The Comparison of Three Analytical Solutions and F.E.M Solutions of Concentrate Forces Acting Inside a Half-Space Solid

• Main Authors: Yung-Kuan Ni, 倪永寬
• Other Authors: Der-Wun Shaw
• Format: Others
• Language: zh-TW
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/18804787198785654408

碩士 === 淡江大學 === 機械工程學系 === 87 === In 1936, R. D. Mindlin published the analytical solution of concentrated force acting inside a half-space solid. Since then, the accuracy of that solution seems seldom been explored. This problem is one of the basic type of problems in the three-dimensional elasticity. Its accuracy has great influence on the research of three-dimensional elasticity. In this work, we analyzed the Mindlin’s Problem by two different analytical methods in addition to Mindlin’s original methods. In Mindlin’s original method, only two functions Bz andβare chosen out of four Papkovitch-Neuber-Boussinesq functions Bx, By, Bz andβ. In this work, we choose three functions Bx, Bz andβout of four functions. Also, we model the Mindlin’s Problem by finite element method. The package of COSMOS/M for the finite element method was used for the solution. The finite element method with increasing number of elements can offer a check for the analytical solutions. However, for practical application of the results, more than one method of analysis is suggested. Then, we compared the solutions by the three analytical methods and the finite element solution. We find that the results of displacement components and stress components have similar graphs and similar physical similarity for all four methods used. The maximum values for the four methods are compared also. We get similar answers with an accuracy that may be acceptable.So, we may conclude that Mindlin’s original work is acceptable. The two different analytical methods proposed in this thesis are also acceptable.