A strain gradient quadrature element for geometrically exact beam with torsion warping

Abstract

Based on the weak form quadrature element method, this paper proposes a geometrically exact strain gradient beam formulation incorporating torsion warping effects. This formulation provides a computationally efficient numerical scheme for analyzing size dependent arbitrarily cross-sectional beams undergoing large displacements and rotations. By accommodating all high order strain and strain gradient terms in the formulation, the Wagner effects that crucial to the model's accuracy are taken into account. The warping functions determined by cross-sectional governing equations involving strain gradients are obtained using a C1 quadrilateral quadrature element procedure. Five numerical tests are presented to demonstrate the validity and accuracy of the proposed formulation, while investigating the influences of size effects and Wagner effects on nonlinear behaviors of beam structures.