Improvement Of Meshless Methods In Structure Computations

In recent years, meshless methods have been proposed and achieved remarkable progress in numerical computations, the main feature of which is mesh can be eliminated wholly or partly, and reducing difficulty in mesh generation of the structure, and not like FEM in which mesh generation can be a very time-consuming and expensive task. Various kinds of meshless methods have been presented. It is accepted generally that a method belongs to a meshless method if only meshes are not used during approximating field functions. The meshless methods based on Galerkin variational principle have complicated computation and background cell structures for quadrature. With satisfying accuracy, the study was developed from reducing computation, and improving computation efficiency and realizing truly meshless. The program was coded in FORTRAN for theory validation, and comparison of numerical results.Radial basis function was used to construct the interpolant, combining collocation method to form radial-basis-function strong-form meshless method (we use the acronym, RBFS). Several 2D Poisson's equations were solved. The relationship between the solution precision and the free parameters in the radial basis functions and some influence factors were investigated. The formula for the optimum value of the free parameters in the radial basis functions were obtained.For making coefficient matrix sparse, the shape function possessing delta property is constructed by radial basis function, then the interpolant is done by the shape function, and combining collocation method to form improved radial-basis-function strong-form meshless method (we use the acronym, IRBFS). By solving the same Poisson's equations that done in RBFS, we got the influence rule of sparse coefficient matrix on accuracy, and proved the appliance of free parameters' optimal value formula in the radial basis functions. By solving 2D elastic examples, we checked that IRBFS, formula for the optimum value of the free parameters and sparse rules were applicable to such problems; and IRBFS is feasible in engineering computation.Displacement funtion was approximated by Sibsonian interpolation and non-Sibsonian interpolation on the basis of natural elements, in which the shape function possesses delta property, combining local Petrov-Galerkin method to form the meshless local Petrov-Galerkin methods based on natural elements. By this meshless method, we solved patch test, torsion of elastic cylinder and cantilever beam, and compared the numerical results with those of FEM and other meshless methods. The conclusions show the accuracy of non-Sibsonian interpolation will reduce and that of Sibsonian interpolation won't reduce obviously when the nodal pattern changes. We got that non-Sibsonian interpolation is more sensitive to nodal patterns, and its advantages are ease of implementation and relatively cheap to evaluate. We attained that the meshless local Petrov-Galerkin method based on natural elements is highly accurate, stable and efficient...