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A finite-strain solid–shell using local L¨owdin frames and least-squares strains

P. Areias
Organization: University of Évora
Department: Department of Physics
C. A. Mota Soares
T. Rabczuk
J. Garc¸˜ao
Journal / Anthology

Computer Methods in Applied Mechanics and Engineering
Year: 2016
Volume: 311
Page range: 112-133

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-ofreference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhancedassumed- strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.