A nodal integration axisymmetric thin shell model using linear interpolation

Abstract

This paper proposed a nodal integration model for elasto-static, free vibration, forced vibration and geometric nonlinear analyses of axisymmetric thin shells using two-node truncated conical elements. The formulation is based on the Kirchhoff–Love theory, in which only the two translational displacements are treated as the independent field variables. A gradient smoothing technique (GST) is employed to relax the continuity requirement for trial function, so that linear shape functions can be used to interpolate both the tangent and normal displacement fields to the meridian. Based on each node, the integration domains are further formed, where the membrane strains and curvature changes are computed using a strain smoothing operation incorporated with a tensor transformation manipulation. The smoothed Galerkin weakform is then used to establish the discretized system equations. In order to accurately track the deformation path in geometric nonlinear analysis, the Newton–Raphson iteration in conjunction with the arc-length technique are employed here to solve the equilibrium equation. Numerical examples demonstrate that the present method can achieves higher accuracy and lower computing cost compared with the conventional finite element model.