元素釋放法(Element Free Method, EFM)是建構在以「移動式最小平方(Moving Least Squares, MLS)」內插的觀念來處理定義域內節點資料之一種無網格(meshless)數值方法。因為只需節點的資料卻不受限於節點與元素間的關聯條件，所以在需要利用「適應性方法(adaptive method)」處理問題時較有限元素法具有更大的靈活性。 以MLS觀念推導位移內插函數時，與取樣點相關連的節點數目遠超過基底函數自由度的數目，必須給予每個節點相對應的權重，方能使數值解能反應取樣點附近的真實物理狀態，如何在正確與合理的範圍選擇加權函數(weighting function)，對EFM而言是重要的課題。 MLS推導位移內插函數時往往要耗費許多時間在相關節點的搜尋上甚不經濟。本論文提出固定影響圓半徑的方法來加快運算時間，數值模擬證明在無元素法中採用規則網格，及確定大小的影響圓，有助於計算時間的節省；尤其節點數目甚多時，節省的時間更是可觀。 本論文在一次基底函數(base function)的情況下，以懸臂樑問題作各種加權函數的測試，並提出選擇加權函數的可行方法。 將基底函數(base function)次數加高，改用二次基底函數，以懸臂樑問題作各種加權函數的測試，數值結果證明採用二次基底函數確實有助於改善數值解，但只限於解析解為x、y二次以下的型式，對於解析解高於二次的問題採用二次基底函數對數值解的改善並不大，對於解答屬高次冪函數的問題，採用適當的加權函數將更為重要。 In this thesis,treatment of the interpolated function including the weighting and base functions in the element free method is studied in detail. The element free method(EFM) is a newly proposed numerical method in applied mechanics. This method is formulated by a technique so called “ moving least square”(MLS) to interpolate the discrete data within the domain to be analysed. Both the weighting and base functions influence the interpolated function which controls the accuracy of solving solid mechanics problems. After introducing many kinds of weighting function,the cantliver beam problems have been solved with EFM in diffrent kind weighting function and different base function. Numerical examples illustrate that some kinds of weighting function will get better solutions than others. After all,the rule of the choice of the weighting function has been presented. Numerical examples illustrate that the 2 order base function will get better solutions than the 1order base function in some problems.
