Existence and Convergence Results for an Elastic Frictional Contact Problem with Nonmonotone Subdifferential Boundary Conditions
Existence and Convergence Results for an Elastic Frictional Contact Problem with Nonmonotone Subdifferential Boundary Conditions
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DOI：
10.1007/s10473-021-0409-5
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发表时间：
2021-06
影响因子：
1
通讯作者：
Yongjian Liu;S. Migórski;V. T. Nguyen;Shengda Zeng
中科院分区：
文献类型：
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作者：
Yongjian Liu;S. Migórski;V. T. Nguyen;Shengda Zeng
本文的目的是研究弹性力学中的非线性静摩擦接触问题的数学模型，其混合边界条件由Signorini单边无摩擦接触条件、非单调多值接触和次微分形式的摩擦定律的组合描述。首先，在适当的假设下，我们给出了接触模型的弱形式，这是一个椭圆型系统的拉格朗日乘子，其中包括一个半变分不等式和变分不等式。然后证明了接触问题的可解性。最后，利用非线性弹性张量H-收敛的概念，给出了在弹性算子、体力和表面力扰动下解的收敛性结果。
The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral frictionless contact condition, and nonmonotone multivalued contact, and friction laws of subdifferential form. First, under suitable assumptions, we deliver the weak formulation of the contact model, which is an elliptic system with Lagrange multipliers, and which consists of a hemivariational inequality and a variational inequality. Then, we prove the solvability of the contact problem. Finally, employing the notion ofH-convergence of nonlinear elasticity tensors, we provide a result on the convergence of solutions under perturbations which appear in the elasticity operator, body forces, and surface tractions.