Assumed stress quasi-conforming technique for static and free vibration analysis of Reissner-Mindlin plates

Abstract

This paper presents a novel formulation based on Hellinger-Reissner variational principle in the framework of quasi-conforming method for static and free vibration analysis of Reissner-Mindlin plates. The formulation starts from polynomial approximation of stresses, which satisfy the equilibrium equations of Reissner-Mindlin plate theory. Then the stress matrix is treated as the weighted function to weaken the straindisplacement equations after the strains are derived by using the constitutive equations. Finally, the string-net functions are introduced to calculate strain integration. As examples, two new plate bending elements, a 4-node quadrilateral element QC-P4-11 and a 3-node triangular element QC-P3-7 , are proposed. Several benchmark examples are demonstrated to show the performance of the elements, and the results obtained are compared with other available ones. Numerical results have proved that both elements possess excellent precision. In particular, the quadrilateral element performs well even when the element shape degenerates into a triangle or concave quadrangle. integration [19,20] and selective integration techniques [21,22]. Unfortunately, these elements are still subjected to some other drawbacks, such as instability for rank deficiency, zero energy modes, or severe accuracy loss on the occasion of mesh distortions. To yield a much higher accuracy and stability of numerical methods, many new formulations, such as the assumed natural strain (ANS) method [23][24][25], the mixed shear projected approach [26,27], and the discrete shear gap (DSG) method [28] have been developed. Other models, including the improved shear strain interpolations approaches derived from Timoshenko's beam function [29,30], the enhanced assumed strain methods [31,32], the mixed interpolated tensorial components (MITC) technique [33][34][35][36] and its extension [37,38] have also been introduced for the linear and nonlinear analysis of plates and shells.To further advance finite element technologies, Chen and Cheung [39-41] developed a series of triangular and quadrilateral plate/shell elements based on the refined non-conforming element method. In their work, the exact displacement function of the Timoshenko's beam is used to derive the element displacements. Numerical examples demonstrated the proposed model is not only free from shear locking but also indeed possesses higher accuracy for both thin and thick plates. The smoothed finite element methods (S-FEM) based on strain smoothing technique [42], including the cell-based S-FEM (CS-FEM) [43], the node-based S-FEM (NS-FEM) [44], the edge-based S-FEM (ES-FEM) [45], were first introduced by Liu et al. [46] into the analysis of plate and shell structures [47]. Cen et al. [48-50] proposed a hybrid displacement function method based on Reissner -Mindlin plate theory, in which the displacement function [51] satisfying all governing equations are used to derive displacement components.Numerical examples had proved that the element models presented in their works perform well...

A novel displacement-based Trefftz plate element with high distortion tolerance for orthotropic thick plates

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A Refined Higher-Order Hybrid Stress Quadrilateral Element for Free Vibration and Buckling Analyses of Reissner-Mindlin Plates

“…After q is determined, element stress or internal forces can be recovered by use of (18) and (11). Thus…”

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4‐node unsymmetric quadrilateral membrane element with drilling DOFs insensitive to severe mesh‐distortion

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