A New Method Applied to the Quadrilateral Membrane Element with Vertex Rigid Rotational Freedom

In order to improve the performance of the membrane element with vertex rigid rotational freedom, a new method to establish the local Cartesian coordinate system and calculate the derivatives of the shape functions with respect to the local coordinates is introduced in this paper. The membrane elements with vertex rigid rotational freedom such as GQ12 and GQ12M based on this new method can achieve higher precision results than traditional methods. The numerical results demonstrate that the elements GQ12 and GQ12M with this new method can provide better membrane elements for flat shell elements. Furthermore, this new method presented in this paper offers a new approach for other membrane elements used in flat shell element to improve the computing accuracy.

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Three-dimensional flat shell-to-shell coupling: numerical challenges

Curved and Layered Structures ◽

10.1515/cls-2017-0020 ◽

2017 ◽

Vol 4 (1) ◽

pp. 299-313

Author(s):

Kuo Guo ◽

Ghadir Haikal

Keyword(s):

Plate Theory ◽

Three Dimensional ◽

Shell Element ◽

Thin Plates ◽

Mindlin Plate ◽

Shell Elements ◽

Contact Formulation ◽

Flat Shell ◽

Surface Contact ◽

Flat Shell Element

Abstract The node-to-surface formulation is widely used in contact simulations with finite elements because it is relatively easy to implement using different types of element discretizations. This approach, however, has a number of well-known drawbacks, including locking due to over-constraint when this formulation is used as a twopass method. Most studies on the node-to-surface contact formulation, however, have been conducted using solid elements and little has been done to investigate the effectiveness of this approach for beam or shell elements. In this paper we show that locking can also be observed with the node-to-surface contact formulation when applied to plate and flat shell elements even with a singlepass implementation with distinct master/slave designations, which is the standard solution to locking with solid elements. In our study, we use the quadrilateral four node flat shell element for thin (Kirchhoff-Love) plate and thick (Reissner-Mindlin) plate theory, both in their standard forms and with improved formulations such as the linked interpolation [1] and the Discrete Kirchhoff [2] elements for thick and thin plates, respectively. The Lagrange multiplier method is used to enforce the node-to-surface constraints for all elements. The results show clear locking when compared to those obtained using a conforming mesh configuration.

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Study on the Explicit Formula of the Triangular Flat Shell Element Based on the Analytical Trial Functions for Anisotropy Material

Mathematical Problems in Engineering ◽

10.1155/2013/486453 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Xiang-Rong Fu ◽

Li-Na Ge ◽

Ge Tian ◽

Ming-Wu Yuan

Keyword(s):

Analytical Solutions ◽

High Efficiency ◽

Shell Element ◽

High Accuracy ◽

Triangular Element ◽

Shell Elements ◽

Hybrid Element ◽

Flat Shell ◽

Flat Shell Element ◽

Integral Formulae

This paper presents a novel way to formulate the triangular flat shell element. The basic analytical solutions of membrane and bending plate problem for anisotropy material are studied separately. Combining with the conforming displacement along the sides and hybrid element strategy, the triangular flat shell elements based on the analytical trial functions (ATF) for anisotropy material are formulated. By using the explicit integral formulae of the triangular element, the matrices used in proposed shell element are calculated efficiently. The benchmark examples showed the high accuracy and high efficiency.

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Thermoviscoelastic analysis of composite structures using a triangular flat shell element

AIAA Journal ◽

10.2514/3.14154 ◽

1999 ◽

Vol 37 ◽

pp. 238-247

Author(s):

Daniel C. Hammerand ◽

Rakesh K. Kapania

Keyword(s):

Composite Structures ◽

Shell Element ◽

Flat Shell ◽

Flat Shell Element

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A free-formulation-based flat shell element for non-linear analysis of thin composite structures

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.1620372206 ◽

1994 ◽

Vol 37 (22) ◽

pp. 3825-3842 ◽

Cited By ~ 26

Author(s):

E. Madenci ◽

A. Barut

Keyword(s):

Composite Structures ◽

Shell Element ◽

Linear Analysis ◽

Flat Shell ◽

Non Linear ◽

Flat Shell Element

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A new 3-node triangular flat shell element

Communications in Numerical Methods in Engineering ◽

10.1002/cnm.421 ◽

2002 ◽

Vol 18 (3) ◽

pp. 153-159 ◽

Cited By ~ 5

Author(s):

J. G. Kim ◽

J. K. Lee ◽

Y. K. Park

Keyword(s):

Shell Element ◽

Flat Shell ◽

Flat Shell Element

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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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