论文标题
形状衍生物，用于惩罚受限的非齿非孔孔维克斯优化：内聚裂纹问题
Shape Derivative for Penalty-Constrained Nonsmooth-Nonconvex Optimization: Cohesive Crack Problem
论文作者
论文摘要
研究了与变异不平等相关的惩罚约束（VI）的一类非平滑和非凸优化问题。出于准脆性断裂引起的特定问题描述了一个弹性体，在裂缝面上不渗透的不平等条件下，弹性裂纹具有内聚力的裂纹。基于Lagrange方法并使用Lavrentiev正则化的平滑惩罚，得出了形状导数的公式。显式公式既包含原始状态又包含伴随状态，并且对于找到梯度算法的下降方向很有用，可以从边界测量中识别最佳的裂纹形状。破坏性测试的数值示例以2D表示。
A class of non-smooth and non-convex optimization problems with penalty constraints linked to variational inequalities (VI) is studied with respect to its shape differentiability. The specific problem stemming from quasi-brittle fracture describes an elastic body with a Barenblatt cohesive crack under the inequality condition of non-penetration at the crack faces. Based on the Lagrange approach and using smooth penalization with the Lavrentiev regularization, a formula for the shape derivative is derived. The explicit formula contains both primal and adjoint states and is useful for finding descent directions for a gradient algorithm to identify an optimal crack shape from a boundary measurement. Numerical examples of destructive testing are presented in 2D.
