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

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

Mathematical Problems in Engineering ◽

10.1155/2016/1045438 ◽

2016 ◽

Vol 2016 ◽

pp. 1-13

Author(s):

Xiaowei Gao ◽

Yunfei Liu ◽

Jun Lv

Keyword(s):

Shell Element ◽

New Method ◽

Membrane Element ◽

Shell Elements ◽

Local Coordinates ◽

Flat Shell ◽

Flat Shell Element ◽

Cartesian Coordinate ◽

Derivatives Of ◽

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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A Conforming Triangular Plane Element with Rotational Degrees of Freedom

Mathematical Problems in Engineering ◽

10.1155/2015/274709 ◽

2015 ◽

Vol 2015 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Xiang-Rong Fu ◽

Ming-Wu Yuan ◽

Chen Pu

Keyword(s):

Isotropic Material ◽

Degrees Of Freedom ◽

High Efficiency ◽

High Accuracy ◽

Triangular Element ◽

Linear Distribution ◽

Rotational Displacement ◽

Plane Element ◽

Rotational Degrees Of Freedom ◽

Integral Formulae

This paper presents a novel way to formulate the triangular plane element with rotational degrees of freedom (RDOF). The linear distribution of rotational displacement is assumed. The conforming displacement along the sides based on the rotational displacement assumption is derived, and the triangular plane element TR3 for isotropic material is formulated. By using the explicit integral formulae of the triangular element, the matrices used in the proposed plane element TR3 are calculated efficiently. The benchmark examples showed thier high accuracy and high efficiency.

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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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