广义支承端弹性地基梁的基本解及应用  

Basic solution and its application to beam on elastic foundation with generalized bearings

作　　者：王赞芝[1] 曹建军[1] 胡如成[1] 赵雅欣[1] 

机构地区：[1]广西工学院土木建筑工程系,广西柳州545006

出　　处：《辽宁工程技术大学学报（自然科学版）》2010年第6期1086-1089,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：广西科学研究与技术开发计划基金资助项目(桂科合0815007─1─10);广西工学院博士基金资助项目(院科博0901);广西工学院2010年大学生科研立项基金资助项目(2010039);广西研究生教育创新计划基金资助项目(2009105940814M02)

摘　　要：为了解决弹性地基梁在不同边界条件下,和不同的荷载工况下需要分别进行求解这一难题,引进了广义支承端弹性地基梁的概念,选择了其对应的基本系统,推导了基本系统的基本解。在基本系统与实际系统之间,采用修正的功的互等定理法,得到了具有广义支承端的实际系统的挠度曲线。通过具体算例,计算了两端刚性固定受均布荷重作用的弹性地基梁的挠曲线、转角、弯矩和剪力方程。研究结果表明:广义支承端弹性地基梁涵盖了实际可能存在的弹性地基梁的各种边界条件,及尽可能多的荷载工况,工程中遇到的实际弹性地基梁问题都是它的特例,因此运用该方法可以直接得到某一具体弹性地基梁问题的解答,而无需进行复杂的推导计算。It is obvious that the beams on elastic foundations with different boundary conditions,and/or with different concentrated and/or distributed loads should be analyzed separately in traditional approaches.In order to overcome this problem,the concept of beam on elastic foundation with generalized bearings was proposed in this paper.In the study,a fundamental system corresponding to this kind of beam was selected,and the fundamental solution to this system was also derived.Subsequently,applying the modified theorem of reciprocal work between the fundamental system and the actual system,a deflection curve of the actual system with generalized bearings was obtained.A case study on the beam on elastic foundation with both built-in ends which subjected to uniform loads was conducted to calculate the deflections,rotating angles,moments,and shear forces along the beam axis.The study result shows that the elastic beam with generalized bearings contains all possible boundary conditions and the most possible load conditions which may exist in actual elastic foundation beam,and the actual elastic foundation beam problems.The beams on elastic foundations encountered in engineering are specific which can be easily modeled using the method proposed in this paper without any complicated deduction.

关 键 词：修正功的互等定理 功的互等法 基本系统 实际系统 广义支承端 初参数法 普日列夫斯基函数 广义位移理论 

分 类 号：TU348[建筑科学—结构工程]