断裂力学中势能的形状导数与能量释放率
Shape derivative of potential energy and energy release rate in fracture mechanics
摘要：
我们研究了势能随磁畴形变变化的一般数学框架。它使裂纹问题中能量释放率的积分公式的严格推导。应用形状灵敏度分析技术，将势能的形状导数表示为一个带参数的变分问题。我们的抽象理论的关键工具是一个新的参数变分原理和经典的巴拿赫空间中的隐函数定理。
英文摘要：
We study general mathematical framework for variation of potential energy with respect to domain deformation. It enables rigorous derivation of the integral formulas for the energy release rate in crack problems. Applying a technique of the shape sensitivity analysis, we formulate the shape derivative of potential energy as a variational problem with a parameter. Key tools of our abstract theory are a new parameter variational principle and the classical implicit function theorem in Banach spaces.
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