Calculation And FEM Analysis Of Simplified Beam Model Based On Derivation Of Rigidity Matrix

The process of automobile design is generally divided into three parts: Concept design, preliminary detailed design and detailed design. Concept design is very important in the whole process because a well done concept design leads to less iterative work. As to final cost, it is estimated that 70% cost of the automobile design has been determined. Auto-body structure and some structure parameters is defined. Of course, one can define a structure parameter referring from a similar car, but has to control the auto-body structure parameter and performance choose the best version by using FEM because of different general layouts and style. So it's necessary to build a FE model which is either easily made or convenient for calculation.Concept design of car-body can help choosing proper auto-body structure layout and optimizing auto-body structure accessory and then determine the parameter of chief auto-body structure. It is not only flexible but also has critical requirements to the model used in the analysis.This paper makes a new method to get the inertia moment and twisting inertia moment by derivation of rigidity matrix, and then applied displacement of simplified model on the detailed model to make a partial analysis.IDerivation of rigid matrix of a beam1. Basic FEM theoryFEM(Finite Element Method )is the method to calculate continuous body using discretization way which is a similar result on mechanical model. Its basic theory is dividing a continuous body into finite elements. These elements are jointed by a set of nodes which have their own DOFs (Degree of Freedom). Thus the continuous body becomes an assembly of finite elements. The unlimited Dofs of continuous body turns into finite ones of dispirited structure.2. Beam of FEMBeam is defined a linear equal section bar which can resist both axial force and moment to the principle axles and torsion to central axle.Here we coincident the local coordinate axle with the section principle axle and make x axle the central axle. Thus we can express the displacements and forces of the two node this way: = [ ]=[ ], = []=[ ]=[ ],[ ]in the equation, and are axial forces on the nodes i, j. ,,, are the shear of y and z axle. , are moments and ,,, are torsion of y and z axle. Then in the matrix, , are inertia moment and is the twisting inertia moment and A is section area. 3. Derivation of rigid matrix When the displacement is known, ,, are separate parameters. One can get these by a FEM analysis.Calculation of inertia moments and twisting inertia momentChose nodes and divide elementsIn this paper, we use Beam (bar2) and shell to simulate simplified model and detailed model. The frame structure of auto-body is not very complicated and dividing elements is not very difficult so we chose the Quad4 (4 nodes) element the element type for shell. Comparing with Quad3 (3 nodes), four nods elements have better quality. Accordingly we chose Beam(bar2) to simulate simplified model because we always use a line to represent a frame structure of auto-body in the concept design. Creating FE model There are many method to join auto-body beam. Forces are delivered through sections. In the simplified model, the beams are joint point to point, there is only one node on the joint. To apply the same load on the detailed model, we define a independent node on the section center and constraint the Dofs of this node with those on section nodes. Thus forces and displacements on the independent node can delivered equally to section nodes. 3.Calculation of inertia moments and twisting inertia momentThis paper uses three different sections and three dimensions for each section to calculate inertia moments and twisting inertia moment of each section. Forces and displacements are applied according to the derivation From equations below: We can get the parameters we need.Certification of simplified model base...