New Generalized Conforming Flat Shell Elements And Their Applications In Linear/Nonlinear Analysis

The 3-node triangular flat shell element, which is included in the element libraries of most famous commercial FEM softwares, is widely used because of its outstanding merits. Therefore, a great deal of attention has been paid to develop an efficient model. In this dissertation, several simple and effective approaches are presented to construct high performance elements for linear and nonlinear analysis of plate and shell structures. The main contributions of this dissertation are as follows: 1. The stabilization matrix of the generalized conforming element GT9, the membrane part of the generalized conforming flat shell element GST18, is derived. Thus, the formulations of the element GST18 are modified and successfully avoid the extra zero energy modes and hourglass phenomenon. Furthermore, the UL formulae of the GST18, including the in-plane large displacement, are also presented. Then the element GST18 is introduced into the commercial FEM software ABAQUS by user element subroutine function. Numerical examples show that the presented element exhibits better precision and efficiency than the same type element used in ABAQUS for geometrical nonlinear problems.2. The FEM incremental equations of element GST18 for elastic-plastic analysis are established and introduced into ABAQUS. The performances of elements GST18 and STRI3 (the triangular flat shell element of ABAQUS) in elastic-plastic analysis are thoroughly compared, including their precision, convergence, sensitivity to mesh orientation and efficiency. It can be seen that higher performance can be obtained by presented model.3. Based on the method of directly assuming rational shear strain and deflection fields, a new generalized conforming triangular, 9 DOF thick-thin plate bending element, named TSL-T9, is successfully constructed using SemiLoof constrains. Its stress solutions are improved by the hybrid post-processing procedure. This element is robust and free of shear locking, and possesses excellent performance for both thin and thick plates. 4. A new simple 3-node triangular flat shell element with 18 DOFs (6 DOFs per node), GMST18, is proposed for the linear and geometrically nonlinear analysis of very thin to thick shell structures. The stabilized formulation of element GT9 is employed as the membrane component. The bending component comes from element TSL-T9. Numerical results show that the proposed element GMST18 exhibits excellent and better performance for the analysis of thin-thick shells in both linear and geometrically nonlinear problems.5. According to the FSDT theory, a new triangular laminated composite shell element is developed from the element GMST18. And its stress solutions are improved by the hybrid post-processing procedure. Thus, excellent results for both displacements and stresses, especially the transverse shear stresses, can be obtained.