A Smoothed Finite Element Method (SFEM) for Linear and Geometrically Nonlinear Analysis of Plates and Shells

Abstract

A smoothed finite element method (SFEM) is presented to analyze linear and geo- metrically nonlinearproblems of plates and shells using bilinear quadrilateral elements. The formu- lationis based on thefirst order shear deformation theory. In the present SFEM, the elements are fur- therdividedintosmoothingcells toperform strain smoothingoperation,andthestrainenergy ineach smoothing cell is expressed as an explicit form of the smoothed strain. The effect of the number of divisionsofsmoothingcellsinelements isinvesti- gatedindetail. Itisfoundthatusingthreesmooth- ing cells for bending strain energy integrationand one smoothing cell for shear strain energy inte- gration achieve most accurate results and hence these numbers recommended for plates and shells in this study. In the geometrically nonlinear anal- ysis, the total Lagrangian approach is adopted. The arc-length technique in conjunction with the modified Newton-Raphson method is utilized to solve the nonlinear equations. The numerical ex- amples demonstrate that the present SFEM pro- vides very stable and most accurate results with the similar computational effort compared to the existing FEM techniques tested in this work.