基于Boussinesq和Winkler地基模型的梁板受力特征差异性研究

发布时间：2018-04-20 02:09

本文选题：弹性地基 + 弹性地基梁(板)　；参考：《河南理工大学》2015年硕士论文

【摘要】：在船厂船台、机场跑道、钢筋混凝土路面、建筑物基础底板等工程结构中,弹性地基梁板是被广泛应用的基础形式。弹性地基梁板的分析虽然是经典课程,但由于新的地基模型、分析方法和计算手段的陆续出现,该课题至今仍在研究之中。本文围绕这一课题,采用Boussinesq地基模型,对弹性地基梁板进行了系统的研究。在弹性地基与地基梁(板)体系中,采用先分后合的方法推导出弹性地基与地基梁(板)体系中分别储存的弹性势能。依据弹性力学中的叠加原理和等效原理,将弹性地基与地基梁(板)作为一个整体来研究,并把地基与梁(板)之间的接触力视为外力,根据作用力与反作用力互等的原理,推导出体系的势能泛函公式,再利用最小势能原理,求解出Boussinesq地基与地基梁(板)的位移大小和内力。建立含位移表达式的方程,并采用Mathematica语言编写程序并对其公式进行推导计算。结合各种算例,利用有关文献,系统研究Boussinesq弹性地基梁板与Winkler地基梁板的位移和内力曲线的差异性。本文的主要研究成果是推导出了Boussinesq弹性地基和弹性地基梁(板)的弹性势能公式,该方法可以作为研究建筑结构与地基共同作用原理的理论基础。
[Abstract]:In shipyard, airport runway, reinforced concrete pavement, building foundation floor and other engineering structures, elastic foundation beam and slab is widely used as foundation form. Although the analysis of beam and slab on elastic foundation is a classical course, the subject is still under study because of the emergence of new foundation model, analysis method and calculation method. In this paper, the Boussinesq foundation model is used to study the beam and plate on elastic foundation. In the elastic foundation and foundation beam (plate) system, the elastic potential energy stored in the elastic foundation and foundation beam (plate) system is derived by the method of first dividing and then closing. According to the superposition principle and equivalent principle in elastic mechanics, the elastic foundation and the foundation beam (plate) are studied as a whole, and the contact force between the foundation and the beam (plate) is regarded as the external force, according to the principle of the interaction between the acting force and the reaction force. The potential energy functional formula of the system is derived, and the displacement and internal force of Boussinesq foundation and foundation beam (plate) are calculated by using the principle of minimum potential energy. The equation with displacement expression is established, and the program is written by Mathematica language and its formula is deduced and calculated. The difference of displacement and internal force curves between Boussinesq elastic foundation beam and Winkler foundation beam and slab is systematically studied by using relevant documents. The main research result of this paper is to deduce the elastic potential energy formula of Boussinesq elastic foundation and elastic foundation beam (plate). This method can be used as the theoretical basis for studying the principle of the interaction between building structure and foundation.
【学位授予单位】：河南理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TU470

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