A Co-Rotational Framework for Quadrilateral Shell Elements Based on the Pure Deformational Method

Abstract

ABSTRACT:In this paper, a novel co-rotational framework for quadrilateral shell element allowing for the warping effect based on the pure deformational method is proposed for geometrically nonlinear analysis. This new co-rotational framework is essentially an element-independent algorithm which can be combined with any type of quadrilateral shell element. As the pure deformational method is adopted, the quantities of the shell element can be reduced, such that it needs less computer storage and therefore enhances the computational efficiency. In the proposed framework, the geometrical stiffness is derived with a clear physical meaning and regarded as the variations of the nodal internal forces due to the motions and deformations of shell element. Furthermore, the warping effect of quadrilateral shell element is considered, and for this reason, the structures undergoing significant warping can be efficiently solved by the proposed formulation. Finally, several benchmark examples are used to verify the validation and accuracy of the proposed method for geometrically nonlinear analysis.Keywords: element-independence, co-rotational method, flat quadrilateral shell element, pure deformation, geometrically nonlinear analysis, explicit tangent stiffness DOI: 10.18057/IJASC. 2018.14.1.6 INTRODUCTIONShell structures and steel frames made up of thin-wall members are commonly used in civil and structural engineering. Generally, it needs huge computer time to analyze a structure by finite shell elements compared with beam-column elements, especially in nonlinear analyses. Thus, the development of shell elements with high performance as well as the co-rotational framework with improved computational efficiency continuously attracts the attention of many researchers.There are three common methods based on the Lagrangian kinematic description for geometrically nonlinear analyses, i.e. total Lagrangian (TL), updated Lagrangian (UL) and co-rotational approaches. The last method is latest and attracts more attention than the others recently due to its simplicity and efficiency. The basic idea of the co-rotational method is that the total motions of an element can be divided into two parts, including the rigid body motions and the pure deformations.To decompose them, a local frame is attached to and co-rotated with the element. Then, the translations and rotations of the local frame are taken as the rigid body movements, while the deformations of the element produced in the local frame are regarded as the pure deformations. In reality, the classification of the Lagrangian kinematic descriptions for geometrically nonlinear analysis is not absolute. The co-rotational approach can be incorporated with either the total Lagrangian (TL) or the updated Lagrangian (UL) formulations. In the following, some research works related to the co-rotational description are discussed.