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arXiv · 1502.06065

Hybrid stress quadrilateral finite element approximation for stochastic plane elasticity equations

Xiaojing Xu·Wenwen Fan·Xiaoping Xie
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Abstract

This paper considers stochastic hybrid stress quadrilateral finite element analysis of plane elasticity equations with stochastic Young's modulus and stochastic loads. Firstly, we apply Karhunen-Lo$\grave{e}$ve expansion to stochastic Young's modulus and stochastic loads so as to turn the original problem into a system containing a finite number of deterministic parameters. Then we deal with the stochastic field and the space field by $k-$version/$p-$version finite element methods and a hybrid stress quadrilateral finite element method, respectively. We show that the derived a priori error estimates are uniform with respect to the Lam$\acute{e}$ constant $\lambda\in (0, +\infty)$. Finally, we provide some numerical results.

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Xiaojing Xu, Wenwen Fan, Xiaoping Xie. 2015-02-21. Hybrid stress quadrilateral finite element approximation for stochastic plane elasticity equations. https://arxiv.org/abs/1502.06065

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