Assumed-metric spherically interpolated quadrilateral shell element

Authors:
P. Areias;T. Rabczuk;D. Dias-Da-Costa
Affiliations:
Physics Department, University of ívora, Colégio Luís António Verney, Rua Romão Ramalho, 59, 7002-554 ívora, Portugal and ICIST, Portugal;Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstraíe 15, 99423 Weimar, Germany;INESC Coimbra, Rua Antero de Quental 199, 3000-033 Coimbra, Portugal and Civil Engineering Department, University of Coimbra, Rua Luís Reis Santos, 3030-788 Coimbra, Portugal
Venue:
Finite Elements in Analysis and Design
Year:
2013

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Abstract

An alternative approach for the analysis of non-linear shells is adopted, based on mixed forms of the spatial metric (both enriched and assumed), spherical linear interpolation for quadrilaterals (for the first time) and covariant fixed frames to ensure the satisfaction of all patch tests (also an innovation). The motivation for the spherical interpolation was the work of Crisfield and Jelenic on geometrically exact beams. Shear deformation is included and rotations are defined relative to the Kirchhoff director. A systematic mixed method for deriving high-performance shell elements is presented in the sense that specific mixed shape functions can be inserted without altering the overall framework. A long-standing restriction of assumed-strain elements in F^eF^p plasticity is circumvented for metal plasticity by using the elastic left Cauchy-Green tensor. Enhanced-assumed metric is also included directly in the metric components. The forces are exactly linearized to obtain an asymptotically quadratic convergence rate in Newton's method. Verification tests of the formulation are performed with very good performance being observed. Applications to hyperelasticity and plasticity are shown with excellent robustness and accuracy.