Semi-analytical Numerical Analysis Of Moderate-Thickness Plate And Subgrade Interaction

By using Vlazov's foundation model, based on Reissner's moderate-thickness plate theory and Hu Hai-chang's flat plate flexure theory with three generalized displacement(considering transverse shear distortion effect), the governing differential equation about two-parameter foundation and medium-thickness plate interaction is established in this thesis. By analyzing plate boundary condition, testing function which accurately satisfies with four tree boundaries condition is found in this thesis. The testing function is composed by triangle progression and multinomial. Usually taking the first item can meet compute precision requirement. As for moderate-thickness plate with four simply supported sides and four fixed sides, then adopt quintic B-splin function as the test function, to analyze curved characteristics of medium-thickness plate by Galerkin's weighted residual value method and least square method. Compared with the results of finite element method and series solution, it is proved that method in the text has high calculation accuracy and small computational effort, convenient parameter analyses and other advantages. Based on it,systemically discuss the influence of the plate thickness h(ratio between flexural rigidity and shear rigidityσ), foundation shear modulus k, foundation rigidity t, the load q and other factors on the deflection and stress characteristic of the moderate-thick plates on two-parameter elastic foundation in the thesis. The three-dimension graphs of deflection and bending moment are given in the thesis. Obtain some conclusions with guiding significance to practical project, at the same time, the program has been designed by Mathematica and MATLAB mathematical software. The procedure is simple and applicable, can be used for engineering computation.It indicates that two-parameter foundation model is better than Winkle foundation model because of considering the transverse shearing of foundation soil. With foundation stillness k and foundation shear modulus t increasing, the deflections and internal forces of the moderate-thickness plate decrease, but the effect of k is greater than t. This shows that t is a factor should consider in interaction analysis but the determinative factor is still foundation stiffness k. plate thickness h has a big effect on deflection but has a little effect on the internal force adjustment of plate, then deflection and internal forces of the plate were obviously influenced by load q on plate, which nearly is the linear growth. Because the superstructure is very sensitive to the foundation differential settlement, through the analysis obtains these results in this thesis, there are two major ways to eliminate and control differential settlement: (1) Increase the thickness of the raft plate (2) Adjust the foundation stillness distribution.