向量式結構運動分析

Vector Form Motion Anylysis of Structure

王仁佐(Ren-Zuo Wang)

指導教授 ： 王仲宇

國立中央大學/工學院/土木工程學系/博士(2005年)

摘要

本論文根據向量式有限元(Vector Form Intrinsic Finite Element，(VFIFE))，簡稱V-5的基本理論，推導可完整且有效模擬結構大變形運動之方法。探討之內容根據結構元型式區分為平面桁架元與剛架元，以及空間桁架元與剛架元四種型式，此外也將材料彈塑性模型納入平面剛架元程序中並探討結構元間撞擊與接觸判斷及碎裂等問題，更進ㄧ歩應用於高壓管路揮擊問題之模擬分析。
此一新的計算方法之基本觀念，乃是將結構體離散為有限個質點之集合，毎個質點的獨立運動則依循由牛頓運動定律，再結合移動式基礎架構(convected material reference frame)與虛構反向剛體運動(fictitious reversed rigid body motion)的作用下，可定出隨體之變形座標(deformation coordinate)系統來合理求出結構元之內力，此些結構元內力滿足靜力平衡，並且將會約束質點之運動。V-5結構元節點與質點彼此的接合型式，可以是剛接、鉸接或其他各種型式，所以此一分析法亦可用來探討柔性多體動力(flexible multibody dynamics 或 FMD)與機構分析等問題，換言之，只要定義適當破壞準則作為解除質點與接點約束之依據，就能輕易模擬結構體由連續到不連續構形之破壞與多體運動行為。
有別於傳統之結構分析法，此一結構運動分析計算程序屬於向量力學，方法簡單與數值計算程序固定，不需建立結構勁度矩陣與任何迭代計算，即可求解具有幾何非線性與材料非線性之力學問題。除此之外亦不需對結構系統設立邊界條件，所以很容易在各個質點上直接施加外力與位移量，來進行各種結構的動靜力運動分析。透過與大量文獻中數值例題的比較驗証，充分顯示向量式有限元方法的特質與優越性，可提供工程分析人員另一有效之工具來處理工程中所面臨之具有挑戰性之非線性動力問題。

關鍵字

虛構反向剛體運動 ； 移動式基礎架構 ； 變形座標

並列摘要

In this thesis, a vector form motion analysis method for structure is developed based on the theory of the Vector Form Intrinsic Finite Element (VFIFE, V-5) method. Formulations of the V-5 type planar and spatial truss and frame elements were derived. Besides, incremental elastic-plastic material models, contact analysis algorithm and failure mechanisms are also included into the simulation code. This newly proposed method has profound theoretical content and application simplicity on studying the spatiotemporal behaviors of structures with highly nonlinearity.
The V-5 method models the analyzed domain to be composed by finite particles and the Newton’s second law is applied to describe each particle’s motion. Thus, the calculation of the V-5 method becomes solving a set of decoupled vector form equations. In the theory of V-5, a convected reference frame, fictitious reversed rigid body motion and updated deformation coordinate system are used to separate the rigid body motion and pure deformation of the system. Then the internal force is calculated from the deformation of element and applied to the mass particle to constrain its motion with other particles. After combining with explicit time integration scheme, the V-5 method can effectively simulate the dynamic behaviors of multi-bodies system having large deformation. The connection between a mass particle and an element node can be rigid or jointed. These connections can be broken into separated bodies according to the failure criteria set in the code.
Different from conventional matrix form structure analysis methods, the vector type motion equation of each mass particle makes the analysis procedure of the V-5 dramatically simple. No iterations are required as conventional methods in nonlinear motion analysis. In addition, due to the nature of discrete independent particle point, it is not required to set essential boundary conditions of the system. It is very easy to prescribe the displacement and forcing conditions on each particle during the procedure of analysis.
Through the numerical analyses of a few benchmark problems with large rotation, elastic-plastic deformation, impact, self-contact, fracture characters, the V-5 method demonstrates its accuracy and efficiency on the analysis of structure motion. It is believed that the V-5 method can be a very effective tool for engineers on the structure motion analysis.

並列關鍵字

fictitious reversed rigid body motion ； convected material reference frame ； deformation coordinate

參考文獻

Agrawal, O. P., Shabana, A. A., “Dynamic analysis of multibody systems using component modes,” Computers and Structures, Vol. 21, No. 6, pp. 1303-1312, (1985).

Agrawal, O. P., Shabana, A. A., “Application of deformable-body mean axis to flexible multibody system dynamics,” Computer Methods in Applied Mechanics Engineering, Vol. 56, pp. 217-245, (1986).

Argyris, J. H., Dunne, P. C., Scharpf, D. W., “On large displacement-small strain analysis of structures with rotational degree of freedom,” Computer Methods in Applied Mechanics Engineering, Vol. 14, pp. 401-451, Vol. 15, pp. 99-135, (1978).

Ashley, H., “Observation of the dynamic behavior of flexible bodies in orbit,” AIAA Journal, Vol. 5, No. 3, pp. 460-469, (1967).

Banerjee, A. K., Dickens, J. M., “Dynamics of an arbitrary flexible body in large rotation and translation,” Journal of Guidance, and Control, and Dynamics, Vol. 13, No. 2, pp. 221-227, (1990).