Applications of Generalized Finite Difference Method and Rigid Body Rule to Geometrically Nonlinear Thin-Plate Theory

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Project title

Code/計畫編號

MOST106-2221-E019-016

Translated Name/計畫中文名

廣義有限差分法與剛體運動法則在薄板幾何非線性分析之應用

Project Coordinator/計畫主持人

Shyh-Rong Kuo

Funding Organization/主管機關

National Science and Technology Council

Co-Investigator(s)/共同執行人

范佳銘

Department/Unit

Department of Harbor and River Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=12240956

Year

2017

Start date/計畫起

01-08-2017

Expected Completion/計畫迄

31-07-2018

Co-Investigator(s)

Chia-Ming Fan

Bugetid/研究經費

591千元

ResearchField/研究領域

土木水利工程

"本計畫應用「廣義有限差分法(Generalized Finite Difference Method)的強形式無網格」及「剛體運動法則(Rigid Body Motion Rule)的力平衡」特性，建立薄板具大變形大轉角的幾何非線性理論及數值分析架構。計畫共分為三階段：(1)根據全量式推演法，提出具有「大變形、大轉角」條件下之顯示型薄板結構幾何非線性理論，並應用大轉角剛體運動法則檢驗此理論的正確性；(2)忽略自然變形的幾何非線性效應及應用剛體運動法則，以廣義有限差分法為數值離散化基礎，提出一個兼顧簡單及計算效率的薄板幾何非線性增量力平衡方程式；(3)利用增量迭代法分析薄板的幾何非線性行為，以驗證本計畫所提出的非線性理論及數值分析架構之合理性。其中(3)所提的增量迭代過程有幾項特色：(1)預測階段—忽略自然變形的幾何非線性效應，建立簡易有效率的線性化增量位移預測方程式；(2)修正階段— 採用全量式顯示型薄板幾何非線性微分方程式以避開更新參考座標，並提升計算效率及正確性。由此，基於強形式無網格法所建立的薄板幾何非線性分析架構，可改善因薄板變形後近似平面之假設所產生的誤差累積，引致精度降低而影響計算效率的問題。""Based on the Generalized Finite Difference Method (GFDM) and the Rigid Body Motion Rule, the geometric nonlinear thin-plate theory with consideration of finite deformations and rotations will be developed in this project. The framework of this project includes: (1) Total Lagrangian formulation of geometric nonlinear thin-plate theory based on the force equilibrium consideration of rigid body rule; (2) GFDM based on strong-form meshless method in an incremental state; and (3) Incremental-Iterative procedure for numerical verifications of the thin-plates in large deformations. The features of the incremental-iterative procedure proposed herein include: (1) Predictor: the geometric effects due to natural deformation were neglected for simplifying construction of linearized incremental equations in predicted stage; (2) Corrector: the use of total Lagrangian formulation of thin-plates can save the CPU time in updating nodal coordinates of the plates during large deformations. Moreover, the computational framework based on the GFDM of strong-form meshless method and rigid body rule can reduce the error accumulation of computations and increase the computational efficiency due to the assumption of rigid plane of conventional thin-plate theory."

Keyword(s)

大變形
大轉角
力平衡
廣義有限差分法
無網格法
剛體運動法則
全量式推演法
Finite Deformations
Finite Rotations
Force Equilibrium
Generalized Finite Difference Method
Meshless Method
Rigid Body Test
Total Lagrangian Formulation

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Applications of Generalized Finite Difference Method and Rigid Body Rule to Geometrically Nonlinear Thin-Plate Theory

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