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Shape sensitivity analysis in linear elastic fracture mechanics

机译：线性弹性断裂力学中的形状敏感性分析

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摘要

Shape sensitivity analysis of an elastic solid in equilibrium with a known load system applied over its boundary is presented in this work. The domain and boundary integral expressions of the first- and second-order shape derivatives of the total potential energy are established, by using an arbitrary change of the domain characterized by a velocity field defined over the initial body configuration. In these expressions we recognize free divergence tensors that are denoted in this paper as energy shape change tensors. Next, shape sensitivity analysis is applied to cracked bodies. For that purpose, a suitable velocity distribution field is adopted to simulate the crack advance of a unit length in a two-dimensional body. Finally, the corresponding domain and the equivalent path-independent integral expressions of the first- and second-order potential energy release rate of fracture mechanics are also derived.
机译：这项工作提出了一种弹性固体的形状敏感性分析，该弹性固体具有在其边界上施加已知载荷系统的平衡状态。通过使用以初始体形上定义的速度场为特征的域的任意变化，可以建立总势能的一阶和二阶形状导数的域和边界积分表达式。在这些表达式中，我们认识到在本文中表示为能量形状变化张量的自由散度张量。接下来，将形状敏感性分析应用于裂纹体。为此，采用合适的速度分布场来模拟二维体内单位长度的裂纹扩展。最后，还推导了断裂力学的一阶和二阶势能释放速率的对应域和等效于路径的积分表达式。

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