A nonlinear extensible 4-node shell element based on continuum theory and assumed strain interpolations (original) (raw)
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A 4-node assumed strain quasi-conforming shell element with 6 degrees of freedom
International Journal for Numerical Methods in Engineering, 2003
Quasi-conforming formulations of 4-node stress-resultant shell elements are presented. The element formulations use interrelated displacement-rotation interpolations. The formulation also includes drilling degrees of freedom, which improves membrane behavior and allows the modeling of sti ened plates and shells. The proposed treatment for bending provides very good results in the 4-node shell element. The sti ness matrices for the present elements are explicitly expressed and the stresses are taken accurately at the nodal points. Compared to elements using Gauss integration, where the stresses are most accurate at the integration points, the extrapolation procedure needed for post-processing is eliminated in the present shell element. A lot of numerical tests were carried out for the validation of the present 4-node shell element and the results are in good agreement with references.
Communications in Numerical Methods in Engineering, 1995
A quadrilateral degenerated C" shell element is presented which relies on extensible director kinematics and which incorporates unmodified three-dimensional constitutive models. It is shown that the direct interpolation of the extensible director field causes severe locking behaviour in the case of thin shell structures. An assumed strain interpolation is proposed to overcome the thin-shell defect. Due to this modification the shell element is able to accommodate large rotations without a rotation tensor, even for very thin shells. Several large deformation examples confirm that the developed shell element is competitive with more elaborate formulations which use rotational degrees of freedom.
A continuum mechanics based four‐node shell element for general non‐linear analysis
Engineering Computations, 1984
A new four-node (non-flat) general quadrilateral shell element for geometric and material non-linear analysis is presented. The element is formulated using threedimensional continuum mechanics theory and it is applic able to the analysis of thin and thick shells. The for mulation of the element and the solutions to various test and demonstrative example problems are presented and discussed.
An eight-node hybrid-stress solid-shell element for geometric non-linear analysis of elastic shells
International Journal for Numerical Methods in Engineering, 2002
This paper presents eight-node solid-shell elements for geometric non-linear analysis of elastic shells. To subdue shear, trapezoidal and thickness locking, the assumed natural strain method and an ad hoc modiÿed generalized laminate sti ness matrix are employed. A selectively reduced integrated element is formulated with its membrane and bending shear strain components taken to be constant and equal to the ones evaluated at the element centroid. With the generalized stresses arising from the modiÿed generalized laminate sti ness matrix assumed to be independent from the ones obtained from the displacement, an extended Hellinger-Reissner functional can be derived. By choosing the assumed generalized stresses similar to the assumed stresses of a previous solid element, a hybrid-stress solid-shell element is formulated. Commonly employed geometric non-linear homogeneous and laminated shell problems are attempted and our results are close to those of other state-of-the-art elements. Moreover, the hybrid-stress element converges more readily than the selectively reduced integrated element in all benchmark problems. Copyright ? 2002 John Wiley & Sons, Ltd.
3D-shell elements for structures in large strains
Computers & Structures, 2013
We present in this paper MITC shell elements for large strain solutions of shell structures. While we focus on the 4-node element, the same formulation is also applicable to the 3-node element. Since the elements are formulated using three-dimensiona l continuum theory with the full three-dimensional constitutive behavior, they are referred to as 3D-shell elements. Specific contributions in this paper are that the elements are formulated usi ng two control vector s at each node to describe the large deformations, MITC tying and volume preserving conditions acting directly on the material fiber vectors to avoid shear locking, and a pressure interpolation to circumvent volumetric locking. Also, we present solutions to some large strain shell problems that represent valuable benchmark tests for any large strain shell analysis capability.
A shell element for finite strain analyses: hyperelastic material models
Engineering Computations, 2007
To develop a simple and efficient shell element for large strains hyperelastic analyses. Approach Based on the classical MITC4 shell element formulation a 3D shell element with finite strain kinematics is developed. The new quadrilateral shell element has 5 d.o.f. per node and two global d.o.f. to model the thickness stretching. The shell element is implemented for hyperelastic material models and the application of different hyperelastic constitutive relations is discussed. Practical Implications The results obtained considering three of the hyperelastic material models available in the literature are quite different when the developed strains are relatively high; this indicates that, for analyzing actual engineering examples, experimental data should be used to decide on the most suitable constitutive relation.
Computers & Structures, 2002
We discuss a theoretical formulation of shell model accounting for through-the-thickness stretching, which allows for large deformations and direct use of 3d constitutive equations. Three different possibilities for implementing this model within the framework of the finite element method are examined: one leading to 7 nodal parameters and the remaining two to 6 nodal parameters. The 7-parameter shell model with no simplification of kinematic terms is compared to the 7-parameter shell model which exploits usual simplifications of the Green–Lagrange strains. Two different ways of implementing the incompatible mode method for reducing the number of parameters to 6 are presented. One implementation uses an additive decomposition of the strains and the other an additive decomposition of the deformation gradient. Several numerical examples are given to illustrate performance of the shell elements developed herein.
A triangular finite shell element based on a fully nonlinear shell formulation
Computational Mechanics, 2003
This work presents a fully nonlinear sixparameter (3 displacements and 3 rotations) shell model for finite deformations together with a triangular shell finite element for the solution of the resulting static boundary value problem. Our approach defines energetically conjugated generalized cross-sectional stresses and strains, incorporating first-order shear deformations for an inextensible shell director (no thickness change). Finite rotations are treated by the Euler-Rodrigues formula in a very convenient way, and alternative parameterizations are also discussed herein. Condensation of the three-dimensional finite strain constitutive equations is performed by applying a mathematically consistent plane stress condition, which does not destroy the symmetry of the linearized weak form. The results are general and can be easily extended to inelastic shells once a stress integration scheme within a time step is at hand. A special displacement-based triangular shell element with 6 nodes is furthermore introduced. The element has a nonconforming linear rotation field and a compatible quadratic interpolation scheme for the displacements. Locking is not observed as the performance of the element is assessed by several numerical examples, which also illustrate the robustness of our formulation. We believe that the combination of reliable triangular shell elements with powerful mesh generators is an excellent tool for nonlinear finite element analysis.
A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation
International Journal for Numerical Methods in Engineering, 1985
This communication discusses a 4-node plate bending element for linear elastic analysis which is obtained, as a special case, from a general nonlinear continuum mechanics based 4-node shell element formulation. The formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate (and shell) element.
Computational Mechanics, 2004
This work presents a fully nonlinear multi-parameter shell formulation together with a triangular shell finite element for the solution of static boundary value problems. Our approach accounts for thickness variation as additional nodal DOFs, using a director theory with a standard Reissner-Mindlin kinematical assumption. Finite rotations are exactly treated by the Euler-Rodrigues formula in a pure Lagrangean framework, and elastic constitutive equations are consistently derived from fully three-dimensional finite strain constitutive models. The corresponding 6-node triangular shell element is presented as a generalization of the T6-3i triangle introduced by the authors in [3].