Full and von Karman geometrically nonlinear analyses of laminated cylindrical panels

Abstract

A total Lagrangian-type nonlinear analysis for prediction of large deformation behavior of thick laminated composite cylindrical shells and panels is presented. The analysis, based on the hypothesis of layerwise linear displacement distribution through thickness, accounts for fully nonlinear kinematic relations, in contrast to the commonly used von Karman nonlinear strain approximation, so that stable equilibrium paths in the advanced nonlinear regime can be accurately predicted. The resulting degenerated surface-parallel quadratic (16-node) layer element, with 8 nodes on each of the top and bottom surfaces of each layer, has been implemented in conjunction with full and reduced numerical integration schemes to efficiently model both thin and thick shell behavior. The modified Newton-Raphson iterative scheme with Aitken acceleration factors is used to obtain hitherto unavailable numerical results corresponding to fully nonlinear behavior of the analyzed panels. A two-layer [0/90] thin/shallow clamped cylindrical panel is investigated to assess the convergence rate for full and reduced integration schemes and to check the accuracy of the present degenerate cylindrical shell layer element. Accuracy of the von Karman nonlinear approximation, currently employed in many investigations on buckling/postbuckling behavior of thin shells, is assessed, in the case of laminated thin cylindrical panels, by comparing the numerical results obtained using this approximation with those due to fully nonlinear kinematic relations, especially in the advanced stable postbuckling regime.