Research On The Plane Equivalent Truss Model Based On The Finite Element Method

The finite element method is grown from the continuous medium mechanic, currently it is a widely Value computational method. the question's premise is various units neighboring boundary displacement coordination. The FEM separates the continual territory into a group of finite elements, then subdivides the elements to approach the solution area. As a result of different connection way and various element shapes, therefore it may adapt the complex geometry solution region. Secondly, uses each element the approximate function (shape function) to express the unknown field function which required on all solution territory. thus turns a continual infinite degree of freedom question into a separate finite degree of freedom question. As long as put out the physical solution on the nodes of all elements, we can determine the components'unknown solutions. Step by step, if we choose the appropriate shape function ,along with grid density reducing, the approximate solution gradually will tend to the exact solution. Thirdly, FEM obtains the sparse belt-shape matrix ,this enhances the computer's memory and computation efficiency greatly ,the FEM has advantage for dealing with the large-scale problems.We can know the principle is simple from above, but as a result of element connection way and element shape multipulication, as well as the appropriate shape function or not , cause the FEM more troublesome aiming at the concrete question. It is well based on suh application background, the paper proposes one kind of simpler practical element model-plane equivalent trusss element model. The model embarks from the macroelement under plane-stress problem, through the equivalent node_displacements,the microelements is equivalent as a truss model with six bars which can only be tensed or compressed along their axis,to analyze the mechanic behavior of the microelement under biaxial or tri-axial stress. the model becomes relatively quite simple ,the amount of the computation is small ,mechanics conception is clear and direct-viewing ,thus this method solves the computation efficiency . The relations between element and element or interior element are all biaxial bars, cause the relations more direct-viewing ,the crush(crash)between elements is easily traced. In a word, the stresses process is clear, and the analysis process is simple,which give the research on the structure or the component's mechanics performance conveniently.Although the model has the above merits, but the domestic and foreign research has just started,many questions are not sufficiency, for instance the shearing–wall model in the structural engineering. Although researchers have obtained the equivalent beam ,column and Diagonal support and section parameter, it is only equalvalent for the frame structure in component, not the axil bar in plane stress. Moreover after the truss model enters the non-linearity period, how to determine the rigidity and the destruction is quite difficult, thus the model is quite limited. So this paper begin from the plane stress element, first, according to the static equivalent principle we turn the plane stress element and the stress into the plane truss model and point load in the truss model, then deduce the rigidity formula. Secondly, use the traditional finite element method's isoparametric element, we can transform the complex quadrangle unit into the regular plane square shape, also make the research for the stress and strain in the linear stage between two element shape. Thirdly, utilize the finite element method and the finite calculate steps, infers the element stiffness matrix, the geometry matrix ,balanced matrix and so on. finally, through the visualization finite element analysis procedure, utilizes this kind of truss model in the reinforced concrete structure. In the model, the concrete element uses the equivalent plane stress model,the steel bar uses the unidemensional pole unit, using the equivalent stress-strain relations to analysis all kinds of component in the civil enigeering, and exploratory proposed the element destruction criterion. The comparison between the method proposed in this paper and the commercial finite element anslysis software ANSYS9.0, the result indicates the method proposed in paper is a simple and feasible method with the same project precision .