论文部分内容阅读
A move limit strategy dedicated to the improvement of stability and convergence rate of the level set based structural optimization is investigated.Move limit strategy is widely used in optimization to restrict the allowable change of a design variable in each iterative step of optimization.The motivation of introducing a move limit strategy into the level set based structural optimization is twofold and is described as follows.First, the optimization algorithms used in the level set based method are usually based on the first order shape sensitivities, for instance the steepest descent method.The objective function and the constraint functions in the optimization are approximated by a linearization at the current design.However, a linear approximation of a nonlinear function is valid only in a small neighborhood.Therefore, it is desirable to define a neighborhood around the current value of design variable where the linear approximations are valid and accurate, and one should also make sure the design variable stay inside the neighborhood after it is updated.Second,in each iterative step of the level set based structural optimization, the free boundary of a structure (i.e., the design variable) moves according to the design velocity (i.e., the descent direction of optimization), but the design velocity is rarely uniform along the free boundary.In fact, it often happens that the design velocity at some local segments is several orders bigger than that of the rest.In such situation, most part of the free boundary will have very little movement when the optimization procedure advances in the descent direction with a moderate step size, as a result the optimization will be evidently slowed down.To enlarge the movement and speed up the convergence, one may advance in the descent direc tion with a big step size.However, this may make the convergence become oscillatory and slow again [6].Moreover, a proper step size generally changes during the optimization and is unknown unless a line-search is performed.But a line-search in structural optimization is computationally costly.In such situation, it is better to let the optimization ad vance in the descent direction with a big step size (i.e., more time for propagation) but subject to a move limit constraint.The benefit is explained as follows.First, because of the move limit, movement of the boundary segments where the design velocity is very big can be effectively constrained to an allowed extent, thus ensuring the stability of convergence.Second, because of the big step size, the movement of boundary segments where the design velocity is small can be made more evident, thus speeding up the convergence rate.In short, the move limit strategy is helpful to improve the stability and convergence rate of the level set based structural optimization.To realize the move limit strategy, a function for modifying the extended design velocity is proposed.Application of the move limit strategy is demonstrated by several numerical examples of 2D structures.