Contribution To Linear And Nonlinear Static And Dynamic Analysis Of Thin Shells By Triangular And Quadrilateral Flat Shell Finite Elements With Drilling Rotational Degree Of Freedom
Résumé: Linear and geometrically nonlinear static and dynamic finite element analysis of thin shells using triangular and quadrilateral flat shell elements with in-plane drilling rotational degree of freedom is presented. The flat shell elements are obtained by combining the “DKT” and “DKQ” Discrete Kirchhoff Theory plate bending elements and membrane elements with drilling rotation. The membrane elements developed are a quadrilateral element with drilling rotation based on the modified HUGHES and BREZZI variational formulation and a triangular element with drilling rotation based on the Enhanced Strain formulation. The transient dynamic analysis is carried out using Newmark direct time integration method, while the nonlinear analysis adopts the updated co-rotational Lagrangian description. In this purpose, in-plane co-rotational formulation that considers the in-plane drilling rotation is developed and presented for triangular and quadrilateral membrane elements. Furthermore, a simple and effective in-plane mass matrix that takes into account the in-plane rotational inertia, which permit true representation of in-plane vibrational modes is adopted. Finally, these developments are implemented into three dimensional flat shell finite elements with six degrees of freedom. A finite element analysis program is also developed to check the accuracy of the developed elements. The developed elements are first thoroughly tested for static and dynamic analysis of plane stress problems, then, they are tested for general shell problems. The effectiveness of these elements shown by the selected numerical examples to predict the nonlinear dynamic response of shell structures while remains economic, is adequate to ascertain that these elements would perform well in the case of nonlinear static and dynamic analysis of general shells.
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