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|Title: ||Asymmetric shell elements based on a corrected updated-Lagrangian approach|
|Authors: ||Areias, Pedro|
Dias da Costa, Daniel
|Issue Date: ||Dec-2012|
|Abstract: ||Surprisingly good displacement results are obtained by using the Petrov-Galerkin method with
assumed and enhanced metric components in the test functions and enhanced metric components in the
trial functions. Cartesian trial functions are required to ensure completeness and assumed/enhanced
metric components are introduced to ensure high coarse-mesh accuracy. In the trial functions, the original
incompatible-mode in-plane Q6 element by Wilson et al. can be used without violating the patch test.
As a bene cial side-e ect, Newton-Raphson convergence behavior for non-linear problems is improved.
Transverse-shear and in-plane patch tests are satis ed while distorted-mesh performance is better than
with symmetric formulations due to the absence of coordinate transformation. Covariant coordinates are
used to calculate the (mixed) test metric and a combination of Cartesian coordinates and quadratic terms
in the metric are used for the trial functions. Classical test functions with assumed metric components
are required for compatibility reasons. Veri cation tests are performed with very good performance
being observed in all of them. Applications to large displacement elasticity and nite strain plasticity
are shown with both low sensitivity to mesh distortion and high accuracy. A equilibrium-consistent (and consistently linearized) updated-Lagrangian algorithm is proposed and tested. Concerning the
time-step dependency, it was found that the consistent updated-Lagrangian algorithm is nearly time-step
independent and can replace the multiplicative plasticity approach if only moderate elastic strains are
|Appears in Collections:||FIS - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica|
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