Geometrically exact hybrid beam element based on nonlinear programming

This work presents a hybrid shear-flexible beam-element, capable of capturing arbitrarily large inelastic displacements and rotations planar frame structures with just one element per member. Following Reissner's geometrically exact theory, the finite problem is herein formulated within nonlinear programming principles, where total potential energy treated as objective function strain-displacement relations are imposed kinematic constraints. The approximation integral expressions conducted by an appropriate quadrature, introducing Lagrange multipliers, Lagrangian minimization program formed solutions sought based on satisfaction necessary optimality conditions. In addition to displacement degrees freedom at two edge nodes, strain measures centroid act unknown variables quadrature points, while only curvature field interpolated, enforce compatibility throughout element. Inelastic calculations carried out numerical integration material stress-strain law cross-section level. locking-free behavior presented discussed, its overall performance demonstrated set well-known examples. Results compared analytical solutions, available, outcomes flexibility-based beam elements quadrilateral elements, verifying efficiency formulation.