A Study on the Theory of Geometric Nonlinear for Thin Plate

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Project title

Code/計畫編號

NSC90-2211-E019-007

Translated Name/計畫中文名

平板結構的幾何非線性理論探討

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=659736

Year

2001

Start date/計畫起

01-08-2001

Expected Completion/計畫迄

01-07-2002

Bugetid/研究經費

322千元

ResearchField/研究領域

土木水利工程

本研究計劃主要是建立一個空間平板幾何非線性虛功方程式，現有文獻上推導平板的幾何非線性增量虛功方程式的過程中，對於非線性應變量並無合理的處理方式，且沒有完整考慮/sup 2/C 狀態的虛功量，因此求得的非線性虛功方程式，無法通過剛體運動的基本法則。本計劃在幾何非線性虛功方程式的推導過程中，將完整考慮包含.eta./sub xx/、.eta./sub yy/、.eta./sub xy/及.eta./sub xz/、.eta./sub yz/、.eta./sub zz/等六項非線性應變，及正確的探討/sup 2/C 狀態旋轉變形產生彎矩引量所做的虛功，由此求得的幾何非線性虛功式將能正確通過非線性剛體運動檢測。 In this project, a geometric nonlinear formulation is presented for the three-dimensional buckling analysis of thin plate which accounts for small strain and rotation effects. Previous buckling theories for plates are not perfect for two reasons. First, they are not general enough to include the instability effects of all kinds of actions. Second, they are not qualified by the rigid body test in the nonlinear sense. The principle of virtual displacements based on the updated Lagrangian formulation will be employed to derive the buckling equations for thin plate, which is based on the Kirchhoff hypothesis. In stead of the conventional approaches that consider only three components of nonlinear strain, all the six components of strain will be taken into account in the present formulation. It is for this that the present approach is referred to as the elasticity approach. By considering all the six components of strain and included through the external virtual work terms of the deformed state, a number of nonlinear virtual work terms that were previously regarded merely as of higher orders and discarded from the formulation can now be converted into physically meaningful terms. This present theory differs from the previous ones in that it was qualified by the nonlinear rigid body test.

Keyword(s)

平板結構
幾何非線性
薄板
Plate structure
Geometric nonlinearity
Thin plate

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A Study on the Theory of Geometric Nonlinear for Thin Plate

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