Hybrid stress quadrilateral finite element approximation for stochastic plane elasticity equations
For researchers in computational stochastic mechanics, this work provides a novel finite element framework that handles incompressibility limits robustly, though it is an incremental extension of existing hybrid stress methods to stochastic settings.
This paper develops a hybrid stress quadrilateral finite element method for stochastic plane elasticity equations, achieving uniform a priori error estimates with respect to the Lamé constant λ ∈ (0, +∞). Numerical results validate the approach.
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 $λ\in (0, +\infty)$. Finally, we provide some numerical results.