置入线弹性地基内梁的精化理论  

A REFINED THEORY OF BEAM POSTING INSIDE LINEAR ELASTIC FOUNDATION SOIL

作　　者：赵宝生[1] 佟继龙[1] 高阳[2] 

机构地区：[1]辽宁科技大学机械工程与自动化学院,辽宁 鞍山114051 [2]中国农业大学理学院,北京100083

出　　处：《工程力学》2009年第A01期16-19,共4页Engineering Mechanics

基　　金：国家自然科学基金项目(10602001,10702077);辽宁省教育厅高等院校科研计划项目(2004F051)

摘　　要：将Cheng氏精化理论的研究方法推广到线弹性地基内梁的研究当中,从位移通解出发对线弹性地基内的梁进行了精确的分析,给出其精化理论。首先给出利用中线上位移及转角表示的弯曲梁的位移场和应力场,再利用线弹性地基条件,获得弹性地基内梁的精确挠度控制方程。由于精确的控制方程不利于实际应用,因此我们利用Lur'e算子函数的展开,获得了近似的挠度控制方程和利用挠度表示的位移场和应力场。若略去控制方程中的高阶项及切向比例常数k1,与Winkler弹性地基内Euler-Bernoulli梁的挠度控制方程一致。Cheng＇s refined theory is extended to investigate the beam posting inside the linear elastic foundation soil, and an exact analysis for the beam is given. Expressions are obtained for all of the displacements and stress components in term of the midline displacement and its derivatives. The exact control equation of the beam is given from boundary conditions. However, exact equation is not applicable in most cases, since they are of infinite order. Using Lur＇e Operator Function series, we obtain the approximate expressions of the midline displacement functions. From the refined theory, the displacement field and the stress field in the beam can be given. In case the term that the higher-order and kl are omitted, the equation in terms of deflection of the refined theory is changed into the Euler-Bernoulli control equation of the beam on Winkler foundation.

关 键 词：数学弹性力学 弹性梁板 精化理论 线弹性地基 位移场 应力场 

分 类 号：O343[理学—固体力学]