Abstract

This paper presents a general and reliable shape optimization scheme for snap-through structures to match a target load-deflection curve. The simulation of the snap-through structures typically requires the Arc Length Control (ALC) method. The adaptive stepping in ALC creates unavoidable discontinuities in the objective function. A discontinuous objective function is often handled by zero-order methods. However, we opt to solve the optimization problems using gradient-only optimization. Numerical examples demonstrate that function value based methods can misinterpret discontinuities as minima and terminate prematurely. In contrast, gradient-only algorithms are demonstrated to be insensitive to numerical discontinuities, and locate the correct solutions reliably.

摘要

本文提出了一种用于快速结构的通用且可靠的形状优化方案，以匹配目标载荷-挠度曲线。快速结构的模拟通常需要弧长控制 (ALC) 方法。ALC 中的自适应步进会在目标函数中产生不可避免的不连续性。不连续的目标函数通常由零阶方法处理。但是，我们选择使用仅梯度优化来解决优化问题。数值示例表明，基于函数值的方法可能会将不连续性误解为最小值并过早终止。相比之下，仅梯度算法被证明对数值不连续性不敏感，并且可以可靠地找到正确的解决方案。