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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Discontinuous Petrov-Galerkin method with optimal test functions for thin-body problems in solid mechanics
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Discontinuous Petrov-Galerkin method with optimal test functions for thin-body problems in solid mechanics

机译：具有最优测试功能的不连续Petrov-Galerkin方法用于固体力学中的薄体问题

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摘要

We study the applicability of the discontinuous Petrov-Calerkin (DPG) variational framework for thin-body problems in structural mechanics. Our numerical approach is based on discontinuous piecewise polynomial finite element spaces for the trial functions and approximate, local computation of the corresponding 'optimal' test functions. In the Timoshenko beam problem, the proposed method is shown to provide the best approximation in an energy-type norm which is equivalent to the i.2-norm for all the unknowns, uniformly with respect to the thickness parameter. The same formulation remains valid also for the asymptotic Euler-Bernoulli solution. As another one-dimensional model problem we consider the modelling of the so called basic edge effect in shell deformations. In particular, we derive a special norm for the test space which leads to a robust method in terms of the shell thickness. Finally, we demonstrate how a posteriori error estimator arising directly from the discontinuous variational framework can be utilized to generate an optimal /ip-mesh for resolving the boundary layer.
机译：我们研究结构力学中薄体问题的不连续Petrov-Calerkin（DPG）变分框架的适用性。我们的数值方法是基于不连续的分段多项式有限元空间的试验函数和相应的“最优”试验函数的近似局部计算。在Timoshenko光束问题中，所提出的方法显示出在能量类型范数中提供最佳近似值，对于所有未知数，该能量类型范数等效于i.2-范数，并且厚度参数一致。对于渐近的Euler-Bernoulli解，相同的公式仍然有效。作为另一个一维模型问题，我们考虑对壳变形中所谓的基本边缘效应进行建模。特别是，我们为测试空间导出了一个特殊的规范，这导致了在壳厚度方面可靠的方法。最后，我们演示了如何直接利用不连续变分框架产生的后验误差估计器来生成最优的/ ip-mesh来解决边界层。

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