应用修正的功的互等法求解大挠度矩形薄板弯曲问题  

Problem of the bending of large deflection rectangular thin plate solved by applying corrected reciprocal method

作　　者：陈英杰[1] 宋小惠 CHEN Ying-jie;SONG Xiao-hui(College of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao 066004, Chin)

机构地区：[1]燕山大学建筑工程与力学学院

出　　处：《塑性工程学报》2018年第2期175-182,共8页Journal of Plasticity Engineering

基　　金：河北省科学技术研究与发展计划科技支撑计划项目(12211024)

摘　　要：应用矩形薄板修正的功的互等法，推导了大挠度弯曲矩形薄板的广义位移解。根据广义位移解，研究了一边固定三边简支固定大挠度矩形薄板在均布荷载作用下的挠曲面问题，根据所得出的公式以及矩形薄板的参数，计算出实际的数值结果，并与ANSYS有限元模拟结果分析比较，证明了应用修正的功的互等法求解大挠度矩形薄板弯曲变形问题的可行性和所得挠曲面方程的正确性。该方法可以表示出任意位移边界条件的横向弯曲矩形板在各种横向荷载作用下的中平面弯曲公式，应用边界条件求解该挠曲面公式的未知数，则平板的弯曲问题即可求解。此方法简单实用，精度较高，可应用于工程实际。According to the corrected reciprocal method of rectangular thin plates, the generalized displacement solution was derived for the bending of rectangular thin plates with large deflection. Based on the generalized displacement solution, the problem of deflection sur- face was studied at a large deflection rectangular plate with three edges simply supported and one side fixed under uniform load. According to the obtained formula and parameters of rectangular thin plates, the actual results were calculated which were compared with the ANSYS finite element simulation analysis results. The result proves that the corrected reciprocal method is feasibility to solve the bending problem of rectangular thin plates with large deflection, and the obtiained deflection surface equation is correct. The method can be used to express the bending formula of mid plane with the transverse bending rectangular thin plates of arbitrary displacement boundary conditions under various transverse loads. The boundary condition was used to solve the unknowns of the deflection surface formula, then the bending prob- lem of the plate could be solved. The method is not only simple but also practical and has higher accuracy, and can be used in practical engineering.

关 键 词：大挠度弯曲薄板 广义位移 修正的功的互等法 弯曲问题 工程实际 

分 类 号：O343[理学—固体力学]