向量式有限元素法之分散式計算應用於平面構架運動分析

Distributed Computations of Vector Form Intrinsic Finite Element Method for Motion Analysis of Planar Frames

賴哲宇(Jhe-Yu Lai)

指導教授 ： 莊清鏘

中原大學/工學院/土木工程研究所/碩士(2006年)

https://doi.org/10.6840/cycu200600008

摘要

中文摘要
本文旨在將分散式計算應用於向量式有限元素法，並以平面構架運動分析為例測試其可行性。有別於傳統以變分為基礎的有限元素法，向量式有限元素法將連續體近似成質點的集合，質點運動遵循牛頓運動定律。藉由虛擬逆向轉動分離剛體運動，並搭配變形座標系統定義變形，進而計算元素的內力。因此，向量式有限元素法能夠有效模擬連續體同時具有大的剛體運動和大的幾何變形行為。近年來由於工程問題日趨龐大、複雜，使得電腦的記憶體容量和計算量需求都大幅增加，為解決此問題本研究嘗試利用個人電腦叢集進行向量式有限元素法平面構架的平行處理。由於向量式有限元素法的各節點與元素可分開在不同叢集節點計算，同時不需涉及求解代數矩陣，因此利用分散式計算應該可達到節省時間的目的。最後利用一個數值算例說明該方法的成果及可行性。

關鍵詞：向量式有限元、分散式處理、平行處理、MPI。

關鍵字

分散式處理 ； 平行處理 ； 向量式有限元 ； MPI。

並列摘要

Abstract
The main objective of this paper is to introduce a distributed computations technology for the vector form intrinsic finite element method. Motion analysis of planar frame structures were presented to demonstrate the efficiency of distributed computations. The vector form intrinsic finite element (VFIFE) method, in contrast to traditional finite element approaches which is based on the variational principles, the analyzed structure is simulated by a group of particles. To evaluate the internal forces, a set of deformation coordinate system is defined to dissect the rigid body motions and deformations of elements. Thus the VFIFE method can effectively simulate overall dynamic motions, either rigid body motion or deformation of continua. Recently, with the rapid growth of complexity of engineering problems, the computational cost is inevitably increased. Therefore, this study attempts to use “PC Cluster” with MPI (Message passing interface) coding technologies to parallelize the procedures of VFIFE for analysis of planar frame structures. The nodes and the elements in the VFIFE can be easily handled by cluster nodes without the resort to solving matrix algebra. The results of presented numerical example reveal that the proposed approach is very suitable in VFIFE method and applicable in analysis of planar frame structures.

Keywords: VFIFE, Distributed computations, Parallel computations, MPI

並列關鍵字

MPI ； Parallel computations ； Distributed computations ； VFIFE

參考文獻

[28] 莊清鏘、賴建豪、王仲宇，「向量式有限元素法於平面構架幾何非線性分析之應用」， 電子計算機於土木水利工程應用，台北科技大學，台北市，民國九十二年七月

[1] Minguet, P. and Dugundji, J., “Experiments and analysis for composite blades under large delfections Part I. static behavior”, AIAA J. 28, 1573-1597 (1990).

[2] Oden, J. T., “Finite Elements of Nonlinear Continua”, McGraw-Hill, New York (1972).

[3] Bathe, K. J., “Finite Elements Procedures in Engineering Analysis”, Prentice-Hall, Englewood Cliffs, NJ. (1982).

[4] Bauchau, O. A. and Hong, C. H. “Large displacement analysis of naturally curved and twisted composite beams”, AIAA J. 25, 1469 - 1475 (1987).