Hybrid stress quadrilateral finite element approximation for stochastic plane elasticity equations

What is it about?

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 derive a priori error estimates which are uniform with respect to the Lam$\acute{e}$ constant $\lambda\in (0, +\infty)$. Finally, we provide some numerical results.

Featured Image