﻿ 岩石圈挠曲-弹性薄板小挠度弯曲的新方程
 海洋与湖沼  2020, Vol. 51 Issue (4): 869-874 PDF
http://dx.doi.org/10.11693/hyhz20191200280

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#### 文章信息

FAN Shou-Zhi, FU Yong-Tao. 2020.

A NEW FORMULA FOR LITHOSPHERE FLEXURE-ELASTIC THIN PLATE SMALL DEFLECTION BENDING

Oceanologia et Limnologia Sinica, 51(4): 869-874.
http://dx.doi.org/10.11693/hyhz20191200280

### 文章历史

1. 中国科学院海洋研究所 海洋地质与环境重点实验室 青岛 266071;
2. 中国科学院海洋大科学研究中心 青岛 266071;
3. 青岛海洋科学与技术试点国家实验室 海洋地质过程与环境功能实验室 青岛 266237

A NEW FORMULA FOR LITHOSPHERE FLEXURE-ELASTIC THIN PLATE SMALL DEFLECTION BENDING
FAN Shou-Zhi1, FU Yong-Tao1,2,3
1. Key Laboratory of Marine Geology and Environment, Institute of Oceanology, CAS, Chinese Academy of Science, Qingdao 266071, China;
2. Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao 266071, China;
3. Laboratory for Marine Geology, Pilot National Laboratory for Marine Science and Technology(Qingdao), Qingdao 266237, China
Abstract: The small deflection bending formula of elastic thin plate,i.e. Kirchhoff Equation,has been used in the study of lithosphere flexure. Be different from that in the elasticity,the assumption of vertical stress is 0 of Kirchhoff Equation in the lithosphere dynamics is obviously argued. This paper derived a new small deflection bending formula of elastic thin plate without leaving vertical stress out of consideration,suitable for lithosphere flexure,from geometrical,physical and static equilibrium equations. This formula has mathematical simplicity same to the well-known Kirchhoff Equation,but its flexural rigidity DFF is little different from the flexural rigidity D of Kirchhoff Equation,about 12.5% higher in case of Poisson's ratio is 0.25.
Key words: lithosphere    elastic thin plate    flexure    Kirchhoff Equation

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1 推导过程

 图 1 弹性薄板与坐标系 Fig. 1 The elastic thin plate and Coordinates

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, 于是, 式(11)变为:

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F1(x, y)及F2(x, y)是任意函数, 待定。

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 图 2 薄板顶面及底面的横向载荷 Fig. 2 Lateral load on the surfaces of elastic thin plate 注: q1、q2分别表示薄板顶面及底面上受到的横向载荷; t为薄板厚度

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2 讨论 2.1 本文推导的弹性薄板小挠度弯曲方程无需垂向应力为0的假设

2.2 在岩石圈挠曲研究中的应用

2.3 新挠曲方程有待于三维数值模拟或光弹性法实验的验证

3 结论

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