Preasymptotic Performance of Modified Mixed Finite Element Schemes for Plates

Abstract

This paper is devoted to numerical investigations on shear-locking free finite element methods for Reißner-Mindlin plates recently introduced in mathematical literature. We verify and improve theoretically predicted convergence rates and provide a technique to handle preasymptotic instabilities. The approximation of stress resultants is monitored by benchmark computation. Moreover we give experimental evidence that a new adaptive automatic mesh-refining algorithm yield superior approximations. Summarizing our comprehensive numerical studies by some typical examples we deduce recommendations for employing the modified mixed finite element schemes in engineering practice.