| 岩石圈挠曲-弹性薄板小挠度弯曲的新方程 |
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| 引用本文： | 范守志,付永涛.岩石圈挠曲-弹性薄板小挠度弯曲的新方程[J].海洋与湖沼,2020,51(4):869-874. |
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| 作者姓名： | 范守志 付永涛 |
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| 作者单位： | 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;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;中国科学院海洋大科学研究中心 青岛266071;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 |
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| 基金项目： | 国家自然科学青年基金项目，40206009号。 |
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| 摘 要： | 岩石圈挠曲研究采用的是弹性薄板小挠度弯曲方程(即克希霍夫方程),克希霍夫方程基于薄板的前提,忽略并假设薄板内垂向应力为0。本文在无需垂向应力为0的这一与地质事实不相符的假设的情况下,由弹性体几何方程、物理方程和静力平衡方程推导出岩石圈挠曲-弹性薄板小挠度弯曲的新中面方程,具有同等的数学简洁性。取泊松比为0.25时,有DFF/D=1.125,即新挠曲方程中的挠曲刚度DFF要比经典的克希霍夫挠曲方程的D值大12.5%。本文推导的新方程不仅可以在岩石圈动力学,也可以在弹性力学中获得应用。
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| 关 键 词： | 岩石圈 弹性薄板 挠曲 克希霍夫方程 |
| 收稿时间： | 2019/12/27 0:00:00 |
| 修稿时间： | 2020/3/22 0:00:00 |
A NEW FORMULA FOR LITHOSPHERE FLEXURE-ELASTIC THIN PLATE SMALL DEFLECTION BENDING |
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| FAN Shou-Zhi,FU Yong-Tao.A NEW FORMULA FOR LITHOSPHERE FLEXURE-ELASTIC THIN PLATE SMALL DEFLECTION BENDING[J].Oceanologia Et Limnologia Sinica,2020,51(4):869-874. |
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| Authors: | FAN Shou-Zhi FU Yong-Tao |
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| Institution: | Key Laboratory of Marine Geology and Environment, Institute of Oceanology, CAS, Chinese Academy of Science, Qingdao 266071, China; Key Laboratory of Marine Geology and Environment, Institute of Oceanology, CAS, Chinese Academy of Science, Qingdao 266071, China;Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao 266071, China;Laboratory for Marine Geology, Pilot National Laboratory for Marine Science and Technology(Qingdao), Qingdao 266237, China |
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| 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. |
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| Keywords: | lithosphere elastic thin plate flexure Kirchhoff Equation |
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