Curved p-version C1 finite elements for the finite deformation analysis of isotropic and composite laminated thin shells in irregular shape

2021 ◽  
Vol 259 ◽  
pp. 113459
Author(s):  
Yang Wu ◽  
Yufeng Xing ◽  
Bo Liu
Keyword(s):  
Finite Elements ◽  
Finite Deformation ◽  
Irregular Shape ◽  
Deformation Analysis ◽  
Thin Shells

Hyperelastic Thin Shells: Equilibrium Equations and Boundary Conditions

2015 ◽  
Vol 82 (9) ◽  
Author(s):  
Chi Zhang ◽  
Jian Wu ◽  
Keh-Chih Hwang
Keyword(s):  
Boundary Conditions ◽  
Finite Deformation ◽  
Deformation Analysis ◽  
Thin Shells ◽  
Membrane Stress ◽  
Equilibrium Equations

The equilibrium equations and boundary conditions in terms of the second Piola–Kirchhoff membrane stress and moment are given in this note, which are necessary for the finite deformation analysis of shells.

A Two-Dimensional Linear Assumed Strain Triangular Element for Finite Deformation Analysis

2005 ◽  
Vol 73 (6) ◽  
pp. 970-976 ◽  
Author(s):  
Fernando G. Flores
Keyword(s):  
Finite Deformation ◽  
Degrees Of Freedom ◽  
Yield Function ◽  
Triangular Element ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Stress Strain ◽  
Metric Tensor ◽  
Assumed Strain ◽  
Non Linear

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

Nonlinear Finite Deformation Analysis of Beams and Columns

1994 ◽  
Vol 120 (10) ◽  
pp. 2136-2153 ◽  
Author(s):  
Ronald Y. S. Pak ◽  
Eric J. Stauffer
Keyword(s):  
Finite Deformation ◽  
Deformation Analysis
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