Finite strain quadrilateral shell using least-squares fit of relative Lagrangian in-plane strains

• Type: Article in International Scientific Journal
• Date: 2015

Authors

P. Areias (Author) Other; T. Rabczuk (Author) Other; J.M. César de Sá (Author) FEUP; J.E. Garção (Author) Other

Journal

Title: Finite Elements in Analysis and Design

Vol. 98

Pages: 26-40

ISSN: 0168-874X

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 5 Citations

ISI Web of Science

Scopus - 6 Citations

Scientific classification

FOS: Engineering and technology > Mechanical engineering

CORDIS: Technological sciences > Engineering > Mechanical engineering

Other information

Authenticus ID: P-00A-79X

DOI: 10.1016/j.finel.2015.01.004

Abstract (EN): This work presents a finite strain quadrilateral element with least-squares assumed in-plane shear strains (in covariant/contravariant coordinates) and classical transverse shear assumed strains. It is an alternative to enhanced-assumed-strain (EAS) formulation and, in contrast to this, produces an element satisfying ab initio the Patch-test No additional degrees-of-freedom are present, unlike EAS. Least-squares tit allows the derivation of invariant finite strain elements which are both in-plane and out-ofplane shear-locking free and amenable to standardization in commercial codes. With that goal, we use automatically generated code produced by AceGen and Mathematica to obtain novel finite element formulations. The corresponding exact linearization of the internal forces was, until recently, a insurmountable task We use the tangent modulus in the least-squares fit to ensure that stress modes are obtained from a five-parameter strain fitting. This reproduces exactly the in plane bending modes. The discrete equations are obtained by establishing a lour Field variational principle (a direct extension of the Plu-Washizu variational principle). The main achieved goal is coarse mesh accuracy for distorted meshes, which is adequate for being used in crack propagation problems. In addition, as an alternative to spherical interpolation, a consistent director normalization is performed. Metric components are fully deduced and exact linearization of the shell element is performed. Full linear and nonlinear assessment of the element is performed, showing similar performance to more costly approaches, often on par with the best available shell elements.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15