On junction problem with damage parameter for Timoshenko and rigid inclusions inside elastic body,ZAMM - Journal of Applied Mathematics and Mechanics

当前位置： X-MOL 学术 › ZAMM › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

On junction problem with damage parameter for Timoshenko and rigid inclusions inside elastic body
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-06-05 , DOI: 10.1002/zamm.202000063
A.M. Khludnev _{1,

2,

3} , T.S. Popova ₄

Affiliation

The paper is concerned with an equilibrium problem for 2D elastic body with a thin elastic Timoshenko inclusion and a thin rigid inclusion. The elastic inclusion is assumed to be delaminated from the elastic body thus forming an interfacial crack with the matrix. Inequality type boundary conditions are imposed at the crack faces to prevent a mutual penetration. A connection between two inclusions at a given point is characterized by a positive damage parameter. Existence of solutions of the problem considered is proved, and different equivalent formulations of the problem are analyzed; junction conditions at the connection point are found. A convergence of solutions as the damage parameter tends to zero and to infinity as well as the rigidity parameter of the elastic inclusion tends to infinity is analyzed. An analysis of the limit models is performed. A solution existence of an inverse problem for finding the damage and rigidity parameters is proved provided that an additional information concerning the derivative of the energy functional with respect to the delamination length is given.

中文翻译：

关于Timoshenko损伤参数与弹性体内刚性夹杂物的结合问题

本文涉及具有弹性蒂莫申科夹杂物和刚性夹杂物的二维弹性体的平衡问题。假定弹性夹杂物从弹性体上脱层，从而与基体形成界面裂纹。在裂纹面上施加不等式边界条件，以防止相互渗透。给定点上两个夹杂物之间的连接的特征是正损伤参数。证明了所考虑问题的解的存在，并分析了该问题的不同等价形式；找到连接点的结点条件。分析了损伤参数趋于零且趋于无穷大以及弹性夹杂物的刚度参数趋于无穷大的解的收敛性。进行极限模型分析。只要给出关于能量函数关于分层长度的导数的附加信息，就证明了找到损伤和刚度参数的反问题的解决方案存在。

更新日期：2020-06-05

点击分享查看原文

点击收藏

阅读更多本刊最新论文