【作者】 王亮；

【导师】 陈英杰；

【作者基本信息】 燕山大学 ， 结构工程， 2010， 硕士

【摘要】 随着国民经济的发展,公路交通、大型工业厂房及高层建筑得到了迅猛发展,弹性板在工程中也得到了大量的应用,尤其是矩形薄板普遍的应用于地下建筑工程、水利工程中,如地下连续挡土墙、水闸闸门、飞机场跑道都可以视作矩形薄板。寻求复杂边界矩形板的解,在一般条件下是相当困难的,在工程实际中,这些项目的设计往往采用经验公式或图表,因而具有较大的误差。这就需要建立一系列精确可靠的理论来指导生产实践。因此本课题的研究有一定的理论意义和工程应用价值。应用弱容许应力、平衡弱容许位移的概念以及功的互等定理建立了小变形混合变量的第一余能原理和第二余能原理,给出了弯曲矩形板混合变量的余能原理和不同边界条件下的余能表达式,与传统的矩形板解法相比,在混合变量第二余能表达式中引入集中载荷P,从而简化了挠曲面方程的求解过程。应用混合变量的第二余能原理求解了在集中载荷和均布载荷作用下的四边简支、四边固定、两邻边固定两邻边自由、四角点支撑等边界条件下弯曲矩形板的平衡问题,给出了不同情况下的挠曲面方程和数值结果。通过与ANSYS数值结果和实验结果进行比较,证明了本文给出的方法在求解矩形板弯曲问题时的通用性和准确性。混合变量的余能原理可以应用于工程实践中,为实际工程提供更多可靠的科学依据。更多还原

【Abstract】 With the rapidly developing of national economy in recent years, highway communications, large industrial workshop and high-rise have developed quickly; elastic plates are widely used in engineering, especially rectangular plates are widely used in underground architectural engineering and water project. like underground diaphragm wall, sluice gate, runway of airfield and so on, are all construed as rectangular plate. It is difficult to get an uncomplicated solution to solve rectangular plate under complicated boundery condation. In some engineering practice, experience formulas and graphs were adopted, thus there were always big errors. Establishing a precise and reliable theory to practical process is becoming urgent. Thus this research is a matter of significance in theorem research and in engineering application.With the definitions of weakly admissible stress, weakly admissible displacement of equilibrium and the reciprocal theorem, this paper established the first and second principle of complementary energy with mixed variables in small deformation, two theorems of complementary energy with mixed variables are given out. The theorem of complementary energy with mixed variables of rectangular plate and the complementary energy equations of rectangular plate under different boundery conditions are given out. Compared with traditional methods of rectangular plate, P is introduced in expression of the second principle of complementary energy with mixed variables, the method to solve the equations of the deflection surface is been simplified. The bending rectangular plate with different boundary conditions under different loads, such as with four edges simply supported under concentrated load or uniform load; four edges fixed under uniform load; four corner points supported under uniform load; two adjacent edges free and the other two adjacent edges fixed under uniform load etc. are solved with the second complementary energy theorem. The equations of the deflection surface and the numerical values were given out. Compared with the results of ANSYS and the experimental results, the method of this paper is correct and general in solving the rectangular plate problems. Finally, the method introduced in this paper can be applied to solve the actual project, giving the actual project more since numerical values.更多还原