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Asymmetric quadrilateral shell elements for finite strains

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Abstract

Very good results in infinitesimal and finite strain analysis of shells are achieved by combining either the enhanced-metric technique or the selective-reduced integration for the in-plane shear energy and an assumed natural strain technique (ANS) in a non-symmetric Petrov–Galerkin arrangement which complies with the patch-test. A recovery of the original Wilson incompatible mode element is shown for the trial functions in the in-plane components. As a beneficial side-effect, Newton–Raphson convergence behavior for non-linear problems is improved with respect to symmetric formulations. Transverse-shear and in-plane patch tests are satisfied while distorted-mesh accuracy is higher than with symmetric formulations. Classical test functions with assumed-metric components are required for compatibility reasons. Verification tests are performed with advantageous comparisons being observed in all of them. Applications to large displacement elasticity and finite strain plasticity are shown with both low sensitivity to mesh distortion and (relatively) 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 present, as is the case of most metals.

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Authors and Affiliations

  1. Physics Department, University of Évora, Colégio Luís António Verney, Rua Romão Ramalho, 59, 7002-554, Évora, Portugal

    P. Areias

  2. ICIST, Lisbon, Portugal

    P. Areias & E. B. Pires

  3. INESC Coimbra, Rua Antero de Quental 199, 3000-033, Coimbra, Portugal

    D. Dias-da-Costa

  4. Civil Engineering Department, University of Coimbra, Rua Luís Reis Santos, 3030-788, Coimbra, Portugal

    D. Dias-da-Costa

  5. Departamento de Matemática, Faculdade de Ciências, Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, Lisbon, 1649-003, Portugal

    N. Van Goethem

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  1. P. Areias
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  2. D. Dias-da-Costa
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  3. E. B. Pires
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  4. N. Van Goethem
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Correspondence to P. Areias.

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Areias, P., Dias-da-Costa, D., Pires, E.B. et al. Asymmetric quadrilateral shell elements for finite strains. Comput Mech 52, 81–97 (2013). https://doi.org/10.1007/s00466-012-0799-2

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