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Proceedings ArticleDOI

Geometrically nonlinear analysis of composite plates and shells using a flat triangular shell element

07 Apr 1997-
TL;DR: In this paper, an updated Lagrangian formulation of a three node flat triangular shell element is presented for geometrically non-linear analysis of laminated plates and shells, which can be used in the near future for the analysis of large inflatable structures which are highly flexible and are expected to undergo large deformations and rotations.
Abstract: An updated Lagrangian formulation of a three node flat triangular shell element is presented for geometrically non-linear analysis of laminated plates and shells. The flat shell element is obtained by combining the Discrete Kirchhoff Theory (DKT) plate bending element and a membrane element that is similar to the Allman element, but a derivative of the Linear Strain Triangular (LST) element. Results are presented for static response analysis (snap-back behavior of a cylindrical panel, large rotation response of a cantilever beam under an end moment, cylindrical shell under pinching and stretching loads and hemispherical shell under pinching and stretching loads); for dynamic response analysis of a cylindrical panel; and for thermal postbuckling analysis of an imperfect square plate and a cylindrical panel. The element will be used in the near future for the analysis of large inflatable structures which are highly flexible and are expected to undergo large deformations and rotations. In order to estimate the accuracy of the present formulation in predicting the nonlinear response of such large flexible structures, static analysis of an apex-loaded circular arch is performed. The arch presented is a building block of a large inflatable structure. The present results are in good agreement with the results available in the existing literature and those obtained using the commercial finite element software ABAQUS, demonstrating the accuracy of the present formulation.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors present a review on geometrically nonlinear analysis of shell structures that is limited to the co-rotational approach and to flat triangular shell finite elements.
Abstract: This paper presents a state of the art review on geometrically nonlinear analysis of shell structures that is limited to the co-rotational approach and to flat triangular shell finite elements. These shell elements are built up from flat triangular membranes and plates. We propose an element comprised of the constant strain triangle (CST) membrane element and the discrete Kirchhoff (DKT) plate element and describe its formulation while stressing two main issues: the derivation of the geometric stiffness matrix and the isolation of the rigid body motion from the total deformations. We further use it to solve a broad class of problems from the literature to validate its use.

47 citations

Journal ArticleDOI
TL;DR: In this paper, the buckling analysis of a composite panel under axial compression by means of a simple shell finite element is presented and validated by solving a complex multi-snap example from the literature.

39 citations

Journal ArticleDOI
TL;DR: In this article, an updated Lagrangian formulation of a three-node flat triangular shell element is presented for geometrically nonlinear analysis of laminated plates and shells, which is obtained by combining the discrete Kirchhoff theory plate bending element and a membrane element that is similar to the Allman element but a derivative of the linear strain triangular element.
Abstract: An updated Lagrangian formulation of a three-node flat triangular shell element is presented for geometrically nonlinear analysis of laminated plates and shells. The flat shell element is obtained by combining the discrete Kirchhoff theory plate bending element and a membrane element that is similar to the Allman element but a derivative of the linear strain triangular element. Results are presented for large-rotation static response analysis of a cantilever beam under end moment, cylindrical shell under pinching and stretching loads, a hemispherical shell under pinching and stretching loads, and a ring plate under a line load; for dynamic response analysis of a cylindrical panel; and for thermal postbuckling analysis of an imperfect square plate and a cylindrical panel. To estimate the accuracy of the present formulation in predicting the nonlinear response of large flexible structures, static analysis of an apex-loaded circular arch is performed. The arch is a building block of a large inflatable structure. The results are in good agreement with those available in the existing literature and those obtained using the commercial finite element software ABAQUS, demonstrating the accuracy of the present formulation. HE two most widely adopted approaches in the finite element analysis of shells are use of curved shell elements based on a suitable shell theory and approximation of the curved structure by an assemblage of flat shell elements in which the membranebending coupling is brought about as a result of material anisotropy and transformation of the element stiffness matrices computed in a local coordinate system to the global coordinate system prior to assembly. The curved shell elements can be computationally very expensive, especially in the case of nonlinear analysis, because of the complexity of the formulation and the need to compute the curvature information. Flat shell elements are more attractive because of their simplicity and the ease with which they can be built from alreadyexisting familiar membrane and plate bending elements. Though a large number of elements are required to accurately model curved structures, the analysis is computational ly less expensive because of extremely simple formulation. Updated Lagrangian formulations have been predominantly used in the flat shell formulations available in the existing literature. In an updated Lagrangian formulation, all of the variables are referred to a known configuration, the reference configuration, which is updated continuously during the deformation process. If the rigid-body modes are removed from the total or incremental displacements, the resulting deformational translations and rotations are very small and hence a linearized incremental formulation1 can be used. In a linearized incremental formulation, the stresses are computed using linear strain-displacement relations. The tangent stiffness matrix contains only the linear stiffness matrix and the initial stress matrix. The stiffness matrices resulting from the nonlinear terms in the strain-displacement relations are neglected, resulting in very economical analysis. If the rigid-body modes are not removed, all nonlinear terms in the strain-displacement relations will have to be considered for computing the stresses and the tangent stiffness matrix. A three-node flat triangular shell element was introduced by Argyris et al.2 for nonlinear elastic stability problems. This formula

