IGA用於船體局部結構振動以及挫曲分析

VIBRATION AND BUCKLING ANALYSIS OF LOCAL SHIP STRUCTURE USING THE IGA METHOD

鄒文懷(W.H. Tsou) ； 孫健庭(C.T. Sun) ； 張耕瑋(K.W. Chang) ； 關百宸(P.C. Guan) ； 陳玉豐(Y.F. Cheng)

《中國造船暨輪機工程學刊》 35卷3期 (2016/08) Pp. 103-114

摘要

在一般網格法的分析流程中，先在CAD軟體中利用B-樣條函數(B-spline)建立幾何，再將幾何匯入分析軟體中，而由於建立幾何所使用的形函數與近似物理場的形函數不同，因此必須再依照近似物理場的形函數需求，重新劃分網格，而此網格劃分的步驟往往會佔總分析時間的80%左右[1]。而等參數幾何分析(Isogeometric analysis, IGA)則是直接使用B-樣條函數近似物理場，因此可以省去網格劃分的步驟，且B-樣條為高階以及高連續性的方程式，可以建立出精確的高階曲面形狀，適合用於接觸問題等需要多次微分的分析。本文利用上述IGA的優點，建立一套針對船體結構的完整分析流程並建立分析程式。在模型匯入程式後，即可以自動劃分網格並完成分析，且依照本文建立數值模型的流程，可以自動連接結構單元(板單元以及樑單元)的自由度，而不需要任何特殊的連接處理方式。最後，將此分析程式應用在局部船體結構振動以及挫曲分析。

關鍵字

等參數幾何分析 ； 非均勻有理B-樣條曲線 ； Mindlin板 ； 加強板 ； 船體結構

並列摘要

In general mesh-based analyzing processes, we always use CAD software, which construct geometry based on the B-spline function, to build geometrical model for engineering purposes, especially for ship structural analysis. The geometrical model is later imported into the finite element method software, which will redundantly rebuild the model again with finite element mesh (discretization). This processes cost about 80% [1] of engineers' time to just go through the routine work and obtain a valid FEM model. If one can skip the processes, it will be great improvement of the working time for engineers. Therefore, in this research, we use the isogeometric analysis (IGA) method to build a complete analyzing procedure for the ship structural analysis. The IGA directly uses B-spline as the shape function, so it can skip mesh generation. Because B-spline is a high order and high continuity function, it can build exact high order surface and analyze contact problems which need high order differentiation. We also build the analysis program according to the analysis procedure. After the model is imported into the program, it can generate the mesh and finish the analysis automatically. According to the procedure of building the numerical model, the program could connect the degree of freedom of the structural element (shell element and beam element) without any specifically connecting method. After we complete the verifycation of the developed program with several benchmark problems, we apply this program to analyze the local ship structure according to the structural design rule.

並列關鍵字

Isogeometric Analysis ； NURBS ； Mindlin Plate ； Stiffened Plate ； Ship Structure