元素釋放法主要是利用移動式最小平方內插的觀念，來建構形狀函數(shape function)。對於相異材料解在界面上為一平滑解(smooth solution)，並且於界面周圍會產生跳動現象（Gibb’s phenomenon），因此所得的數值解精度較差。目前元素釋放法在處理不連續材料界面之主要方法有二:1.節點搜尋經過特別的修正，於界面上施加界面乘子(Lagrange multipliers)。2. Krongauz和Belytschko於1998年提出在界面上，加上特別的跳躍函數(special jump function)，以及給予強度(strength)的參數。 本論文則考慮利用波傳的概念，來處理相異材料界面上節點之選取;利用波傳的觀念，建立一不同於跳躍函數而具有其物理意義的形狀函數。方法有二: 1.波傳之方法僅應用於界面:於界面上利用波傳的觀念，配合節點搜尋的修正。在界面上利用Snell定理推導權值分佈，使界面上為一緊密區間。利用此方法我們可避免界面乘子的施加，減少前處理的時間，不需擴增矩陣即可得到不錯的結果。 2.將波傳應用於整個定義域:考慮將整個定義域以波傳的歷時觀念，進行搜尋整體節點的動作，不同的材料節點彼此會互相影響。以歷時為參數，建立不同的權值曲線，利用不同的權值分佈，使不同的材料具有不同的形狀函數。利用此方法，我們不需在界面上施加節點，經由適當的節點編排，一樣可以得到不錯的結果。 The EFM utilized “moving-least-sqares” (MLS) interpolants to construct the shape function. So that partial derivatives of the approximations, such as strains in the problem are smooth. But smooth solutions then exhibit the well-know Gibb’s phenomenon at the line(or surface) of the discontinuity and the accuracy is poor. Therefore, in the present EFM, we have two methods to deal with material’s interfaces. 1.At the interfaces, We use different methods to search the nodes and add Lagrangian multipliers.2.The technique enriches the approximation by adding special jump shape function at the line of discontinuity with parameters that govern its strength. In this paper, we try to use another method, utilize the concept of waves to deal with the line of discontinuity, utilize the concept of wave’s traveltime to construct the different shape-function in different materials. 1. The snell’s law was only applied in the line of discontinuity: At the interface, we utilize the concept of waves combine with the modification node’s search .We use snell’s law to decide the weighting . 2. The concept of wave’s traveltime was applied in all domain : No matter the nodes in what materials, the node will be influence each other. We use traveltime as parameter to construction different weighting curves and use different weighting distribution to construction different shape-functions in different materials. Use this method, we don’t need adding nodes in the interface. Through us arrange nodes appropriately, we also can obtain good solve.
