【作者】 丁翔；

【导师】 李刚；

【作者基本信息】 湖南大学 ， 岩土工程， 2008， 硕士

【摘要】 弹性地基上板是土木工程中较常见的一种结构形式,应用非常广泛,如建筑物的基础,机场跑道,公路路面,试验台等,其分析方法得到广大理论工作者和工程人员的重视。随着现代工程建设的发展,对基础板的分析提出了更高的要求。本文采用有限条法和弹簧体系分析了弹性地基上板的静动响应,并将结果与有限元线法、有限条法、级数精确解等进行比较,证明本文方法具有足够的精确性与实际的可行性。有限条法是一种半解析单元法,是解析方法与数值方法相结合的一种方法。它兼有数值方法和解析法的优点,因而在许多工程分析中得到应用。计算中本文应用Matlab数学软件编制出求解该问题的有限条程序,程序适用性较强,可以求解双参数弹性地基上任意边界条件组合下任意竖向荷载(包括板面上任意位置的均布荷载、集中荷载以及两者的组合)作用下的板内任意点的位移场、内力场以及弹性地基板的自由振动频率。本文利用该程序计算大量的算例,对所得结果进行了分析与研究,并总结了各种边界条件下板与地基相互作用的规律,即探讨了地基参数k、t以及荷载q等不同因素对于双参数地基上的板挠度、内力和自由振动频率的影响。给出了双参数地基上板在荷载作用下的内力分布图和挠度变化的表面三维图,从而可以从总体上直观的观察到板的内力分布和挠度变化的规律。本文最后计算了弹性地基上不同宽厚比板的中点挠度值,并与中厚板理论的加权残值解进行比较,根据其相对的误差绝对值,对弹性地基上薄板和中厚板尝试进行了大致的界定。更多还原

【Abstract】 ThePlateonelasticfoundationisacommonmodelforseveraltypesofcivilengineeringstructures, which has received considerable attention from researchers and engineers. Thebuildingfoundation,runways ofairports, roadways andtest-bedareusuallymodeledas platesonelasticfoundation.Withtherapiddevelopments inthefieldofconstruction,theanalysis oftheplatesonelasticfoundationisofvitalimportance.Aprocedure incorporating the finite strip method and a spring system has been used totreat the static and dynamic response of plates resting on elastic foundation. The finite stripmethod results were compared with other methods such as finite element method of lines,finite element analysis and closed solutions, showing the finite strip method is correct andfeasible. Finite strip method is a semi-analytical numerical method which has advantages ofthe analytical methods and numerical methods. Finite strip method is a procedureincorporating analytical method and numerical method which was used widely in theconstructional analysis. In this article, a program about the finite strip method is compiled byusing Matlab mathematics software to treat the static and dynamic response of the plates ontwo-parameter elasticfoundation.Theprogram has broad applicability,whichcan analyzethedisplacement fields and the internal force fields of plates on two-parameter elastic foundationwith arbitrary boundary and arbitrary loading conditions(contains uniform line load,concentrated load or combined loads on arbitrary position of plates). This program is alsoapplied on the dynamical analysis of plates on two-parameter elastic foundation, the naturefrequencyof plates with arbitraryboundarywas researched. Analyzingand researchingin theresultsoftheplate’sdeflection、bendingmomentandthenaturefrequencyfromcalculatingamass of examples by the program. The laws of interactions of plates and foundation witharbitrary boundary are summarized. Namely, discuss the influence of the foundation’sparametersk,t,theloadqandotherfactorsonthedeflection、bendingmomentandthenaturefrequency of plates on two-parameter elastic foundation. The distributed chart of bendingmoment and the surface 3-D chart of deflection are given, from which we can visuallyobserve the distributing of bending moment and the variational directions of deflection as awhole. The article gives the results of rectangular plates under various width -thickness ratiosand the results are compared with the Reissner’s plate’s solution which was given by aweighted residual method. At last the article gives a rough limitation between thin and thickplatesaccordingtotheabsolutevaluesoftheirrelativeerrors.更多还原