinear exist-null combined body is proposed to raise the efficiency of the searching optimum solution of structural topology optimization based on a physical model. As an example of topology optimization for a frame structure, a mathematical model for the minimization of structural weight is implemented to realize in procedure coding. In different with the linear exist-null combined body, the nonlinear one is a combination with infinite numbers of infinitesimal exist cells and nulls cells according to their nonlinear lengths. Owing to invariance property in sum of lengths between exist cells and nulls cells for each beam element, its topological variable can be expressed by total lengths of its exist cells. Structural weight and displacements constraints are deduced to build an optimization model. The model is solved by the algorithm of the linear programming to show the increasing efficiency of an optimizing point. The comparison of ICM (Independent, Continuous and Mapping) as a mathematical transformation method, the physical model presented has also different approaches but equally satisfactory results. A nonlinear relationship in length of the latter replaces the filter functions of element weight and displacements constraints of the former. Similarities and differences between the mathematical transformation method and the physical model method are an interesting problem affording for thought.