Geometrical Stiffness Matrix of Spatial Thinwalled Beams in TotalLagrangian Formulation

Abstract:

Based on the theories of Timoshenko’s beams and Vlasov’s thinwalled members, a new geometrically nonlinear beam element model is developed by placing an interior node in the element and applying independent interpolation to bending angles and warp, in which factors such as shear deformation, coupling of flexure and torsion, and second shear stress are all considered. Thereafter, geometrical nonlinear strain in TotalLagrangian is formulated and geometrical stiffness matrix is deduced. Examples manifest that the developed model is accurate and feasible in analyzing thinwalled structures.