| 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。 |
| 关键词: 岩石圈 弹性薄板 挠曲 克希霍夫方程 |
| DOI：10.11693/hyhz20191200280 |
| 分类号:P312.3;O343.1 |
| 基金项目:国家自然科学青年基金项目，40206009号。 |
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| A NEW FORMULA FOR LITHOSPHERE FLEXURE-ELASTIC THIN PLATE SMALL DEFLECTION BENDING |
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FAN Shou-Zhi1, FU Yong-Tao1,2,3
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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
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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. |
| Key words: lithosphere elastic thin plate flexure Kirchhoff Equation |
