A low-order mimetic finite difference (MFD) method for Reissner-Mindlin plate problems is considered. Together with the source problem, the free vibration and the buckling problems are investigated. Details about the scheme implementation are provided, and the numerical results on several different types of meshes are reported.

In this paper, we study the Weissman-Taylor rectangular element for the Reissner-Mindlin plate [12] model and provide a convergence analysis for the transverse displacement and the rotation. We show that the element is stable and locking free, thereby improve the results of [8] and [9].

Finite element methods for the Reissner–Mindlin plate theory are discussed. Methods in which both the tranverse displacement and the rotation are approximated by finite elements of low degree mostly suffer from locking. However a number of related methods have been devised recently which avoid locking effects. Although the finite element spaces for both the rotation and transverse displacement ...

Abstract. In this paper, we derive and analyze a Reissner–Mindlin–like model for isotropic heterogeneous linearly elastic plates. The modeling procedure is based on a Hellinger– Reissner principle, which we modify to derive consistent models. Due to the material heterogeneity, the classical polynomial profiles for the plate shear stress are replaced by more sophisticated choices, that are asymp...

In this article, the Second Strain Gradient (SSG) theory proposed by Mindlin is used within a Wave Finite Element Method (WFEM) framework for dynamic analysis of one-dimensional Euler–Bernoulli bending beam and torsional bar. Firstly, strong forms continuum models including governing equations boundary conditions torsion cases, respectively, are derived using Hamilton’s principle. New “non-loca...

The mixed method for the biharmonic problem introduced in [12] is extended to the Reissner-Mindlin plate model. The Reissner-Mindlin problem is written as a system of first order equations and all the resulting variables are approximated. However, the hybrid form of the method allows one to eliminate all the variables and have a final system only involving the Lagrange multipliers that approxim...

Free vibration and buckling of three-phase bidirectional functionally graded sandwich (BFGSW) plates are studied in this paper for the first time by using an efficient nine-node quadrilateral (Q9) element. The core is pure ceramic, while two skin layers a material. element derived on basis Mindlin plate theory linked interpolations. Fundamental frequencies loads computed with various boundary c...

A novel approach for solving the stiffened shell structures by using an edge-based smoothed MITC3 finite element method (ES-MITC3) is presented in this paper. The ES-MITC3 efficient combining (ES-FEM) with original triangular to not only significantly improve accuracy but also overcome shear-locking phenomenon Reissner–Mindlin analysis. In study, applied and then reinforced stiffeners based on ...

An ordinary state-based peridynamic (PD) model based on the Mindlin plate theory is presented to deal with fracture mechanics problems. Static and dynamic stress resultant intensity factors regarded as primary parameters for structures are evaluated by displacement extrapolation method. Owing PD surface effect, however, accuracy of field near crack surfaces significantly affected. Therefore, ar...