初始纵向、横向荷载效应对薄板静力性能影响分析

摘要/Abstract

摘要： 摘要：运用能量变分原理，给出了同时考虑初始纵、横向荷载效应情况下板的应变能表达和静力平衡微分方程；推导了同时考虑初始纵、横向荷载效应的板单元刚度矩阵.运用Galerkin法求解了同时考虑初始纵、横向荷载效应情况下3种典型板（固支矩形板、固支和简支圆形板）的后期横向荷载位移近似解.验证了考虑初始纵、横向荷载效应的板单元刚度矩阵和3种典型板的后期荷载位移近似解的正确性,并分析了初始纵、横向荷载效应对板的后期横向荷载位移的影响.结果表明：初始纵、横向荷载效应改变了板的弯曲刚度，将影响板承受后期横向荷载的静力性能；同时考虑初始纵、横向荷载效应情况下，板的静力性能主要受初始纵向和横向荷载、板的厚度及边界条件等因素的影响.

关键词: 初始纵、横向荷载效应, 板, 静力, 板单元

Abstract: Abstract： Using the energy variation principle, the strain energy expression and static equilibrium differential equation for plates considering the effect of both initial inplane and transverse loads were proposed. Meanwhile, the finite plate element considering the effect of both initial inplane and transverse loads was presented. To verify the finite plate element, the approximate solutions of later transverse load displacement for three typical plates (clamped rectangular plate, clamped and simply supported circular plates) considering the effect of both initial inplane and transverse loads were derived by using the Galerkin method. The later transverse load displacements obtained by the finite plate element agreed well with the approximate solutions. The reliability and efficiency of the presented finite plate element and those later transverse load displacement approximate solutions were verified. Numerical examples show that the bending stiffness of plates are changed when the effect of both the effect of both initial inplane and transverse loads are considered, and that the key physical factors governing the effect of initial loads on the frequencies of plates are the initial loads (both inplane and transverse), thickness and boundary condition etc.

Key words: Key words： effect of both initial inplane and transverse loads, plate, static, finite plate element

中图分类号:

TU 313

刘德贵, 周世军, 王宁, 姚勇. 初始纵向、横向荷载效应对薄板静力性能影响分析[J]. 上海交通大学学报, 2016, 50(03): 336-344.

LIU Degui, ZHOU Shijun, WANG Ning, YAO Yong. Analysis of Effect of InPlane and Transverse Loads on Static Performance of Plates[J]. Journal of Shanghai Jiao Tong University, 2016, 50(03): 336-344.

参考文献

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