物件導向非線性靜動態三維結構分析程式之擴充

Extension of An Object-Oriented Nonlinear Static and Dynamic 3D Structural Analysis Program

游宜哲(Yi-Jer Yu)

指導教授 ： 蔡克銓

國立臺灣大學/工學院/土木工程學研究所/碩士(2006年)

https://doi.org/10.6342/NTU.2006.01933

摘要

PISA3D(Platform of Inelastic Structural Analysis for 3D System)為一非線性靜動態三維結構分析程式。此程式以C++程式語言撰寫，採物件導向之概念，搭配Design Patterns建立一個彈性的程式架構，使得此軟體具有高度的可擴充性及可維護性。本研究在此程式中擴充新的動力分析方法以及非線性結構元件，提供原有程式無法進行的分析、提升程式的運算效率，並且能與原有程式函式庫作結合，搭配組合下強化整個程式的分析功能。論文內容亦介紹物件導向開發的程式架構，討論其程式彈性及擴充性。
本研究對PISA3D功能上的擴充項目主要有下列兩點：
1. 在PISA3D的非線性動力分析方法中，新增Operator Splitting(OS)分析方法。此演算法利用Predictor-Corrector的技巧，使得結構進入非線性時，不需更新結構整體勁度矩陣，在結構受震產生非線性行為時，此法可大量減少程式運算所需的時間，並且兼顧分析的準確性。
2. 擴充PISA3D的結構元件庫，包括：
(1) 三維的旋轉彈簧，可同時模擬三向結構梁柱交會區的Panel Zone效應。
(2) 六個自由度的無長度接點元件，其六個自由度可定義不同材料特性，各自發生不同的非線性反應。
(3) 可定義Open長度，純受壓不受拉之Gap元件。
(4) 以柔度法為基礎的Fiber BeamColumn Element。此方法以Force Interpolation Function配合在桿件及斷面階層的疊代流程，解決了勁度法以Shape Function造成Discretization Error的問題，使得分析者能用較少的纖維即可模擬出準確的非線性行為，並且能考慮不同形式的橫向載重對元件的影響，而不只是以固端力來考慮。此元件將桿件同時延軸向及斷面上細分為許多較小的元素，使用者透過不同纖維元素的性質及其位置的安排，可模擬出異於塑鉸模型所提供的勁度及強度性質，以及塑性區在軸向及斷面上的擴展現象。可精確模擬複合材料斷面(如鋼筋混凝土)構件的材料非線性行為。

關鍵字

物件導向 ； 設計模式 ； 結構分析程式 ； 動力分析 ； 纖維 ； 柔度法

並列摘要

PISA3D is a nonlinear static/dynamic 3D structural analysis program. The program is completely written in C++, a programming language with object-oriented mechanisms. In constructing this software framework, the Design Patterns are applied so the PISA3D software framework is well extensible and easy to maintain. The objectives of this research include the extension of the dynamic analysis method library and nonlinear structural element library in the PISA3D program. The frameworks of the object-oriented programming applied for these developments, including the PISA3D and the enhancements made in this research are also described.
The main extension of this research is described as follows:
1. The Nonlinear Dynamic Analysis Method – Operator Splitting (OS) Method. This analysis method can compute the structural responses under three -dimensional ground accelerations. The OS integration algorithm uses techniques of merging predictor-corrector/implicit-explicit in nonlinear finite element analysis. Extensive analyses illustrate the OS method can save a great amount computing time and get equally-well analytical accuracy in nonlinear time history dynamic analysis.
2. The Nonlinear Structural Element Library:
(1) 3D Rotational Joint, which can be conveniently used in modeling the 3D panel zone effects of beam-to-column joint.
(2) 6D Joint Element. The element have 6 individual nonlinear DOFs. This element is a zero-length element.
(3) Gap Element. User can define its gap-opening length. This element is compression-only.
(4) The Fiber BeamColumn Element. The element formulation is flexibility –based. It relies on force interpolation functions that strictly satisfy the equilibrium of bending moments and axial force along the element. The force interpolation function does not involve a discretization error so that less discretization and consequently less computational effort are required to achieve comparable accuracy. The element can readily incorporate distributed element loads by the addition of exact internal force distribution function. A fiber beam-column element is subdivided into several sections, and each section consists of several fibers of individual nonlinear material. The elements can accurately simulate the response of composite beam-column members consisting of reinforcing steel and concrete material.

並列關鍵字

PISA3D ； Object-Oriented ； Design Patterns ； Operator Splitting ； Fiber ； Flexibility based

參考文獻

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