Geometrically nonlinear analysis of laminated composite thin shells using a modified first-order shear deformable element-based Lagrangian shell element

A Galerkin meshfree approach formulated within the framework of stabilized conforming nodal integration (SCNI) is presented for geometrically nonlinear analysis of large deflection shear deformable plates. This method is based upon a Lagrangian curvature smoothing in which the smoothed curvature is constructed within a nodal representative domain on the initial configuration. It is shown that the Lagrangian smoothed nodal gradients of the meshfree shape function is capable of exactly representing arbitrary constant curvature fields in the discrete sense of nodal integration. The consistent linearization is performed on the weak form of large deflection plate in the context of the total Lagrangian description. Subsequently, the discrete incremental equations are obtained by the method of SCNI in which to relieve the locking as well as ensure the stability of the present scheme, the bending contribution is evaluated using the smoothed nodal gradients, while the membrane and shear contributions are computed with the direct nodal gradients. The effectiveness of the present method is thoroughly demonstrated through several numerical examples.

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A new stiffened shell element for geometrically nonlinear analysis of composite laminates

Computers & Structures ◽

10.1016/s0045-7949(99)00201-1 ◽

2000 ◽

Vol 77 (1) ◽

pp. 11-40 ◽

Cited By ~ 14

Author(s):

A. Barut ◽

E. Madenci ◽

A. Tessler ◽

J.H. Starnes

Keyword(s):

Nonlinear Analysis ◽

Composite Laminates ◽

Shell Element ◽

Geometrically Nonlinear ◽

Geometrically Nonlinear Analysis ◽

Stiffened Shell

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Element-Independent Pure Deformational and Co-Rotational Methods for Triangular Shell Elements in Geometrically Nonlinear Analysis

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455418500657 ◽

2018 ◽

Vol 18 (05) ◽

pp. 1850065 ◽

Cited By ~ 1

Author(s):

Y. Q. Tang ◽

Y. P. Liu ◽

S. L. Chan

Keyword(s):

Nonlinear Analysis ◽

Nonlinear Problems ◽

Shell Element ◽

Benchmark Problems ◽

Element Formulation ◽

Geometrically Nonlinear ◽

Plate Element ◽

Membrane Element ◽

Geometrically Nonlinear Analysis ◽

Shell Elements

Proposed herein is a novel pure deformational method for triangular shell elements that can decrease the element quantities and simplify the element formulation. This approach has computational advantages over the conventional finite element method for linear and nonlinear problems. In the element level, this method saves time for computing stresses, internal forces and stiffness matrices. A flat shell element is formed by a membrane element and a plate element, so that the pure deformational membrane and plate elements are derived and discussed separately in this paper. Also, it is very convenient to incorporate the proposed pure deformational method into the element-independent co-rotational (EICR) framework for geometrically nonlinear analysis. Thus, on the basis of the pure deformational method, a novel EICR formulation is proposed which is simpler and has more clear physical characteristics than the traditional formulation. In addition, a triangular membrane element with drilling rotations and the discrete Kirchhoff triangular plate element are used to verify the proposed pure deformational method, although several benchmark problems are employed to verify the robustness and accuracy of the proposed EICR formulations.

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Geometrically nonlinear analysis of thin shell by a quadrilateral finite element with in-plane rotational degrees of freedom

European Journal of Computational Mechanics ◽

10.13052/ejcm.19.707-724 ◽

2010 ◽

pp. 707-724

Author(s):

Djamel Boutagouga ◽

Abdelhacine Gouasmia ◽

Kamel Djeghaba

Keyword(s):

Nonlinear Analysis ◽

Thin Shell ◽

Degrees Of Freedom ◽

Shell Element ◽

Local System ◽

Second Phase ◽

Geometrically Nonlinear ◽

Geometrically Nonlinear Analysis ◽

Rotational Degrees Of Freedom ◽

Quadrilateral Finite Element

We present in this research article, the improvements that we made to create a four nodes flat quadrilateral shell element for geometrically nonlinear analysis, based on corotational updated lagrangian formulation. These improvements are initially related to the improvement of the in-plane behaviour by incorporation of the in-plane rotational degrees of freedom known as “drilling degrees of freedom” in the membrane displacements field formulation. In the second phase, a co-rotational spatial local system of axes which adapts well to the problems of quadrilateral elements is adopted, while ensuring simplicity and effectiveness at numerical level. The required goal being mainly to have a robust thin shell element associated with a simplified formulation. The obtained element remains economic, and showing a robust behaviour in delicate situations of tests.

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