Papers by Keyword: Fundamental Solution

Abstract: The basic theory of fast multipole virtual boundary element method (VBEM) is discussed through expanding the fundamental solution, and the algorithm can make the complexities of operation and memory about solution of the equations to be of linear proportion to the freedoms of the problem. Numerical examples are presented to demonstrate the feasibility, accuracy and efficiency of the method. At the same time, the relationships between the order for expansion and the storage capacity, computing time, precision are analyzed, and the influence of boundary points in the leaf to the calculation efficiency is discussed. The corresponding reference value is put forward for the convenience of engineering application.

Abstract: In this work, the spatial theoretical solutions of concentrated normal forces acting in the substrate and at the interface of semi-infinite coating materials have been deduced based on the image point method. The explicit solution is given in the series of the displacement functions corresponding to each image point. It is found that all displacement functions can be deduced by the order of the image point. Numerical analysis has been carried out to verify the theoretical deductions. It is found that the accurate enough theoretical solution can be obtained by only taking the displacement functions corresponding to the first several image points into account. The fundamental solutions for a concentrated force acting at interface of two bonded semi-infinite bodies is also deduced, which is necessary in the analysis of coating materials by using these theoretical solution as the fundamental solution.

Abstract: The problem of a normal force acting in the thin layer of semi-infinite coating materials has been studied by adopting the image point technology in this paper. The explicit fundamental solution is given in the series of the displacement functions corresponding to each image point. The displacement functions corresponding to the higher order image points can be determined from those to the lower ones by the recurrence formula presented in this paper. Numerical analysis by means of the finite element method has been carried out to verify the theoretical results. It is found that the accurate enough theoretical solution can be obtained by only taking the displacement functions corresponding to the first several image points into account.

Abstract: In this paper we shall give practical, numerical and explicit representations of inverse mappings of n-dimensional mappings (of the solutions of n-nonlinear simultaneous equations) and show their numerical experiments by using computers. We derive those concrete formulas from very general ideas for the representation of the inverse functions.