Study On Element Stiffness Matrix Of Parabolic Member

Curved beam is found frequently in civil,mechanical and aerospace engineering because of its beautiful shape and smooth line.With the improvement of city construction and human aesthetic,building is becoming increasingly diversified,more and more curved beams are used,especially the parabola member,is found in roof structures,arch bridges and other arc-shaped buildings.It has important value to study parabola member which is the basic component of those complicated systems.The quadratic parabola member with in-plane deformation has been studied in this dissertation.The research work and results are as follows:First of all,a method to derive the element stiffness matrix of the curved beam has been given by using the principle of virtual work,and its correctness has been proved through the constant curvature member.Secondly,by analyzing the infinitesimal element of the parabola member with in-plane deformation,equilibrium differential equations of the internal forces were established,and then the computational formulations of the internal forces for any cross-section and end points were given.Using the internal forces-stress relationships,the constitutive equation and the strain-displacements relationship,the internal force-displacement relationships for any cross-section were given.Using the computational formulations of the internal forces and the internal force-displacement relationships for any cross-section,the differential equations of the axial displacement and radial displacement were established,and then the computational formulations of the displacements for any cross-section and end points were given.Thirdly,using the principle of virtual work and matrix operation,the element stiffness matrix of quadratic parabola member has been given.Finally,the element stiffness matrix of quadratic parabola member has been applied in studying the half parabola member,symmetric parabola structure,asymmetric parabola structure and the structure with two types of parabola member.The internal forces,displacements for any cross-section and the constraint forces have been given.For the quadratic parabola member with in-plane deformation,the element stiffness matrix has been given,which provide a basis for the finite element analysis of structure with parabola member in it.