Abstract

Under consideration are the variational problems concerning the equilibrium of plates containing a crack. Two new mathematical models are proposed in which the nonpenetration conditions define the corresponding nonconvex sets of admissible functions. The first model describes the equilibrium of a Timoshenko plate with a crack, and the second corresponds to a composite plate containing a crack along a Kirchhoff–Love elastic inclusion. The proposed approach is substantiated by an explicit example. We prove the existence of solutions for the corresponding variational problems and show that the equilibrium equations are satisfied for each of the problems.

中文翻译：

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几何非线性非穿透条件的Timoshenko板垂直裂纹的平衡问题。

摘要

考虑中的是关于包含裂纹的板的平衡的变化问题。提出了两个新的数学模型，其中非渗透条件定义了相应的允许函数的非凸集。第一个模型描述了带有裂纹的Timoshenko板的平衡，第二个模型对应于沿着Kirchhoff-Love弹性夹杂物的包含裂纹的复合板。一个明确的例子证实了所提出的方法。我们证明了相应的变分问题解的存在，并表明每个问题都满足平衡方程。