初始荷载效应对板力学性能非线性影响研究

发布时间：2018-05-29 21:33

本文选题：板 + 初始荷载效应　；参考：《重庆大学》2014年博士论文

【摘要】：随着结构设计理念和经济化的发展，在保证结构安全的前提条件下，板朝轻型、高强和更薄的方向发展是今后的趋势；而随着板厚度的进一步减小，初始荷载效应对板的力学性能的影响则更为突出。本文采用理论分析与数值模拟相结合的方法，就初始荷载效应（包括初始竖向荷载效应和初始中面荷载效应）对板的静、动力性能和稳定性的非线性影响进行了较为系统的研究。本文取得主要研究成果如下： ①推导了考虑初始竖向荷载效应、同时考虑初始竖向荷载效应和初始中面荷载效应情况下板的静、动力平衡微分方程；针对轴对称情形圆形板，采用坐标变换方法，得到了圆形板考虑初始竖向荷载效应、同时考虑初始竖向荷载效应和初始中面荷载效应情况下的极坐标形式的静、动力平衡微分方程。 ②推导了考虑初始竖向荷载效应、同时考虑初始竖向荷载效应和初始中面荷载效应情况下板的静、动力有限元公式；提出了考虑初始竖向荷载效应的等参板单元、同时考虑初始竖向荷载效应和初始中面荷载效应的矩形板单元和等参板单元，运用MATLAB编制了相应的有限元程序；分析了初始荷载效应及相关因素对板的静、动力性能的非线性影响。 ③解得了不同形状板考虑初始竖向荷载效应、同时考虑初始竖向荷载效应和初始中面荷载效应的后期竖向荷载位移、基频近似解；解得了简支矩形板考虑初始竖向荷载效应、同时考虑初始竖向荷载效应和初始中面荷载效应的前三阶频率近似解； ④推导了考虑初始竖向荷载效应情况下板的稳定平衡微分方程和有限元公式；解得了三种板考虑初始竖向荷载效应的屈曲临界荷载系数近似解；分析了初始竖向荷载及相关因素对板稳定性的影响。 ⑤板的初始荷载效应主要受初始荷载、几何尺寸、厚度及边界条件的影响；一般情况下，初始荷载越大、板的刚度越低、厚度越小、边界条件约束越弱，则初始荷载效应对板的静动力性能和稳定性的非线性影响越明显。
[Abstract]:With the concept of structural design and economic development, the development of light, high strength and thinner direction is the trend in the future under the premise of ensuring structural safety. With the further reduction of plate thickness, the effect of initial load effect on the mechanical properties of the plate is more sudden. This paper combines theoretical analysis with numerical simulation. In this paper, the nonlinear effects of initial load effect (including initial vertical load effect and initial middle surface load effect) on the static, dynamic and stability of the plate are studied systematically. The main research results are as follows:
The initial vertical load effect, considering the initial vertical load effect and the initial middle surface load effect, is derived. The dynamic equilibrium differential equation of the plate is considered. The circular plate is taken into consideration of the initial vertical loading effect, considering the initial vertical load effect and the initial vertical load effect. The static and dynamic equilibrium differential equations in polar coordinates under the load effect of the middle surface.
Secondly, the static and dynamic finite element formulas considering the initial vertical load effect and the initial vertical load effect and the initial middle surface load effect are derived. The isoparametric plate element, considering the initial vertical load effect, and the rectangular plate element and the isoparametric element which consider the initial vertical load effect and the initial middle surface load effect are proposed. The corresponding finite element program is compiled by MATLAB, and the nonlinear influence of initial load effect and related factors on static and dynamic performance of plate is analyzed.
Thirdly, the initial vertical load effect is considered in different shape plates, and the initial vertical load effect and the initial vertical load effect of the initial middle surface load effect are considered, and the basic frequency approximate solution is taken into consideration. The initial vertical load effect is considered by the simple supported rectangular plate, and the first three orders of the initial vertical load effect and the initial middle surface load effect are considered. Frequency approximate solution;
(4) the stable equilibrium differential equation and finite element formula of the plate under the consideration of the initial vertical load effect are derived. The approximate solution of the critical buckling load coefficient of the three kinds of plates is solved with the initial vertical load effect, and the influence of the initial vertical load and the related factors on the stability of the plate is analyzed.
The initial load effect of the plate is mainly influenced by initial load, geometric size, thickness and boundary condition. In general, the larger the initial load is, the lower the stiffness of the plate, the smaller the thickness, the weaker the boundary conditions, the more obvious the nonlinear effect of the initial load effect on the static and dynamic properties and stability of the plate.
【学位授予单位】：重庆大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU31

【参考文献】