應用有限單元法於工程問題分析時，常需考慮複雜的單元設計及單元切割，不但費時耗力，且當劇烈大變形發生時，會因單元嚴重扭曲，而影響解之收斂性及精確度。但利用無網格法(meshless method)分析時，沒有單元連結，可容易地移動、嵌入或刪除節點，因此非常適合進行適應分析。然而，在面對劇烈大變形問題時，嚴重扭曲的節點分佈依然是必須面對之難題。
本論文旨在以無單元Galerkin法 (element-free Galerkin method, EFGM)為基礎，發展一個高效率的三維無網格適應分析法來探討包含幾何與材料非線性及接觸行為的三維結構劇烈大變形問題。此無網格適應分析法係以更新的Lagrangian增量型式(Updated Lagrangian Formulation)推導，結合一均勻分佈之背景網格(uniform background grid)，於施加負載後，以可移動之邊界節點(moving boundary node)及內部節點(interior node)分別描述待分析三維結構之表面及內部。因內部節點係選自部份的均勻分佈之背景網格，於每個負載增量中，雖然選取的內部節點組成不盡相同，但均仍呈現均勻分佈，因而可成功地克服劇烈大變形時節點分佈扭曲所衍生之難題。
本論文更進一步提出一新穎的適應分析方法，以均勻分佈之背景網格為基礎，於擬分析結構內部，透過誤差估計，發展一適應分析策略。藉由此內部適應分析方法，可將新增的適應分析節點嵌入某些區域來改善其解的精確度。此外，本研究亦採用三角形表面描述技巧(triangular surface scheme)來分析任意三維結構體之幾何外形，並更進一步於結構體表面提出新穎的表面適應分析策略。應用此適應分析法，可因而精確分析複雜之三維結構體，即使此結構體有劇烈大變形產生時依然具優越效果。而且，當結構體有接觸行為發生時，也可準確地定義出其接觸區域。本論文所提出的無網格適應分析法，不僅可應用於無單元之Galerkin法，亦可很容易廣泛應用於其他無網格方法，如無網格局部Petro-Galerkin法(meshless local Petro-Galerkin method, MLPG)等。
本論文最後以數個三維工程問題分析示例顯現所發展方法之準確性及效能，其計算結果與已有文獻相較皆頗為脗合。

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