Research on the Correctness of Boussinesq''s Problem

• Main Authors: Yun-Bin Huang, 黃雲斌
• Other Authors: Der-Wun Shaw
• Format: Others
• Language: zh-TW
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/28379120011911727370

碩士 === 淡江大學 === 機械工程學系 === 87 === In 1885, J. Boussinesq published the analytical solution for a concentrated force acting on the surface of a half-space solid. Since then through many works had been done in the fields of elasticity based on Boussinesq''s Problem, yet, the accuracy of Boussinesq''s Problem seems seldom been explored. In this paper, we compare the analytical solutions and the numerical solutions by the finite element method. The analytical solutions include: (1) the Boussinesq''s original work which assumed Bz andβout of four Papkovitch-Neuber-Boussinesq functions Bx,By,Bzandβ, (2) the solution from Saada''s book which used cylindrical coordinates to obtain the same results as in (1), and, (3) we use three functions Bx,Bzandβout of four Papkovitch-Neuber-Boussinesq functions Bx,By,Bzandβ. By comparing the results at different points, we can find that the results have the similar values and similar graphs for the three analytical solutions and similar results for FEM solutions with different element size. So, we may conclude that the Boussinesq''s original method, Saada''s solution, and the analytical method proposed in this thesis are all correct for the problem of a concentrated force acting on the surface of a half-space solid.