【作者】 范守志； 付永涛；

【Author】 Fan Shouzhi;Fu Yongtao;Key Laboratory of Marine Geology and Environment,Institute of Oceanology,CAS,Chinese Academy of Science;Center for Ocean Mega-Science,Chinese Academy of Sciences;Laboratory for Marine Geology,Pilot National Laboratory for Marine Science and Technology (Qingdao);

【机构】 中国科学院海洋研究所海洋地质与环境重点实验室； 中国科学院海洋大科学研究中心； 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；

【摘要】 弹性薄板小挠度弯曲方程（即克希霍夫方程）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D_FF/D=1.125,即新挠曲方程中的挠曲刚度D_FF要比经典的克希霍夫挠曲方程的D值大12.5%。本文推导的新方程可以在弹性力学中获得应用。更多还原

【Abstract】 The small deflection bending formula of elastic thin plate,i.e.Kirchhoff Equation,has been used.This paper derived a new small deflection bending formula of elastic thin plate without leaving vertical stress out of consideration,from geometrical,physical and static equilibrium equations.This formula has mathematical simplicity same to the well-known Kirchhoff Equation,but its flexural rigidity D_FF is little different from the flexural rigidity D of Kirchhoff Equation,about 12.5% higher in case of Poisson’s ratio is 0.25.更多还原