A New Fast Algotithm Method Using Response Surface In Structural Reliability Of Elasticity-Plasticity

It is common to re-analyze the elastic-plastic structure because of the design variables are changed when using Finite element method (FEM) to analyze in the engineering. It's uneconomical to solve new plastic finite element equation every time directly in a large structure system which usually involves very large computational costs. As a result, an algorithm that can calculate quickly and effectively will have practical significance to reanalyze the elastic-plastic finite element. According to the documents and research in and out of China, less attention is being paid on elastic-plastic structure when compared with that of the elastic structure. This paper gives a quick calculation method to resolve the problem above. In the calculation of the bars of the lowest reliability, it is a common method to use the response surface to calculate the reliability of the structure when the limit state equation is unknown. This method, which needs to calculate functional values of the structure related repeatedly, involves many samples and variables of these samples have narrow randomness. So the quick calculation method can be used when response surface method is used to calculate the reliability of elastic-plastic structure.In the first part, it introduces the calculation procedures of the Finite Element Method as well as the basic theories like isoperimetric element and gauss integral on the one hand; and theories of elastic-plastic that include the constitutive relations, yield criterion, strengthening model etc on the other hand. What's more, it also gives a brief introduction to theories of the elastic-plastic finite element and numerical method of nonlinear equations like iteration, Load increment method and mixed method and so on. Meanwhile, programs of elastic-plastic FEM is complied and compared the results with calculations made by ABAQUS finite element software.It shows the programs complied is right.In the second part, it is mainly about the optimum design of the elastic-plastic structure and calculation of structure reliability among different samples by means of stochastic analysis. The principle and computation procedure of these samples are the same. The only difference lay in the change of one or some of the material or the Geometric Parameters. So there is certain similarity with those samples used in calculation. Consequently, based on the elastic-plastic finite element, a kind of quick algorithm of obtaining informations of an unknown sample is developed by making use the informations of a prior known sample. The principal process of this algorithm is to use the calculation of the standard samples to predicate information of the unknown samples, therefore the number of iteration is reduced and the computing efficiency of the algorithm is improved too. Meanwhile, programs of elastic-plastic FEM is complied and compared the results with calculations made by ABAQUS finite element software. It shows this method is practicable and the idea is right.In the third part, many mature algorithm methods, like JC Method, Geometry Method and Response Surface Method can be used to calculate the reliability of structure. As a general rule, Response Surface Method is used to calculate samples when limit state equation of structure is unknown. In the process of calculation, finite element method and experiments are used repeatedly to make sure of functional values of samples needed. The quick algorithm is applied to obtain the objective function values of structure and the computing result is compared with result made by common elastic- plastic process. Numerical calculating analysis shows that it is feasible and effective to obtain structure reliability by using of this new quick algorithm which can cut down iteration times.To get high reanalysis computational efficiency of the elastic-plastic finite element, a new algorithm is put forward and applied to practice in this paper. It has the certain impetus function and application value to the improvement of computing efficiency in Elastic-plastic finite element reanalysis.