A Finite Element Model Of Spatial Thin-walled Beams With Arbitrary Cross Section

Very similar to the case of ordinary beams,when stout thin-walled beams loaded by a lateral force,shear deformation is predominant in the whole traverse displacement and must be included in calculation.Otherwise a great error would be made.And if the kind of thin-walled beams simultaneously subjected to torsion,traverse and torsional shear deformation might be coupled.In regard to those thin-walled beams with sections whose centroid and shear center don't coincide,there would be additional torsion following flexure,namely coupling of flexure and torsion.When non-uniform torsion occurs,the second torque that the second shear stress produces about the shear center would have certain effect on torsion.In view of mention above,a new spatial thin-walled beam element model considering forementioned those effects and available in the analysis of thin-walled structures is aimed to be established.Based on the Bernoulli-Euler beam's plane cross-section hypothesis under flexure and Vlasov's rigid contour premise under non-uniform torsion,a spatial thin-walled beam element with 2 nodes and 14 DOF is developed by independently interpolating bend angles about two prime inertial axes of cross section and warp angle with an interior node set at the midpoint of the element length and the goal is achieved.Thereafter,the established elastic finite element model is extended to nonlinear analysis.In the aspect of geometrical nonlinearity,from the incremental virtual work equation described in the referential configuration at the moment of T=0 and T=t, geometrical stiffness matrices in TL formulation and UL formulation are deduced respectively.In the aspect of material nonlinearity,assume that the material is perfect plastic, complying with Von-Mises's yielding rule and related flowing rule.With the finite segment method,one of distributed plasticity models,where certain Guassian points are collocated along the element length and the natural coordinate of cross section,the element elasto-plastic stiffness matrix is derived by Guassian quadrature.In every incremantal step,constitutive integration is performed by the generalized midpoint method.Also,on the basis of the geometrically nonlinear model and material nonlinear model,a spatial thin-walled beam element with doubly nonlinear behavior is produced. According to the model brought forward,coorespondent program is worked out by object-orientated C#.NET.Some examples are enumerated and their results calculated by the model are compared with theoretical solutions of material mechanics,thin-walled structure mechanics and structure mechanics,and with numerical solutions of beam189 beam element and shell181 shell element of ANSYS.The comparison illuminates that the model excels beam189 element in the aspect of precision and reliablility with results much closer to the theorectical solutions and numerical solutions of shell181.Finally,the model is applied to the engineering structure and Koiter shell under the central load is numerically analyzed.Comparison of the results with beam189 element manifests that the model is accurate and efficient,and that its application without being confined to single thin-walled members covers the field of spatial thin-walled structures.