Recovery of strong equilibrium from displacement-based finite element models of Reissner-Mindlin plates

2018 ◽  
Vol 114 (4) ◽  
pp. 375-398 ◽  
Author(s):  
E. A. W. Maunder ◽  
J. P. Moitinho de Almeida
Keyword(s):  
Finite Element ◽  
Finite Element Models ◽  
Strong Equilibrium ◽  
Displacement Based

scholarly journals Finite elements for problems of the elasticity theory with the discontinuous stress approximation

2020 ◽  
Vol 224 ◽  
pp. 02012
Author(s):  
A Lukashevich ◽  
N Lukashevich ◽  
E Kobelev
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Approximation Schemes ◽  
Stress Fields ◽  
Penalty Function Method ◽  
Finite Element Models ◽  
Equilibrium Equations ◽  
Additional Energy ◽  
Calculation Results ◽  
Displacement Based

The paper deals with the development of the finite element models on the basis of stress approximation. At present, the displacementbased finite element method is mainly used for engineering calculations. Finite element formulations in stresses are not so widely spread, but in some cases these formulations can be more effective in particular with respect to the calculating stresses and also obtaining a two-sided estimate of the exact solution of the problem. The finite element models based on the approximation of discontinuous stress fields and the use of the penalty function method to satisfy the equilibrium equations are considered. It is shown that the continuity of both normal and tangential stresses only on the adjacent sides of the finite elements contributes to the expansion of the class of statically admissible stress fields. At the same time, the consistent approximation is provided, both of the main part of the functional of additional energy, and its penalty part. The necessary matrix relations for rectangular and triangular finite elements are obtained. The effectiveness of the developed models is illustrated by numerical studies. The calculation results were compared with the solution on the FEM in displacements, as well as with the results obtained using other schemes of approximating the stresses in the finite element. It is shown that the model of discontinuous stress approximations gives the bottom convergence of the solution, both in stresses and in displacements. At the same time, the accuracy on the stresses here is much higher than in the displacement-based FEM or when using conventional stress approximation schemes.

NONCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS

2011 ◽  
Vol 08 (03) ◽  
pp. 349-368 ◽  
Author(s):  
WOORAM KIM ◽  
J. N. REDDY
Keyword(s):  
Finite Element ◽  
Mixed Models ◽  
Mixed Model ◽  
Mixed Finite Element ◽  
Beam Theory ◽  
Finite Element Models ◽  
Various Boundary Conditions ◽  
Beam Bending ◽  
Displacement Based ◽  
Euler Bernoulli Beam

In this study, mixed finite element models of beam bending are developed to include the membrane forces and shear forces in addition to the bending moments and displacements. Mixed finite element models were developed based on the weighted residual statements of governing equations. The Euler–Bernoulli beam theory (EBT) and the Timoshenko beam theory (TBT) are used. The effectiveness of the new mixed models is evaluated in light of other mixed models to show the advantages. Each newly developed model is examined and compared with other models to verify its performance under various boundary conditions. In the linear analysis, solutions are compared with available analytical solutions and solutions of existing models. In the nonlinear case, direct and Newton–Raphson methods are used to solve the nonlinear equations. The converged solutions are compared with available solutions of the displacement models. Post-processed data of the mixed model developed herein shows better accuracy than the conventional displacement-based model.

A Finite Element Analysis of the General Rolling Contact Problem for a Viscoelastic Rubber Cylinder

1988 ◽  
Vol 16 (1) ◽  
pp. 18-43 ◽  
Author(s):  
J. T. Oden ◽  
T. L. Lin ◽  
J. M. Bass
Keyword(s):  
Finite Element ◽  
Variational Principles ◽  
Standing Waves ◽  
Rolling Contact ◽  
Finite Element Models ◽  
Viscoelastic Cylinder ◽  
Element Analysis ◽  
Elastic Rubber ◽  
Frictional Effects ◽  
Rough Foundation

Abstract Mathematical models of finite deformation of a rolling viscoelastic cylinder in contact with a rough foundation are developed in preparation for a general model for rolling tires. Variational principles and finite element models are derived. Numerical results are obtained for a variety of cases, including that of a pure elastic rubber cylinder, a viscoelastic cylinder, the development of standing waves, and frictional effects.

Affordable structural optimization for large-size dynamic finite element models

1997 ◽  
Author(s):  
Francois Hemez ◽  
Emmanuel Pagnacco ◽  
Francois Hemez ◽  
Emmanuel Pagnacco
Keyword(s):  
Finite Element ◽  
Structural Optimization ◽  
Finite Element Models ◽  
Dynamic Finite Element ◽  
Large Size
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