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doi:10.1016/S0045-7825(02)00308-0 
Copyright © 2002 Elsevier Science B.V. All rights reserved.
Elasto-plastic analysis of shells with the triangular element TRIC
Received 22 September 2001;
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Abstract
TRIC is a simple but sophisticated three-node shear-deformable isotropic and composite facet shell element suitable for large-scale linear and nonlinear engineering computations of thin and moderately thick anisotropic plate and complex shell structures. In the present work an elasto-plastic constitutive model based on the von Mises yield criterion with isotropic hardening is incorporated into the element. The characteristic feature of this formulation is that the nonlinear material behaviour is taken into account entirely in the natural system of the element. This is achieved by transforming quantities such as equivalent plastic strain, equivalent stress, the expression of the yield surface and the components of flow vector from the material coordinate system to the natural coordinate system. These transformations lead to simple and elegant expressions for the respective quantities in the natural system which eventually result to an efficient and cost effective treatment of the nonlinear analysis of arbitrary shells including material and geometrical nonlinearities.
Author Keywords: Natural mode method; Elasto-plastic shells; Von Mises yield criterion
Subject-index terms: 28; 59; 65
Article Outline
- 1. Introduction
- 2. The TRIC shell element
- 2.1. Kinematics of the element
- 2.2. Natural modes and generalized forces and moments
- 2.3. Axial and symmetric bending stiffness terms
- 2.4. The geometric stiffness
- 3. Elasto-plastic material behaviour
- 3.1. The continuum elasto-plastic constitutive matrix
- 3.2. Equivalent natural yield stress
- 3.3. Natural flow vector
- 3.4. Return mapping algorithm
- 3.5. Consistent constitutive matrix formulation
- 3.6. The tangential stiffness matrix
- 4. Numerical examples
- 4.1. Scordelis–Lo roof under gravity load
- 4.2. Cylindrical panel under point load
- 4.3. Pinched short cylinder
- 4.4. Pinched hemispherical shell
- 5. Conclusions
- References
