Study On The Theory And Accuracy Of Element-free Method In Elastic Foundation Plate

Meshless methods, which are new kinds of numerical methods, are developed in recent years. They only need information of nodal parameters instead of elements information. Furthermore, they also have other merits, including the high accuracy, the convenience of the postprocessor, the elimination of the volume-lock, the improvement of the convergence and continuity and so on. Among these meshless methods, Element-free Galerkin method is one of the most typical and promising meshless methods.In this dissertation, many works have been done on the basis of the summarization of the merits of all kinds of meshless methods after a large number of relevant references are read and studied. The basic ideas, principles of meshless methods and their development in the recent years are introduced synoptically. Applications of Element-free Galerkin method in elastic foundation plate are studied deeply and some useful conclusions are obtained as follows: (1) Comparisons between numerical solutions and analytical solutions for several different styles of weight functions, including Gaussian weight function, spline weight function and singular weight function etc, are performed. The results show that Gaussian weight function is the best one. (2) Ranges of relevant parameters for Gaussian weight function are given. (3) Influences of nodal distribution schemes and the number of Gaussian integrated dots on computational results are discussed. In conclusion, if we adopt the Gaussian weight function, the appropriate selection of their parameters and suitable nodes densification in boundaries, then a good result will be obtained in the computation of elastic foundation plate by Element-free Galerkin method. The results also illustrate the rationality and validity of Element-free Galerkin method in treating the high-order continuous problems.