曲線梁於工程應用上非常普遍，然而其分析上卻常以多段直線梁加以近似模擬，如此將造成使用者之不便且不易掌握分析之精度。曲線梁之專門推導及程式雖多見於過往之文獻中，但其方法皆以圓柱座標系統表達其相關應變，因此僅方便於圓弧形之曲線梁，而對於任意變化之空間曲線梁則不易模擬，且對於完全直線之梁因其曲率半徑為無窮大，亦無法直接模擬。本文之方法係以一雙曲殼元素(Ahmad shell element)加以特殊化使之適用於曲線梁。該推導之元素共有兩種，其一為每元素六個節點，每一節點具有五個自由度。另一為每元素三個節點，每一節點具有三個自由度，但僅限於平面曲線梁之分析。文中列出驗證之例題，並以不同之積分點個數探討剪應變鎖定及薄膜應變鎖定現象。 Curved beams are popular applications in engineering practice. However, the analysis of the curved beams are often simulated by many straight beams. It is inconvenient and inaccurate. Specialized analysis can be seem in the literature. The past methods use cylindrical coordinates for the derivation. This kind of derivation is restricted to the circular shape beams, also it is inconvenient for a straight beam analysis. The method developed in this paper modified the doubly curved shell element (Ahmad shell element) to adapted it to a curved beam problem. There are two elements developed. The first one has six nodes in each element. Each node has five degrees of freedom. The other one has three nodes in each element, and three degrees of freedom in each node. The three-node element can be used in plan problems only. Examples are shown to prove the correctness of these two elements. The reduced integration method was used to solve the shear locking and membrane locking phenomena.
關聯:
八十八年電子計算機於土木水利工程應用研討會論文集(二)=Proceedings of the Conference on Computer Applications in Civil & Hydraulic Engineering，頁 1714-1720
