Theoretical Optimization Of Element-Free Galerkin Method And Its Application In Numerical Calculation Of Elastic Foundation Palte

Compared with the finite element method,the element-free method discards the concept of the element,and the establishment of the shape function only needs to rely on the node data.This feature makes the element-free method possible to solve some of the legacy problems that are difficult to be solved with the finite element method,such as transient impact,dynamic simulation,large deformation of structures,etc.As a mature element-free method,the element-free Galerkin method has a wide range of applications in the field of elasticity mechanics.Its advantages are flexible node arrangement,simple pre-processing,high precision,and good convergence of calculation results.At the same time,the solution process of the elementless Galerkin method is very open,from the selection of basic function,weight function,weight function parameters,Gaussian integral order,to the introduction of the essential boundary conditions,node distribution form,node integration form.All the selection criteria can be adjusted by human to make them adaptive to different solution environments.This makes the element-free Galerkin method a very promising tool for numerical calculation,which has became one of the research hotspots in the field of mechanics in recent years.However,there are also some disadvantages such as large amount of computation,' and a series of uncertain factors,lack of strong theoretical guidance which brought by strong openness.the bending problem of elastic foundation slab is discussed in detail by means of calculation procedure based on the current research trends of the related issues of the element-free Galerkin method,:(1)Make In-depth discussion of the nature of different weight functions,the selection criteria of weight function parameters,and the influence on the nature of shape functions;(2)The uniform distribution method,the adaptive radius adjustment method,the random approximation uniform generation method,the finite element software generation method have been proposed in this paper,The purpose of using the algorithm to automatically generate high quality nodes is realized,and a basis has also been provided for the manual adjustment of node distribution;(3)The point integral form is improved,and the threshold parameter L is used to filter out the low contribution rate nodes to improve the computational efficiency.(4)Derived the error test formula to design the self-test procedure and screen out the unqualified background grid;(5)Derived the form of combining the element-free Galerkin method with the elastic substrate theory,discussed the method of dealing with the concentrated force;(6)In the foundation plate bending example,different weight functions,point distribution forms,point integral forms,and Gaussian integral order effects on the calculation results are discussed.The reasonable selection range of weight function parameters is obtained,and all the calculation results are compared with the analytical solution and Ansys solution.The case study shows that the calculation program is effective and feasible in this paper.The method proposed in this paper can greatly improve the calculation efficiency under the premise of ensuring the calculation accuracy.It has a certain guiding significance for practical engineering applications.