On shear and extensional locking in nonlinear composite beams

A displacement beam finite element is derived based on a nonlinear kinematic model for a pretwisted composite beam. Elements based on linear, quadratic and cubic interpolation functions are developed. The reduced/selective integration technique is employed to investigate shear and membrane locking for each type of element. Various numerical integration rules are examined to determine the best integration scheme. Numerical results are presented on a wide range of beam problems to evaluate the performances of the three types of elements. None of the Gauss quadrature rules investigated, in particular, the three uniform reduced rules, have shown spurious mechanisms. Using the best scheme for each element, the performance studies carried out have shown that the cubic interpolation was the most efficient for almost all the problems studied.