Continuous finite element methods for Reissner-Mindlin plate problem. Issue 2 (March 2018)

• Record Type: Journal Article
• Authors: DUAN, Huoyuan; MA, Junhua
• Is Part Of: Acta mathematica scientia. Volume 38:Issue 2(2018)
• Page Start: 450
• Page End: 470
• Publication Date: 2018-03
• Subjects: Reissner-Mindlin plate -- continuous element -- triangle element -- quadrilateral element -- finite element method -- uniform convergence; 65N30; Mathematical physics -- Periodicals; 530.15
• DOI: 10.1016/S0252-9602(18)30760-4
• Languages: English
• ISSNs: 0252-9602

Abstract

Abstract: On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these methods, the transverse displacement is approximated by conforming (bi)linear macroelements or (bi)quadratic elements, and the rotation by conforming (bi)linear elements. The shear stress can be locally computed from transverse displacement and rotation. Uniform in plate thickness, optimal error bounds are obtained for the transverse displacement, rotation, and shear stress in their natural norms. Numerical results are presented to illustrate the theoretical results.