Space Equivalent Truss Element And Its Application

The finite element method(FEM) is applied widely in engineering as a numerical analysis method, but the traditional finite element method has shortcomings such as the complexity of traditional finite element method and the inaccurate description of cracks. In order to deal with these disadvantages, a new element—space equivalent truss element was proposed in this article, basing on the three-dimensional entity element in the elastic mechanics and combining with the analytical method of plane equivalent truss element. Space equivalent truss element, which is inferred from the space stress element of corresponding size based on the principle of stiffness equivalent and intensity equivalent, is a cuboid element composed of eight hinge points and twenty four truss bars. This element can turn three-dimensional force of an entity element into axial force of truss bars, making calculation simplified, and it also can describe the cracks directly and conveniently by fracture of truss bar. This article includes following contents:Firstly, based on the stiffness equivalent and intensity equivalent of space equivalent truss element and three-dimensional entity element, the equivalent element rigidity, the equivalent area of the truss and the formula of axial force were analyzed, and in order to prove that the theory is also applicable to the non linear elastic material, space equivalent truss element under any stress was also analyzed. Then problems related to how space equivalent truss element used in nonlinear analysis of reinforced concrete structures were discussed, such as material constitutive relation, failure criteria, the finite element model of reinforced concrete, crack simulation, solutions of nonlinear equations, steps of nonlinear analysis of reinforced concrete structures and so on. Afterwards, computer programs based on the space equivalent truss element for linear analysis and nonlinear analysis were written by MATLAB language. At last, a simply supported beam under uniform distributed load and a reinforced concrete bridge pier under two-way excentral pressure were analyzed by the theory and the finite element programs above, and the results were compared with which got from the traditional finite element method and material mechanics method, the causes of error and the methods to reduce the error also were discussed. The results show that this model is feasible to analyze reinforced concrete structure, and it can satisfy the requirements of engineering precision and accurately describe the cracks.