A theory and finite element formulation of shells at finite deformations involving thickness change : circumventing the use of a rotation tensor
TLDR
In this article, a nonlinear shell theory, including transverse strains perpendicular to the shell midsurface, as well as transverse shear strains, with exact description of the kinematical fields, is developed.Abstract:
A nonlinear shell theory, including transverse strains perpendicular to the shell midsurface, as well as transverse shear strains, with exact description of the kinematical fields, is developed. The strain measures are derived by considering theGreen strain tensor of the three-dimensional shell body. A quadratic displacement field over the shell thickness is considered. Altogether seven kinematical fields are incorporated in the formulation. The kinematics of the shell normal is described by means of a difference vector, avoiding the use of a rotation tensor and resulting in a configuration space, where the structure of a linear vector space is preserved. In the case of linear constitutive equations, a possible consistent reduction to six degrees of freedom is discussed. The finite element formulation is based on a hybrid variational principle. The accuracy of the theory and its wide range of applicability is demonstrated by several examples. Comparison with results based on shell theories formulated by means of a rotation tensor are included.read more
Citations
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Journal ArticleDOI
A unified approach for shear-locking-free triangular and rectangular shell finite elements
TL;DR: In this article, a new concept for the construction of locking-free finite elements for bending of shear deformable plates and shells, called DSG (Discrete Shear Gap) method, is presented.
Journal ArticleDOI
A systematic development of 'solid-shell' element formulations for linear and non-linear analyses employing only displacement degrees of freedom
R. Hauptmann,Karl Schweizerhof +1 more
TL;DR: In this article, the authors proposed a solid-shell concept which incorporates only displacement degrees of freedom, and several modifications of the solidshell concept are proposed to obtain locking-free solidshell elements, leading also to formulations which allow the use of general threedimensional material laws and which are also able to represent the normal stresses and strains in thickness direction.
Reference EntryDOI
Models and finite elements for thin-walled structures
TL;DR: In this paper, the authors provide an overview of modeling and discretization aspects in finite element analysis of thin-walled structures, focusing on nonlinear finite element formulations for large displacements and rotations in the context of elastostatics.
Journal ArticleDOI
Non-linear vibrations of shells: A literature review from 2003 to 2013
Farbod Alijani,Marco Amabili +1 more
TL;DR: In this paper, a review of geometrically non-linear free and forced vibrations of shells made of traditional and advanced materials is presented, including closed shells and curved panels made of isotropic, laminated composite, piezoelectric, functionally graded and hyperelastic materials.
Journal ArticleDOI
Large deformation analysis of functionally graded shells
R.A. Arciniega,J. N. Reddy +1 more
TL;DR: In this article, a tensor-based finite element formulation with curvilinear coordinates and first-order shear deformation theory is used to develop the functionally graded shell finite element.
References
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Book
The finite element method
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Book
Mathematical foundations of elasticity
TL;DR: In this article, the mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis are discussed. But the authors do not discuss the application of functional analysis to the problem of elasticity.
Journal ArticleDOI
A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation
TL;DR: In this article, a 4-node plate bending element for linear elastic analysis is presented, as a special case, from a general nonlinear continuum mechanics based four-node shell element formulation.
Journal ArticleDOI
Rational approach for assumed stress finite elements
Theodore H. H. Pian,K. Sumihara +1 more
TL;DR: In this paper, a new method for the formulation of hybrid elements by the Hellinger-Reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element.
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