Applications of Time-Discretized Energy Identity and Strong-Form Meshless Method to Geometrically Nonlinear Dynamic Analysis of Beam Structures

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Project title

Code/計畫編號

MOST109-2221-E019-002

Translated Name/計畫中文名

離散時間能量差分式及強形式無網格法在梁桿件之動力幾何非線性分析應用

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=13535874

Year

2020

Start date/計畫起

01-08-2020

Expected Completion/計畫迄

31-07-2021

Bugetid/研究經費

785千元

ResearchField/研究領域

土木水利工程

本研究計劃是應用離散時間梁桿件之能量恆等式及剛體運動法則，配合強形式無網格廣義有限差分法，建立時間離散梁桿件在幾何非線性大變形(含大旋轉)狀態下的顯型全量式動量方程式及動力分析計算架構。本計劃採用顯型全量式動量方程式，便於針對構件大變形問題進行運動過程描述，研究主體共分三階段，(1)提出新的全量式動量推導方法，配合離散時間能量恆等式之差分運算，建立滿足線動量守恆、角動量守恆及能量守恆之時間離散梁桿件幾何非線性動量控制方程式；(2)應用剛體運動法則，將梁桿件位移分解成剛體平移、剛體旋轉及自然變形，再通過離散時間能量恆等式的差分運算，求得滿足前述三大守恆定律的時間離散梁桿件大變形動量微分方程式，以為下一階段的強形式無網格數值計算之用；(3)建立梁構件幾何非線性動力無網格數值分析架構。此階段首先是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，並忽略自然變形的幾何非線性效應以簡化梁內力計算，應用剛體運動法則求得線性化增量組成律，從而提出一套簡單且計算效率佳的梁構件線性化增量組成律；最後配合增量迭代與無網格數值法，分析梁構件的幾何非線性動力行為，以驗證本計畫所提方法之正確及合理性。 In this study, the time-discretized energy identity and strong-form meshless method will be applied to geometrically nonlinear dynamic analysis of beam elements considering large deformations that can satisfy rigid body motion rule. With the total Lagrangian formulation of moment equations, the present research includes the following three parts: (1)Considering the time-discretized energy identity, a new formulation of moment equations that can satisfy the conservation of momentum and energy for the geometrically nonlinear dynamic analysis of beam elements in an incremental form; (2)Apply the rigid body motion rule to the formulate the incremental equations of beam element based on the time-discretized energy identity for large deformation analysis of beam structures; (3)Computational framework of strong-form meshless method applied to geometrically nonlinear dynamic analysis of beam structures. Here, point (3) indicates that in predictor phase, the rigid body motion rule is used to extract the incremental linearized constitutive relations from the incremental deformations of the beams; then the incremental-iterative meshless method is employed to compute the dynamic response of the beam structure; finally, the numerical verification and rationality will be carried out to implement the computational efficiency of the proposed method.

Keyword(s)

能量守恆
動量守恆
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
Conservation of energy
Conservation of momentum
Geometrically nonlinear dynamic incremental equilibrium equations
Generalized finite difference method
Meshless method
Rigid body motion rule

DSpace CRIS

Applications of Time-Discretized Energy Identity and Strong-Form Meshless Method to Geometrically Nonlinear Dynamic Analysis of Beam Structures

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