A finite-strain solid–shell using local Löwdin frames and least-squares strains

• Autor(a) principal: Areias, Pedro
• Data de Publicação: 2016
• Outros Autores: Mota Soares, Carlos, Rabczuk, Timon, Garção, José
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10174/19830; https://doi.org/P. Areias, C.A. Mota Soares, T. Rabczuk, J. Garção, A finite-strain solid–shell using local Löwdin frames and least-squares strains, Computer Methods in Applied Mechanics and Engineering, Volume 311, 1 November 2016, Pages 112-133, ISSN 0045-7825, http://dx.doi.org/10.1016/j.cma.2016.07.044. ---Bibtex--- @article{Areias2016112, title = "A finite-strain solid–shell using local Löwdin frames and least-squares strains ", journal = "Computer Methods in Applied Mechanics and Engineering ", volume = "311", number = "", pages = "112 - 133", year = "2016", note = "", issn = "0045-7825", doi = "http://dx.doi.org/10.1016/j.cma.2016.07.044", url = "http://www.sciencedirect.com/science/article/pii/S0045782516304285", author = "P. Areias and C.A. Mota Soares and T. Rabczuk and J. Garção", keywords = "Finite-strain solid–shell", keywords = "Least-squares", keywords = "Assumed-strains", keywords = "Singular value decomposition " }; https://doi.org/http://dx.doi.org/10.1016/j.cma.2016.07.044
• topic: Finite-strain solid–shell; Least-squares; Assumed-strains; Singular value decomposition; Finite elemento method

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-of-reference 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 enhanced-assumed-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.