Solving Axisymmetric Problems By The Meshless Intervention-Point Method And Its Engineering Applications

In this paper,the meshless intervention-point(MIP)method is used to solve axisymmetric Laplace equations,Poisson equations and Helmholtz equations and two kinds of axisymmetric elasticity body problems,at the same time,the MIP method is applied to calculate soil resilient modulus by laboratory bearing plate.The numerical tests show that the MIP method has an advantage over the common collocation method in solving axisymmetric problems,such as high accuracy,good stability and fast convergence speed.Firstly,some meshless methods are introduced for solving axisymmetric problems,at the same time,the features,advantages and disadvantages of meshless methods are summarized.The weighted residuals method,the moving least squares method for constructing the shape functions of meshless method and the application of essential boundary conditions are introduced.The principle of the MIP method and the moving least square core approximation are introduced in detail.The detailed numerical formulas are obtained by deducing the discrete system equation of the MIP method,and the axisymmetric Laplace equation,the Poisson equation and Helmholtz equation were solved by examples.The numerical results show that the MIP method can solve these axisymmetric equations well,at the same time,it shows that the MIP method is better than the common collocation method in accuracy,convergenceSecondly,according to the characteristics of spatial axisymmetric elasticity problems,it is divided into two types of spatial axisymmetric problems.That is,the axisymmetric tensor problem is the first spatial axisymmetric problem,and the axisymmetric rotation problem is the second spatial axisymmetric problem.The discrete system equations of the MIP method for these two types of axisymmetric problems are derived respectively,and their detailed numerical calculation formula are obtained.To test the advantages of the MIP method for solving these problems,simply supported circular plates,thick-walled cylinders and variable section cylinders are solved,the results show that the MIP method is superior to the common collocation method in terms of accuracy and convergence.Finally,to test the application of the MIP method in road engineering,the MIP method was applied to the numerical simulation of soil resilient modulus by laboratory bearing plate.Through numerical simulation,the results show that the MIP method is effective.