Weighted Residual Method For The Analysis Of The Interaction Of Moderate-Thick Plates On Two-Parameter Elastic Foundation

With the rapid developments in the fields of construction, large modern airport, offshore dock, container yard, heavy traffic road construction etc, the problem of adapting design re-quirements of plates on elastic foundations to the developments in these fields becomes more and more outstanding. In general analysis, as the limitation of assumptions of Kirchhoff clas-sical plates theory, it makes error when the plates are thicker, which can't meet the require-ments of engineering precision. Therefore, the research in bending problem of moderate-thick plates and the analysis in the interactions of plates and foundation becomes more important in engineering practice.This article discusses the Reissner's plates on elastic foundation. The elastic foundation model is considered as two-parameter elastic foundation model and its effect to moderate -thick plates are taken into account by a set of governing differential equations. United with Hu Hai-chang's function, least squares collocation weighted residual method which uses B-spline function as trial function is put forward for solving the bending problems. Compare with the results of finite element method of lines, spline finite strip method, accurate solution of series etc. It is proved that the method in this article has adequate accuracy and practical feasibility. In this article, a program about the weighted residual method is compiled by using Matlab mathematics software to solve this problem. The program has broad applicability, which can analyze the displacement fields and the internal force fields of moderate-thick plates on two-parameter elastic foundation with arbitrary boundary and arbitrary loading con-ditions(contains uniform line load, concentrated load or combined loads on arbitrary position of plates). Analyzing and researching in the results of the plate's deflection and bending mo-ment from calculating a mass of examples by the program. The laws of interactions of plates and foundation with arbitrary boundary are summarized. Namely, discuss the influence of the thickness of plates h, foundation's parameters k, t, the load q and other factors on the deflec-tion and bending moment of the moderate-thick plates on two-parameter elastic foundation. The distributed chart of bending moment and the surface 3-D chart of deflection are given, from which we can visually observe the distributing of bending moment and the variational directions of deflection as a whole. The article gives the results of rectangular moderate-thick plates under various length-width ratios and various thickness-width ratios and the results are compared with corresponding series solution about thin plates. At last the article gives a rough limitation between thin and thick plates according to the absolute values of their relative er-...