38 citations

Journal ArticleDOI
TL;DR: A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given.
Abstract: A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given. The bibliography at the end of the paper contains 1,726 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1996‐1999.

23 citations

Journal ArticleDOI
TL;DR: In this paper, a geometric stiffness matrix is derived from load perturbation of the discrete equilibrium equations of a given linear finite element formulation, and an out-of-plane geometric stiffness matrices is then introduced to account for the effect of rigid body rotations on member forces.

20 citations

References
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Book
01 Jan 1989
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.
Abstract: Keywords: methodes : numeriques ; fonction de forme Reference Record created on 2005-11-18, modified on 2016-08-08

17,327 citations

Journal ArticleDOI
TL;DR: In this article, a modified version of the Newton-Raphson method is proposed to overcome limit points in the finite element method with a fixed load level and a constraint equation.

1,581 citations

Journal ArticleDOI
TL;DR: In this article, an assessment of flat triangular plate bending elements with displacement degrees-of-freedom at the three comer nodes only is presented, with the purpose of identifying the most effective for thin plate analysis.
Abstract: SUMMARY An assessment of flat triangular plate bending elements with displacement degrees-of-freedom at the three comer nodes only is presented, with the purpose of identifying the most effective for thin plate analysis. Based on a review of currently available elements, specific attention is given to the theoretical and numerical evaluation of three triangular 9 degrees-of-freedom elements; namely, a discrete Kirchhoff theory (DKT) element, a hybrid stress model (HSM) element and a selective reduced integration (SRI) element. New and efficient formulations of these elements are discussed in detail and the results of several example analyses are given. It is concluded that the most efficient and reliable three-node plate bending elements are the DKT and HSM elements.

800 citations

Journal ArticleDOI
TL;DR: In this paper, finite element incremental formulations for non-linear static and dynamic analysis are reviewed and derived starting from continuum mechanics principles, and a consistent summary, comparison, and evaluation of the formulations which have been implemented in the search for the most effective procedure.
Abstract: SUMMARY Starting from continuum mechanics principles, finite element incremental formulations for non-linear static and dynamic analysis are reviewed and derived. The aim in this paper is a consistent summary, comparison, and evaluation of the formulations which have been implemented in the search for the most effective procedure. The general formulations include large displacements, large strains and material non-linearities. For specific static and dynamic analyses in this paper, elastic, hyperelastic (rubber-like) and hypoelastic elastic-plastic materials are considered. The numerical solution of the continuum mechanics equations is achieved using isoparametric finite element discretization. The specific matrices which need be calculated in the formulations are presented and discussed. To demonstrate the applicability and the important differences in the formulations, the solution of static and dynamic problems involving large displacements and large strains are presented.

789 citations