Journal ArticleDOI
Genuinely resultant shell finite elements accounting for geometric and material non-linearity
TLDR
In this article, the authors examined the development of computational procedures employing the Newton-Kantorovich linearization process and the Galerkin type discretization method, the treatment of finite rotations through an arbitrary parametrization of the rotation group, the interpolation procedure of SO(3)-valued functions underlying the construction of finite element basis.Abstract:
The underlying theory is statically and geometrically exact, and it naturally includes small strain and finite strain problems of thin as well as thick shells. This paper examines the development of computational procedures employing the Newton-Kantorovich linearization process and the Galerkin type discretization method, the treatment of finite rotations through an arbitrary parametrization of the rotation group, the interpolation procedure of SO(3)-valued functions underlying the construction of finite element basis.read more
Citations
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BookDOI
Non-Linear Finite Element Analysis of Solids and Structures: de Borst/Non-Linear Finite Element Analysis of Solids and Structures
TL;DR: De Borst et al. as mentioned in this paper present a condensed version of the original book with a focus on non-linear finite element technology, including nonlinear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity.
Journal ArticleDOI
A survey of recent shell finite elements
TL;DR: A comprehensive survey of the literature on curved shell finite elements can be found in this article, where the first two present authors and Liaw presented a survey of such literature in 1990 in this journal.
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
A 4-node finite shell element for the implementation of general hyperelastic 3D-elasticity at finite strains
TL;DR: In this paper, a finite shell element for large deformations is presented based on extensible director kinematics, which is an interface to arbitrary three-dimensional material laws and is characterized by a course mesh accuracy and distortion insensitivity compared with bilinear displacement approaches.
Journal ArticleDOI
Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures
R.A. Arciniega,J. N. Reddy +1 more
TL;DR: In this article, a tensor-based finite element formulation is presented to describe the mathematical model of a shell in a natural and simple way by using curvilinear coordinates, and a family of high-order elements with Lagrangian interpolations is used to avoid membrane and shear locking, and no mixed interpolations are employed.
References
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Book
Theory of plates and shells
TL;DR: In this article, the authors describe the bending of long RECTANGULAR PLATES to a cycloidal surface, and the resulting deformation of shels without bending the plates.
Journal ArticleDOI
A three-dimensional finite-strain rod model. Part II: Computational aspects
Juan C. Simo,Loc Vu-Quoc +1 more
TL;DR: In this article, a variational formulation and computational aspects of a three-dimensional finite-strain rod model, considered in Part I, are presented, which bypasses the singularity typically associated with the use of Euler angles.
Journal ArticleDOI
On a stress resultant geometrically exact shell model. Part III: computational aspects of the nonlinear theory
TL;DR: In this article, a configuration update procedure for the director (rotation) field is developed, which is singularity free and exact regardless the magnitude of the rotation increment, and the exact linearization of the discrete form of the equilibrium equations is derived in closed form.
Journal ArticleDOI
Nonlinear finite element analysis of shells: Part I. three-dimensional shells
Thomas J. R. Hughes,Wing Kam Liu +1 more
TL;DR: In this article, a nonlinear finite element formulation is presented for the three-dimensional quasistatic analysis of shells which accounts for large strain and rotation effects, and accommodates a fairly general class of nonlinear, finite-deformation constitutive equations.
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On a stress resultant geometrically exact shell model. Part III: computational aspects of the nonlinear theory
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