Large displacement extension of consistent shell element for static and dynamic analysis

The superior performance of the consistent shell element in the small deflection range has encouraged the authors to extend the formulation to large displacement static and dynamic analyses. The nonlinear extension is based on a total Lagrangian approach. A detailed derivation of the non-linear extension is based on a total Lagrangian approach. A detailed derivation of the non-linear stiffness matrix and the unbalanced load vector for the consistent shell element is presented in this study. Meanwhile, a simplified method for coding the nonlinear formulation is provided by relating the components for the nonlinear B-matrices to those of the linear B-matrix. The consistent mass matrix for the shell element is also derived and then incorporated with the stiffness matrix to perform large displacement dynamic and free vibration analyses of shell structures. Newmark's method is used for time integration and the Newton-Raphson method is employed for iterating within each increment until equilibrium is achieved. Numerical testing of the nonlinear model through static and dynamic analyses of different plate and shell problems indicates excellent performance of the consistent shell element in the nonlinear range.