Vlazov地基上Reissner板相互作用的加权残值分析法  

Weighted Residual Method for the Analyzing of the Interaction of Reissner's Plate on Vlazov's Elastic Foundation

作　　者：李刚[1] 罗世平[1] 尚守平[1] 

机构地区：[1]湖南大学土木工程学院,湖南长沙410082

出　　处：《湖南大学学报（自然科学版）》2006年第1期20-24,共5页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(50278033)

摘　　要：以Vlazov双参数弹性地基上Reissner中厚板为研究对象,建立地基与中厚板相互作用的控制微分方程,运用B样条函数为试函数的加权残值法进行了分析求解,并结合Matlab软件编制程序进行算例分析.算例表明,对于Vlazov地基上四边简支的Reissner板,板的弯剪刚度比的增大可有效地减小板的挠度,亦即减小地基的变形;考虑地基的横向连续性可合理地修正板的挠度和弯矩的值,使其与工程实际更相符.本方法只需划分稀疏的离散网格,便可得到与精确解吻合较好的数值结果,其计算效率与精度均优于全域离散的有限元法.This paper discussed the Reissner＇s plates on elastic foundation. The elastic foundation model was considered as Vlazov＇s two-parameter elastic foundation model and its effect on medium-thick plates were taken into account with a set of governing differential equations. A weighted residual method which used B-spline function as the trial function was put forward to solve the bending problems. As to the Reissner＇s plate with simply supported edges on Vlazov＇s foundation, calculations showed that the accretion of plate＇s stiffness ratio of bending to shearing could effectively reduce the plate＇s deflection, i.e. reduce the deformation of foundation. Projects will benefit notably from the consideration of the transverse continuity of the foundation, which will amend the values of the plate＇s deflection and bending moment. Only by plotting sparse grids could the method get the results which agreed well with the accurate answers, and both its calculation efficiency and precision were superior to finite element method.

关 键 词：REISSNER板 Vlazov双参数弹性地基 B样条函数 加权残值法 相互作用 

分 类 号：TB122[理学—工程力学]