Theoretic Solution Of Internal Force And Displacement For Thickness And Ladder Type Square Plate On Foundation With Four Edges Free

In the structural analysis of flexible foundation, the flexible foundation buried in elastic foundation usually simplified as four edges free rectangular plate on half space infinite body. But when solving bending problem of four edges free rectangular plate on elastic foundation, not only must meet four order differential bending equation of the board face, and also meet the geometry boundary conditions and internal force boundary conditions of the four free edge. And the analytical solution of different reverse force distribution foundations of is also different. So it is a complex and practical work to explore displacement and internal force of bending analytical solution for four edges free rectangular plate on elastic foundation considering the force distribution foundation. The foundation reverse force is linear distribution in the traditional calculation method and code for design of building foundation.Introducing symmetry conditions, this paper get the displacement function when symmetric loading and respectively against says loading based of the displacement function with complement remainder raised by Yanzongda. According to bending equation and boundary conditions of the plate, and through Fourier series development and programming by Maple, we can get those undetermined coefficient of the displacement function when foundation reverse force is a linear distribution. Then according to load and symmetrical against says load act on the square board, we can get the analytical solution of the displacement and internal force of thickness and ladder square plate on elastic foundation when four edges free. When solving this analytical solution, this paper will cut ladder square plate in the ladder, and then formed a segregated square thickness plate and a isolation body with a hole. At the same time, we put forward a reasonable hypothesis of the distribution form for the forces between the segregated bodies. At last, we compare the analytical solution are obtained in this paper with ANSYS numerical calculation results, and analysis its accuracy.Concerning the foundation of the small building, linear distribution hypothesis of foundation reverse force can meet the engineering need. However, if the foundation is for the large building, then considering foundation reverse force as linear distribution still may produce large error. Based on the measured results and the reverse force function of foundation raised by WangGuoTi, this paper put forward the reverse force function adjust to the symmetric loading. And Contrast analysis with numerical solution through ANSYS simulation of the contact stress between ground base and foundation, we can find the reaction function of the subgrade raised in this paper is not only very accurate, but also have a widely using range. At last, this paper analyses analytical solution for internal force of four edges free square plate symmetrical loaded on elastic foundation with the results according to the code for design of building foundation when the subgrade reaction is nonlinear.