Application of Rigid Body Motion Rule to Nonlinear Geometric Analysis of Thin-Shells Using the Strong-Form Meshless Method

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Project title

Code/計畫編號

MOST107-2221-E019-004

Translated Name/計畫中文名

剛體運動法則在薄殼幾何非線性強形式無網格數值分析方法之應用

Project Coordinator/計畫主持人

Shyh-Rong Kuo

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Harbor and River Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=12618847

Year

2018

Start date/計畫起

01-08-2018

Expected Completion/計畫迄

31-07-2019

Bugetid/研究經費

644千元

ResearchField/研究領域

土木水利工程

本計畫旨在以剛體運動法則作為具有大變形及大轉角特性之薄殼幾何非線性理論的檢驗基礎，從而建立強形式無網格數值分析架構。整個計畫共分為三階段：(1)根據全量式推演法提出具有「大變形、大轉角」條件下之薄殼結構幾何非線性理論；(2)忽略自然變形的幾何非線性效應及應用剛體運動法則，以求得考量幾何非線性效應之增量組成律，並提出一個兼顧簡單及計算效率的顯示型薄殼幾何非線性增量力平衡方程式；(3)利用本計畫建立的無網格數值分析架構，配合增量迭代法分析薄殼的幾何非線性行為，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。本計畫所提的強形式無網格幾何非線性數值分析的增量迭代過程有幾項特色：(1)應用薄殼中曲面三個正交的活動標架系統，建立一個簡明顯示型式的薄殼幾何非線性理論，以利進行強形式無網格數值分析；(2)預測階段—忽略自然變形的幾何非線性效應，將增量位移分成剛體運動及自然變形 (小變形) 二個部分，由小變形線性理論的組成律求自然變形的增量力，而剛體運動是應用剛體運動法則求得其對應的增量力，藉此建立簡易有效率的線性化增量位移預測方程式；(3)修正階段—採用全量式顯示型薄殼幾何非線性微分方程式，以提升計算效率及正確性。 Based on the rigid body motion rule, a computational framework of strong-form meshless method will be established for nonlinear geometrical analysis of thin-shells considering large deformations and large rotations. Three stages in theoretical development of the nonlinear geometric analysis of thin-shells are considered in this project: (1) Total Lagrangian formulation of the nonlinear geometrical shell theory considering large deformation and large rotations; (2) incremental form of the flexible shell theory that takes nonlinear effects on constitutive law into account; (3) Computational framework of strong-form meshless analysis associated with incremental-iterative method. The features of the present strong-form meshless analysis associated with incremental-iterative method are listed as follows: (1) A three orthogonal moving coordinate system is defined on the curved surface of a shell element for the theoretical formulation and numerical computations using the present strong-form meshless method; (2) In predictor stage for nonlinear analysis, an efficient prediction approach is proposed to compute the incremental force due to natural deformations based on constitutive law of small deformations; (3) In corrector stage for nonlinear analysis, a total Lagrangian formulation is used to increase the computational performance and correction. With the present strong-form meshless based on computational procedures listed above, one can perform the nonlinear geometric analysis with large deformations and rotations of shells.

Keyword(s)

增量組成律
大變形
大轉角
強形式無網格法
剛體運動法則
薄殼
Incremental constitutive law
Large deformation
Large rotation
Strong-form meshless method
Rigid body motion rule
Shell

DSpace CRIS

Application of Rigid Body Motion Rule to Nonlinear Geometric Analysis of Thin-Shells Using the Strong-Form Meshless Method

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