Grey Systematic Model And Its Application In Problem Of Stress Concentration

The main content of this paper is to study the application and scope of application of GM (1,1) Model in stress concentration. Firstly, the existing extrapolating method of stress concentration factor from measured neighboring stress or strain is reviewed briefly, then, course of GM (1,1) Model, error source and criterion of examining precision are introduced. Electro motive strain is a common method used to measure the maximum strain in stress concentration district, or mostly to extrapolate certain unknown value of stress utilizing some known value. But in fact, a problem lies in the process of using Electro motive strain; we find that, to the same question, precision of results predicted by GM (1, 1) Model differ widely when sampling positions are different. According to the problem that sampling position has certain influence on precision of the GM (1,1) model, in this paper, we try to find out the best sampling position to solve maximum value of stress or strain when using Electro motive strain and extrapolating method of GM (1, 1) Model, so as to offer a theoretical foundation for applying Electro motive strain more reasonably.To compare and analyze, the similar theoretical solution of limitless pulled board with a kind of triangle hole or a kind of square hole is derived using knowledge of Complex Function, and the analytical solution is gained. Combined with circular hole, we give some data groups, through analysis of the result predicted, we know, when sampling position is within specific limits, setting up GM (1,1) Model directly can get to better precision, or else precision is worse.To improve the precision of GM (1, 1) model and to meet the need of the project, GM (1, 1) model needs to be improved. In this paper, production of weighted average is applied into the course of gray systematic GM (1,1) modeling on the basis of proving some properties of it and make traditional GM (1,1) model improved. Better result was gained when improved model is applied to stress concentration. This indicates that this modeling method has certain probability.