Finite element corotational formulation for geometric nonlinear analysis of thin shells with large rotation and small strain

Based on the consistent symmetrizable equilibrated(CSE) corotational formulation,a linear triangular flat thin shell element with 3 nodes and 18° of freedom,constructed by combination of the optimal membrane element and discrete Kirchhoff triangle(DKT) bending plate element,was extended to the geometric nonlinear analysis of thin shells with large rotation and small strain.Through derivation of the consistent tangent stiffness matrix and internal force vector,the corotational nonlinear finite element equations were established.The nonlinear equations were solved by using the Newton-Raphson iteration algorithm combined with an automatic load controlled technology.Three typical case studies,i.e.,the slit annular thin plate,top opened hemispherical shell and cylindrical shell,validated the accuracy of the formulation established in this paper.

Based on the consistent symrnetrizable equilibrated （CSE） corotational formulation, a linear triangular flat thin shell element with 3 nodes and 18~ of freedom, constructed by combination of the optimal membrane element and discrete Kirchhoff trian- gle （DKT） bending plate element, was extended to the geometric nonlinear analysis of thin shells with large rotation and small strain. Through derivation of the consistent tangent stiffness matrix and internal force vector, the corotational nonlinear finite element equations were established. The nonlinear equations were solved by using the Newton-Raphson iteration algorithm combined with an automatic load controlled technology. Three typical case studies, i.e., the slit annular thin plate, top opened hemispherical shell and cylindrical shell, validated the accuracy of the formulation established in this paper.