Discontinuous Galerkin approximations for near-incompressible and near-inextensible transversely isotropic bodies
Discontinuous Galerkin approximations for near-incompressible and near-inextensible transversely isotropic bodies
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近不可压缩和近不可扩展横观各向同性体的不连续伽辽金近似
DOI：
10.1016/j.camwa.2019.04.016
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
B. Reddy
中科院分区：
文献类型：
--
作者：
B. J. Grieshaber;F. Rasolofoson;B. Reddy
本文研究了均匀横观各向同性线弹性体边值问题的间断Galerkin（DG）近似。采用三角形上的低阶近似，使用三种内部惩罚DG方法，即非对称，对称和不完全。对于各向同性情形，这些方法在不可压缩极限下是一致收敛的。这项工作的重点是行为的横向各向同性的不可扩展的限制。一个错误的估计表明的可能性，拉伸锁定，数值实验证实的功能。作为一种补救措施，下集成的延伸边缘条款。这种修改导致的误差估计是一致的锁定自由的行为。数值试验证实了一致收敛的行为，在一个最佳的速度，下集成计划。
This work studies discontinuous Galerkin (DG) approximations of the boundary value problem for homogeneous transversely isotropic linear elastic bodies. Low-order approximations on triangles are adopted, with the use of three interior penalty DG methods, viz. nonsymmetric, symmetric and incomplete. It is known that these methods are uniformly convergent in the incompressible limit for the isotropic case. This work focuses on behaviour in the inextensible limit for transverse isotropy. An error estimate suggests the possibility of extensional locking, a feature that is confirmed by numerical experiments. Under-integration of the extensional edge terms is proposed as a remedy. This modification is shown to lead to an error estimate that is consistent with locking-free behaviour. Numerical tests confirm the uniformly convergent behaviour, at an optimal rate, of the under-integrated scheme.