The Analytical Solutions of Two Concentrated Normal Forces Acting At The Centers of The Top and Bottom Surfaces of A Rectangular Block

• Main Authors: Kuang-Hung Chen, 陳冠宏
• Other Authors: Der-Wun Shaw
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/30676075268154211260

碩士 === 淡江大學 === 機械工程學系 === 90 === Title of Thesis: Total Pages:111 The Analytical Solutions of Two Concentrated Normal ForcesActing At The Centers of The Top and Bottom Surfaces of A Rectangular Block Keyword: Papkovitch-neuber-boussinesq functions, Analytical solution, Mathematica, Ansys, Numerical solutions Name of Institute: Graduate Institute of Mechanical Engineering, Tam-Kang University Graduate Date: June, 2002 Degree Conferred: Master Name of Student: Kuang-Hung Chen Advisor: Der-Wun Shaw 陳 冠 宏 Fung-Huei Yeh Abstract: In this study, The Green-Shaw functions is studied to substitute for traditional of the Green functions, from the stress of relation formula and then to compute the analytical solutions of two concentrated normal forces acting at the centers of the top and bottom surfaces of a rectangular block, also to make data of the numerical and drafting by Mathematica is used, in the end, The FEM software of Ansys to produce verify is operated, and to confer the theory have correctness. The main topic of this paper is to use Green-Shaw functions for a rectangular solid, then take 26 terms (64 terms). With the Green’s function in integral form, another reason is that according to proof of Eubanks [1] and Sternberg [11], any three independent Papkovitch-Neuber-Boussinesq functions are required for any geometrical shaped convex domain in 3D space, so the selction of the three functions Bx ,Bz ,β are justified, solve the Bx ,Bz and β, the analytical solutions of two concentrated normal forces acting at the centers of the top and bottom surfaces of a rectangular block was then derived, and we use Mathematica to draw the analytical solutions of displacement and stress distribution digrams and the numerical solution of displacement and stress on the different surfaces to test and verify FEM software of Ansys to get the numerical solution to draw the digrams and the numerical solution of displacement and stress on contrast surfaces, to go deep into physics rationality, further to analyze a contrast both sides difference and equally. For many problems that haven’t the analytical solutions of the stress and displacement in the future, must to consult and develop an important analytical method.