Accurate And Efficient Eight-node And Six-node Nonlinear Solid-shell Elements Based On The Quasi-conforming Element Technique

It is important to develop accurate and efficient 3D finite element models for the high-performance scientific computing in various engineering problems involving in the multi-nonlinearities,complicated conditions and large-scale numerical modeling.The solid-shell element is a new type of 3D finite element,which can be used to efficiently analyze the engineering structures with the topological characteristics of the plate/shell-like structure.Nevertheless,the many solid-shell elements based on the conventional element formulation suffer from the problems of locking and superfluous zero energy modes.The alternative method used to overcome locking problems is the hybrid/mixed finite elements based on the multi-field variational principle.In general,these hybrid/mixed finite elements always possess the complicated formulation that results in the high computational cost.Furthermore,most nonlinear solid-shell elements use the polar decomposition theory of the deformation gradients of continuum to deal with the geometrical nonlinear problems,which also leads to more computations.Particularly,this polar decomposition theory used in the solid-shell element formulation could not always provide the best rotation in the Cartesian coordinate system.Therefore,it is necessary to explore an efficient method for the formulation of the reliable and accurate linear/nonlinear solid-shell element.Based on the quasi-conforming(QC)element technique,this thesis presents the element formulations of the reliable,accurate and efficient eight-node and six-node solid-shell elements including both linear and nonlinear elements.The detailed studies are as follows.(1)A series of the proper assumed element strain fields for the eight-node QC solidshell elements are given by the rational element method(REM).Then the optimal assumed element strain field is selected through the performance assessments of the corresponding elements.(2)The formulations of eight-node and six-node QC solid-shell elements that possess explicit element stiffness matrices are presented.The accuracy and stability of the present solid-shell elements are verified by the popular benchmark tests.The numerical results show that the QC solid-shell elements with the properly interpolated strain fields can pass both membrane and bending patch tests.Furthermore,in the analysis of the plate/shell problems,the numerical results evaluated by the present elements demonstrate that the QC solid-shell elements possess high computational accuracy and efficiency,even in the cases of the coarse mesh,irregular mesh and severely distorted mesh.(3)The accurate and efficient geometrical nonlinear eight-node QC solid-shell elements are presented.The generalized weak form of equilibrium equations for the small strain but large deformation problems in the U.L.formulation is derived as the theoretical basis of the element formulation.The updates of coordinates and displacements are only implemented in the coordinate-transformation matrix due to the use of co-rotational coordinates.The tangential element stiffness matrix is given by the QC element technique.The geometrical nonlinearity is incorporated into the QC formulations by using the von Karman nonlinear plate theory.The modified Newton-Raphson iteration method associated with the arc length method is used to solve large-scale nonlinear equations.The accuracy and stability of the present nonlinear solid-shell elements are also verified by the benchmark numerical examples.(4)The eight-node QC solid-shell element is applied to the 3D stress analysis the laminated composite plates.All the six components of the stress can be evaluated directly by the present solid-shell element in terms of the 3D constitutive equation.The performance of present element is evaluated by typical examples of laminated composite plates.The numerical results indicate that the present element can give accurate evaluations of displacements and stresses as well as the accurate prediction of interlaminar stresses for laminated composite plates.The performance studies show that of the linear and nonlinear QC solid-shell elements given in this thesis are very accurate and reliable.Furthermore,because of their explicit element stiffness matrices,the present solid-shell elements possess the high computational efficiency in comparison with the solid-shell elements given in the literature that use numerical integration to compute element stiffness matrices.The present solid-shell elements possess the high computational accuracy compared with the solid-shell elements installed in the commercial codes,particularly in the analyses with the coarse mesh,irregular mesh and the mesh with distorted elements.