Simulation Of Ribbed Plates Static Crack By The Meshfree Galerkin Method

Ribbed plate is a composite structure which consists of flat plate and ribbed strip, and it is often used in bridges, ships and aerospace and other engineering fields. Due to the ribbed strip, ribbed plate can provide stronger stiffness than ordinary flat plate, while whose weight are almost the same.In this paper, the element-free Galerkin method is adopted to simulate the problem of ribbed slab static crack, of which the research status have been summarized; and its structure of the approximation function and selection of some of parameters which includes basis functions and the weight functions, nodes, radius of influence domain etc. are discussed, at the same time, the correction of discontinuous problem is also detailed. And then through the first-order shear deformation theory and the moving least square approximation, the displacement field and stress strain field of flat plate and ribbed strip of ribbed plate are given independently, and which are coupled by the displacement coordination equation. Meshfree equation is derived according to the principle of minimum potential energy for the linear bending of ribbed plate. The displacement and stress of ribbed plate are determined by applying the essential boundary conditions with complete transformation. Finally the corresponding stress intensity factor is determined by using the J-integral. The paper adopt a new weight function based on the distribution of t-lwhen constructing shape function of ribbed plate, and use the diffraction law to modify displacement item, of which the basis function use expansion basis function with singularity. By using the method of this paper can avoid grid refactoring which emerge in traditional finite element method when solving crack propagation problem.The C++language is used to establish the calculation program of ribbed plate with crack in this paper, at the same time a large number of examples are analyzed, of which the results obtained will be compared with solutions of ANSYS finite element software to verify the accuracy of the method in this paper.