Discussion On Element Stiffness Matrix Of Connecting Elements In Finite Element Method

As the basis of the finite element method,the element participates in the finite element calculation in the form of element stiffness matrix,which has an important influence on the results.Various finite element software provides many conventional elements,such as beam element,shell element and solid element,etc.The derivation method and stiffness matrix form of these elements are clear.However,in the field of structural analysis of civil engineering,in addition to the conventional elements,a variety of connection elements are often required,such as elastic connection elements and master-slave constraints.clearly.Therefore,this paper takes the elastic connection elements and master-slave constraints commonly used in the finite element software MIDAS and ANSYS as the objects,and explores the derivation method and specific form of the stiffness matrix respectively,so as to provide guidance and help for engineering applications.The specific work and conclusions are as follows:(1)For the elastic connection element in MIDAS,based on the analysis idea of Euler-Bernoulli beam element stiffness matrix,a variety of specific loads of an elastic connection element under three boundary conditions of cantilever,simply supported and sliding-simply supported Taking the action as an example,by analyzing the relationship between the rod end force and the rod end displacement,the stiffness matrix of the elastic connection element under specific parameters is clarified.Finally,the obtained stiffness matrix is verified by the forced unit displacement of the nodes according to the basic concept of each vector in the stiffness matrix.Through parameter adjustment,the influence of parameters such as the distance ratio R of the shear elastic support position,the element length 1 and the stiffness value in each direction on the stiffness matrix is further analyzed,and the influence of each parameter on the stiffness matrix of the elastic connection element is clarified.Stiffness matrix expressions for elastic connections in MIDAS are presented.On the basis of the above analysis results,aiming at the COMB IN 14 element in ANSYS,by extracting the overall stiffness matrix of a single elastic connection element,the specific form of the stiffness matrix of the COMBIN14 element is clarified,and the COMBIN14 element in ANSYS and the elastic connection element in MIDAS are analyzed.difference.(2)Aiming at the master-slave constraints commonly used in MIDAS and ANS YS,the concept of macrocell is proposed based on the direct elimination method.The constraint relationship between the master and slave nodes in the macrocell and the coordinate transformation matrix of the ordinary beam element in the macrocell are studied,and the coordinate transformation matrix including the master-slave constraint characteristics is constructed,and then the element stiffness of the macrocell in the global coordinate system is obtained matrix.Aiming at the two situations in which the direction of the master-slave constraint local coordinate system is from the master node to the slave node and from the slave node to the master node in practical applications,the influence of the direction of the master-slave constraint local coordinate system on the stiffness matrix of the macrocell is analyzed,and the direction coefficient Λ is introduced.The macroecell stiffness matrices of the two master-slave constraints local coordinate system directions are unified.Finally,for three representative application examples of master-slave constraints,a finite element program containing the stiffness matrix of macrocells was written in MATLAB for calculation,and the calculation results were compared with the finite element software MIDAS and ANSYS.The element implements the correctness of the master-slave constraint method in the finite element program.(3)Since the aforementioned method integrates the master-slave constraint characteristics into the macro-unit coordinate transformation matrix,only the unit stiffness matrix of the macro-unit in the global coordinate system can be obtained,but the element stiffness matrix in the local coordinate system cannot be obtained.In view of this,with the concept based on macrocell,under the condition that the macrocell rod end force vector and rod end displacement vector remain unchanged,the macrocell rod end displacement relationship expansion matrix and rod end force relationship expansion matrix are constructed.The matrix obtains the transition stiffness equation of the macrocell in the local coordinate system.The obtained transition stiffness equation is analyzed,the meaning of each term of the rod end force transition vector is clarified,and the method of sorting out the stiffness equation is given.Finally,the element stiffness matrix of the macrocell in the local coordinate system is obtained,which improves the macrocell.applicability.Finally,through the coordinate transformation matrix of the conventional element,the stiffness matrix of the macrocell is converted from the local coordinate system to the global coordinate system,and compared with the stiffness matrix of the macrocell in the global coordinate system obtained by the previous method,it is clarified that the obtained macrocell is in the global coordinate system.Correctness of the element stiffness matrix in the local coordinate system.