A drill rotation formulation for geometrically exact shells

DOI10.1016/0045-7825(92)90002-2zbMath0764.73050OpenAlexW1971013052MaRDI QIDQ1205672

David D. Fox, Juan C. Simo

Publication date: 1 April 1993

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(92)90002-2

zbMATH Keywords

variational formulationBiot stressadditional Lagrange multiplier termnonlinear shell modelsshell balance equations

Mathematics Subject Classification ID

Related Items (27)

Computational aspects of the mechanics of complex materials ⋮ A new enhanced assumed strain quadrilateral membrane element with drilling degree of freedom and modified shape functions ⋮ Consistent tangent operator for an exact Kirchhoff rod model ⋮ AN ALGORITHM FOR INTEGRATING THE SPIN ON CONVECTED BASES ⋮ Existence theorems in the geometrically non-linear 6-parameter theory of elastic plates ⋮ A GEOMETRICALLY EXACT PLANAR COSSERAT SHELL-MODEL WITH MICROSTRUCTURE: EXISTENCE OF MINIMIZERS FOR ZERO COSSERAT COUPLE MODULUS ⋮ Generalization of the \(C^1\) TUBA plate finite elements to the geometrically exact Kirchhoff-Love shell model ⋮ The membrane shell model in nonlinear elasticity: A variational asymptotic derivation ⋮ On a stress resultant geometrically exact shell model. VII: Shell intersections with 5/6-DOF finite element formulations ⋮ Stress resultant geometrically nonlinear shell theory with drilling rotations. I: A consistent formulation ⋮ The Cosserat surface as a shell model, theory and finite element formulation ⋮ Finite element analysis of smooth, folded and multi-shell structures ⋮ A weak form quadrature element formulation of geometrically exact shells incorporating drilling degrees of freedom ⋮ A quadrature element formulation of geometrically nonlinear laminated composite shells incorporating thickness stretch and drilling rotation ⋮ Unnamed Item ⋮ The isotropic Cosserat shell model including terms up to \(O(h^5)\). II: Existence of minimizers ⋮ Finite element linear and nonlinear, static and dynamic analysis of structural elements: a bibliography (1992‐1995) ⋮ On the parametrization of finite rotations in computational mechanics. A classification of concepts with application to smooth shells ⋮ A co-rotational triangular finite element for large deformation analysis of smooth, folded and multi-shells ⋮ On nonlocal geometrically exact shell theory and modeling fracture in shell structures ⋮ Poincaré's equations for Cosserat media: application to shells ⋮ On generalized Cosserat-type theories of plates and shells: a short review and bibliography ⋮ An implicit \(\operatorname{G}^1\)-conforming bi-cubic interpolation for the analysis of smooth and folded Kirchhoff-Love shell assemblies ⋮ Geometrically exact shell theory from a hierarchical perspective ⋮ Finite rotation three and four nodes shell elements for functionally graded carbon nanotubes-reinforced thin composite shells analysis ⋮ A geometrically exact Cosserat shell-model including size effects, avoiding degeneracy in the thin shell limit. I: Formal dimensional reduction for elastic plates and existence of minimizers for positive Cosserat couple modulus ⋮ Existence of minimizers in the geometrically non-linear 6-parameter resultant shell theory with drilling rotations

Cites Work

• On drilling degrees of freedom
• On a stress resultant geometrically exact shell model. I: Formulation and optimal parametrization
• A three-dimensional finite-strain rod model. II. Computational aspects
• On a stress resultant geometrically exact shell model. IV: Variable thickness shells with through-the-thickness stretching
• Formulations of finite elasticity with independent rotations
• The (symmetric) Hessian for geometrically nonlinear models in solid mechanics: Intrinsic definition and geometric interpretation
• On a stress resultant geometrically exact shell model. III: Computational aspects of the nonlinear theory
• The influence of the reference geometry on the response of elastic shells
• Theories of elasticity with couple-stress
• On a Variational Theorem in Elasticity and Its Application to Shell Theory
• On the Form of Variationally Derived Shell Equations

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