Application Of Unified Analytical Beam &finite Nodal-Line Method In The Analysis Of Thick-Walled Open Section Members

In view of the situation that the existing beam theories are not applicable to the mechanics characteristic analysis of thick-walled open section members,this thesis adopts a unified analytical beam(UAB)model and a finite nodal-line method(FNLM)to study the bending and torsional problems of the thick-walled open section members.The unified analytical beam model is a model that cannot be limited by the cross-sectional shape and size of a beam-like member,as well as by the loading modes applying to the member,and can be applied to a beam-like member with an arbitrary aspect ratio;the finite nodal-line method is a specially designed novel numerical analysis methodology for the unified analytical beam model.Using the unified analytical beam model and finite nodal-line method can not only solve the transverse-force bending problems of the thick-walled open section members under arbitrary loads,but also attain the uneven warping deformations,numerical results of maximum warping normal stress and maximum shear stress,and stress distributions on the cross section of the member under the action of constraint torsion.The main work and major conclusions of the thesis are as follows:(1)How to establish the governing equation and boundary conditions for the static problem of the thick-walled open section members are discussed by using the unified analytical beam model and finite nodal-line method.(2)The method for determining the cross-sectional stiffness matrices that correspond to the basic unknown displacement functions in the governing equation is investigated,and the finite element isoparametric transformation thought is introduced into the method successfully.(3)The computational results of the finite nodal-line method are compared with those of Euler-Bernoulli or Timoshenko beam,as well as the finite element software ANSYS so as to illustrate the rationality and feasibility of the unified analytical beam model and finite nodal-line method.(4)The mechanics problems of several typical thick-walled open section members are computed with the unified analytical beam model and finite nodal-line method so as to deeply understand the mechanical characteristics of the thick-walled open section members due to their transverse loads or concentrated torques.(5)The computational results indicates that: the thick-walled open section members have a similar mechanical characteristic to thin-walled open section members,in other words,a thick-walled open section member has a torsional(bending)center which is inconsistent with its cross-sectional centroid;when the external loads do not pass through its torsional center,the member will produce a coupled bending-torsional deformation;different from a thin-walled open section member,the warping normal stress and shear stress distributions on the cross section of a thick-walled open section member distribute nonlinearly under the action of a centralized torque,and the maximum stress varies with the cross-sectional shape and size of the member.