The Numerical Simulation Methods For Non-Linear Stochastic Structure

The stochastic problem of engineer structure is analyzed by the stochastic finite element method generally. Aim at the efficiency and precision of the stochastic FEM, two kind of new stochastic FEM are put forward and the correlative theories and methods are established:1 The stochastic FEM based on Gauss integral methodEstablish the method of Stochastic FEM based on the Legendre integration. The method could be used for all sorts of random variable using equiprobable transform formula. Studied the influence of the integrate points to the response random. The result show that the first moment reach high precision although the integration points is fewer. The precision of second moment is higher as the increase of the integration points. In general, the integration points is fewer. The examples show the efficiency of the method and verified by Monte-Carlo stochastic FEM. On the base. Stochastic FEM including random multi-variables is developed. In order to decrease the computation, a reduction form is deduced to get the response of random multi-variables from single variable, and verified by Monte-Carlo stochastic FEM.As Legendre integration is one of Gauss integration, it is nature to apply the others Gauss integration into stochastic FEM. Stochastic FEM based on Hermite is established concretely. On computing random multi-variables problem, the method is same as Legendre integration.2 The theory and method for multi-samples redundancyOn the base of studying Neumann stochastic FEM, propose the two conceptions: multi-samples redundancy and compressed redundancy algorithm. Establish the Monte-Carlo stochastic FEM based on compressed redundancy algorithm.The research also is effective for all sorts of intelligent computing method, such as genetic algorithm simulated annealing algorithm, in the term of the efficiency and precision.Prove the equivalence between the Neumann Stochastic FEM and the equated-stiffness iteration method. Two more efficient methods are introduced into Monte-Carlo stochastic FEM according to Neumann Stochastic FEM. Establish PCG compressed redundancy method. The characteristic sample is chose as Preconditioned matrix, and the problem solved as the Conjugate Gradient; Establish quasi-Newton compressed redundancy method using Borden 1 order algorithm. The efficiency of the two methods are proved in theory. The examples show that the two methods could apply in larger-scale random variable problem. Solve the problem of large variation that the Neumann Stochastic FEM can't do.Specially, in quasi-Newton compressed redundancy method, the study shows that approximate inverse-matrix is just required in the method. On this base, develop the sample organized technique. The examples prove efficiency of the method. At last, establish the load-random compressed redundancy method about non-linear problem. 3 Stochastic analysis about vessel stent.According to material and technical of manufacture, make certain that the width and the thickness of shank section are 1 -dimension random field.On the base of 2-dimension part modeling and developed stochastic theory, study new vessel stent in detail, using stochastic FEM. Get the stochastic response of axis-shrink ratio and radial-spring ratio.