Research On Fuzzy Stochastic Element-free Galerkin Method Of The Structure With Crack

Uncertainty mainly includes fuzziness, randomness and unascertained characteristics. It is closely related to our daily life and is in existence in many projects. Fuzziness and randomness is the main research task of this paper. Fuzziness is originated from the discrepancy between people's perception of an object and the nature of the object. Randomness is decided by the characteristics of an object and it involves many irregularities, and possibilities.The meshless method has gone through over thirty years of development and it is still a new subject in the numerical calculation, but it compensates for huge calculation volume and low accuracy in the finite element method in dealing with issues like the stress soncentration, large deformation, explosion, impact, crack propagation.In spite that the meshless method is not in a dominant position, it is still an excellent method and can be applied to many domains. With the development of science and technology, it will become a mainstream method in mechanics numerical analysisIn view of the limitations of fuzzy finite element, stochastic finite element and fuzzy-stochastic finite element, this paper combines fuzzy random theory and element free Galerkin method to conduct research on some issues with regard to element free Galerkin method, uncertainty and fracture mechanics.â… . It introduces the beginning, history and current development of the meshless method and generalizes related theories of uncertainty.â…¡. It systematically narrates the basic theory of element free Galerkin method and studies the characteristics of the nature and selection of basis function and weight function.â…¢. By studying the fuzzy random theory and fuzziness theory, the paper presents a new solution to solve uncertainty----Fuzzy Stochastic Meshless Method. An equilibrium equation has been successfully deduced and validity its correctness has been tested.â…£. This paper conducts research on fracture mechanics and applies the new solution into cracked structures. The numerical example proves the correctness.