Computational Framework of Strong-Form Meshless Method for Geometrically Nonlinear Dynamic Analysis of Beam Structures

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基本資料

Project title

Code/計畫編號

MOST108-2221-E019-002

Translated Name/計畫中文名

梁幾何非線性動力分析之強形式無網格法建構

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=13122108

Year

2019

Start date/計畫起

01-08-2019

Expected Completion/計畫迄

31-07-2020

Bugetid/研究經費

557千元

ResearchField/研究領域

土木水利工程

本研究旨在應用剛體運動法則的特性，建立時間域梁大變形大轉角之強形式無網格幾何非線性動力數值分析架構。研究共分三階段:(1)提出具有大變形、大轉角之顯示型全量式幾何非線性動力理論，應用剛體運動法則，建立時間域離散條件下之大變形大轉角的幾何非線性動力增量平衡式，以作為強形式無網格數值分析之使用；(2)建立考量幾何非線性效應之增量組成律—考慮以剛體運動為主的幾何非線性效應，應用廣義有限差分法提出一套簡單且計算效率佳的梁構件線性化增量組成律；(3)建立考量幾何非線性動力特性的梁構件無網格數值分析架構—配合增量迭代法與無網格數值法，分析梁構件的幾何非線性動力行為，以驗證本研究所提方法之正確及合理性。本研究所提強形式無網格幾何非線性動力數值分析的增量迭代過程有幾項特色：(1)建立在時間離散化下具大變形大轉角特性的幾何非線性動力增量方程式；(2)建立簡易有效的線性化增量位移預測模式，即在增量迭代過程的預測階段，將增量位移分成剛體運動位移及自然變形（小變形）兩部分，忽略自然變形的幾何非線性效應，應用剛體運動法則求得線性化增量組成律；(3)採用顯型全量式非線性動力方程式，有助提升在增量迭代過程修正階段數值分析的計算效率及正確性。 The purpose of this project is to establish a strong form meshless computational framework for geometrically nonlinear dynamics of beam structures considering large deformations and large rotations based on the rigid body motion rule. The whole project is divided into three stages: (1) An explicit total form geometric non-linear dynamic formulation considering large deformations and large rotations is proposed. Its virtual strain energy is consistent with the virtual work-based force equilibrium. Then, by applying the rigid body motion rule, the geometric non-linear dynamic incremental equilibrium equations are established in temporal domain for strong form meshless method; (2) In formulating the incremental constitutive law considering the geometric nonlinearity with rigid body motions, the geometric nonlinearity of natural deformations is neglected. The incremental equations of geometric nonlinearity in conjunction with generalized finite difference method for beam elements considering has the following characteristics of simplicity and computational efficiency; (3) Establish the computational framework of meshless method for beam elements considering the geometric nonlinearity to verify the feasibility and validity of the proposed method. The proposed computational framework of strong-form meshless method for geometrically nonlinear dynamic analysis of beam structures has the following characteristics: (1) Formulate the geometrically nonlinear dynamic increment equation considering large deformations and large rotations; (2)Establish a concise and effective linearized incremental prediction phase: the naturaldeformation induced geometrical nonlinearity will be neglected during the prediction phase of incrementaliterative stage so that one can divide the increment into rigid body motions and natural deformations (in small deformation), from which the incremental forces induced by constitutive law of natural deformation and the ones by rigid body motion based on rigid body motion rule are obtained; (3) Adopt the explicit total form geometric nonlinear dynamic formulation to improve the computational efficiency and numerical validity in correction stage of incremental-iterative method.

Keyword(s)

大變形
大轉角
幾何非線性動力增量方程式
廣義有限差分法
無網格法
剛體運動法則
Large deformation
Large rotation
Geometric non-linear dynamic incremental equilibrium equations
Generalized finite difference method
Meshless method
Rigid body motion rule

DSpace CRIS

Computational Framework of Strong-Form Meshless Method for Geometrically Nonlinear Dynamic Analysis of Beam Structures

基本資料

Description