A Uniformly Accurate Finite Element Method for the Reissner–Mindlin Plate

1989 ◽  
Vol 26 (6) ◽  
pp. 1276-1290 ◽  
Author(s):  
Douglas N. Arnold ◽  
Richard S. Falk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mindlin Plate ◽  
Element Method

Coupled Analysis of Structural–Acoustic Problems Using the Cell-Based Smoothed Three-Node Mindlin Plate Element

2016 ◽  
Vol 13 (02) ◽  
pp. 1640007 ◽  
Author(s):  
Z. X. Gong ◽  
Y. B. Chai ◽  
W. Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Solid Mechanics ◽  
Mindlin Plate ◽  
Coupled Analysis ◽  
Plate Element ◽  
Fem Model ◽  
The Face ◽  
Smoothed Finite Element Method ◽  
Element Method

The cell-based smoothed finite element method (CS-FEM) using the original three-node Mindlin plate element (MIN3) has recently established competitive advantages for analysis of solid mechanics problems. The three-node configuration of the MIN3 is achieved from the initial, complete quadratic deflection via ‘continuous’ shear edge constraints. In this paper, the proposed CS-FEM-MIN3 is firstly combined with the face-based smoothed finite element method (FS-FEM) to extend the range of application to analyze acoustic fluid–structure interaction problems. As both the CS-FEM and FS-FEM are based on the linear equations, the coupled method is only effective for linear problems. The cell-based smoothed operations are implemented over the two-dimensional (2D) structure domain discretized by triangular elements, while the face-based operations are implemented over the three-dimensional (3D) fluid domain discretized by tetrahedral elements. The gradient smoothing technique can properly soften the stiffness which is overly stiff in the standard FEM model. As a result, the solution accuracy of the coupled system can be significantly improved. Several superior properties of the coupled CS-FEM-MIN3/FS-FEM model are illustrated through a number of numerical examples.

AN OPTIMAL LOW-ORDER LOCKING-FREE FINITE ELEMENT METHOD FOR REISSNER–MINDLIN PLATES

1998 ◽  
Vol 08 (03) ◽  
pp. 407-430 ◽  
Author(s):  
D. CHAPELLE ◽  
R. STENBERG
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Convergence Rates ◽  
A Priori ◽  
Mindlin Plate ◽  
Plate Model ◽  
Simple Modification ◽  
Optimal Convergence Rates ◽  
Priori Error Estimates ◽  
Element Method

We propose a simple modification of a recently introduced locking-free finite element method for the Reissner–Mindlin plate model. By this modification, we are able to obtain optimal convergence rates on numerical benchmarks. These results are substantiated by a complete mathematical analysis which provides optimal a priori error estimates.

scholarly journals About the edge-based smoothed finite element method for the Reissner-Mindlin plate-bending problem

2009 ◽  
Vol 31 (2) ◽  
pp. 75-86
Author(s):  
Nguyen Xuan Hung ◽  
Nguyen Thoi Trung
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mindlin Plate ◽  
Stiffness Matrices ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
Discrete Shear Gap ◽  
Transverse Shear Locking ◽  
Element Method

The paper further develops the edge-based smoothed finite element method (ES-FEM) for analysis of Reissner-Mindlin plates using triangular meshes. The bending and shearing stiffness matrices are obtained using strain smoothing technique over the smoothing domains associated with edges of elements. Transverse shear locking can be avoided with help of the discrete shear gap (DSG) method. The numerical examples show that the present ES-FEM-DSG method obtains very accurate results compared to the exact solution and other existing elements.

scholarly journals A Stochastic Wavelet Finite Element Method for 1D and 2D Structures Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Xingwu Zhang ◽  
Xuefeng Chen ◽  
Zhibo Yang ◽  
Bing Li ◽  
Zhengjia He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Polynomial Interpolation ◽  
Virtual Work ◽  
Structural Response ◽  
Mindlin Plate ◽  
Stochastic Finite Element ◽  
Wavelet Finite Element Method ◽  
Rigid Frame ◽  
Element Method

A stochastic finite element method based on B-spline wavelet on the interval (BSWI-SFEM) is presented for static analysis of 1D and 2D structures in this paper. Instead of conventional polynomial interpolation, the scaling functions of BSWI are employed to construct the displacement field. By means of virtual work principle and BSWI, the wavelet finite elements of beam, plate, and plane rigid frame are obtained. Combining the Monte Carlo method and the constructed BSWI elements together, the BSWI-SFEM is formulated. The constructed BSWI-SFEM can deal with the problems of structural response uncertainty caused by the variability of the material properties, static load amplitudes, and so on. Taking the widely used Timoshenko beam, the Mindlin plate, and the plane rigid frame as examples, numerical results have demonstrated that the proposed method can give a higher accuracy and a better constringency than the conventional stochastic finite element methods.

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