二維及三維異向彈性體 受時間週期性荷重之格林函數

Abstract

本文所要推導的是，無邊際（ Unbounded ）均質( Homogeneous )異向彈性體( Anisotropic elastic materials ) 於二維（ Two - dimension ）狀況下承受線性時間週期性荷重（ Line time - harmonic load ），或於三維（ Three - dimension ）狀況下承受點時間週期性荷重（ Point time - harmonic load ）之格林函數（ Green’s function ）。此格林函數需要處理積分表示和邊界積分的問題，可以運用邊界元素法( Boundary element method ) 推導此格林函數。由於邊界元素法在處理等向彈性體分析波傳( Wave propagation) 方面問題時，扮演著相當重要的角色，所以希望藉由邊界元素法在處理異向彈性體於彈性動力方面問題時，能與處理等向彈性體一樣的容易。本文將以推導所得到的格林函數，於等向彈性體材料與參考文獻上的解析解比對，以確認推導所得到的格林函數其正確性。於二維異向彈性體材料，推估格林函數其數據結果；於三維異向彈性體材料，與參考文獻比較數據結果是否吻合。另外運用傅立葉轉換的方式，解決二維及三維異向彈性體受時間週期性荷重狀況下所會遭遇到的問題，可以證明除了運用Radon轉換來推導格林函數，當然也可以使用傅立葉轉換來處理相同狀況的問題。本文期望運用座標轉換方式，先將材料性質轉換到新座標系，在得到轉換成新座標系後的結果，再次運用座標轉換的方式，轉換回原始座標系，即可得到原始座標系下，所欲求得的結果，亦即經由座標轉換，來處理觀察點方向不同時的狀況。

Abstract Generally speaking , no matter which kind of material want to ask the displacement or the strain , it is the way that tries to get the Green’s function under this state . This paper is to determine the Green’s function in an unbounded homogeneous anisotropic media generated by the application of a two-dimensional time-harmonic point load , or the application of a three-dimensional time-harmonic line load . This paper based on the Fourier transform is presented to determine the Green’s function in a anisotropic media due to the application of a time-harmonic load .This Green's function needs to deal with the problem of integral representations and boundary integral equations by the boundary element method . Because the boundary element method has been playing a very important role in analyzing wave propagation problems in isotropic media . It hopes to deal the elastodynamic problems for anisotropic media as easy as isotropic media . In the isotropic media , it needs to estimate its data result of the Green's function with the data result of the analytical solution . This paper expects to use the coordinate transformed to deal the state with different viewpoint directions.