Scaled Boundary Finite Element Analysis For Elastic Problems With Interval Parameters

There are often existing errors or uncertainty of physical properties, boundary conditions and initial conditions in the practical engineering cases, because of the limitation of the factors such as test level, knowledge and manufacturing process. The error or uncertainty may lead to the result’s wide deviation even though they are very small. The probability model and the fuzzy model are the earlier two types of methods of uncertainty problems, in which a great amount of sampling information on the uncertainty is needed to build the precise probability distributions or fuzzy membership functions. But it seems very difficult or sometimes expensive to obtain sufficient uncertainty information, and hence these two types of methods will encounter much limitations in applicability. The interval model is a lately-developed uncertain calculation method. In this model, interval is applied to describe the uncertainty of a variable. It can be modeling only required the upper and lower bounds of the variables were obtained through the less information.The scaled boundary finite-element method (SBFEM) is a new high-precision numerical method which is semi-analytic and with the advantages both of the finite element and the boundary element methods. The SBFEM applied in the field of solid mechanics first. A new coordinate system which is made up of a radial coordinate and a circumferential coordinate is used by SBFEM. Compared with FEM, only the boundary is numerical discretized in SBFEM, resulting in the decrease of the spatial dimension. Another extrude advantage of SBFEM is that it does not need the fundamental solution so that there is no exist of the problem of singular integral. The scaling centre is chosen on the crack tip when it is applied to fracture mechanics problems, the crack surface require no discretization. The displacements and stress can be evaluated analytically in the radial direction and the stress intensity factors can be calculated accurate and convenient.This article gives a new computational method for uncertainty problem by combining the SBFEM and the interval analysis method. And this method will be a new tool for uncertainty analysis of displacement, stress and SIF. Compared the solution of this method with combination method, we can see that the method of this article is efficient and accurate.