Analytical Solution Of Bending Problem Of Medium Thick Plate Under Vertical Elastic Constraint

The elastic rectangular plate is a common structural form and widely used in many engineering fields.Complex and super-large structures emerge with the economy growth and more loads need to be supported by these structures.The application of moderately thick plates is becoming more and more widely used.In the bending process of rectangular slabs,the load transmission is achieved by the self-locking action of concrete aggregates.The self-locking effect of the concrete aggregate is reduced when displacement settlement occurs and Towel bars are needed to avoid uneven displacement settlement.This paper simplifies the Towel bars into a vertical elastic support and works out the analytical solution of the bending problem of moderately thick plates with vertical elastic support with finite integral transformation method.The governing equations and finite integral transformation method for moderately thick plates bending problems are introduced,and the Fourier expansion of trigonometric functions is derived.Instead of defaulting deflection function,the finite integral transformation method starts from the control equation and transforms the control equation of the moderately thick plate into the integral transformation domain.The boundary conditions help determine the unknown constants and then the linear equation expressed by the constants are determined.The inverse transformation obtains the analytical solution of the deflection and internal force of the rectangular medium and thick plates.The finite integral transformation method is clear,easy to understand,and more widely used.By changing the spring stiffness,the vertical elastic support of the boundary conditions of medium and thick plates is compared to four-sided freedom,four-sided simply supported,and the other side simply supported and free.The moderately thick plate models with the boundary conditions above are numerically calculated with the finite element tool to verify the validity of the formula derivation.Comparing with the analytical solution of the formula derivation,the correctness of the formula derivation can be verified from the data results.Comparing the deflection function graphs of the four-sided free plate and the four simply supported edge plate,it comes to a conclusion that vertical elastic supports can effectively prevent pavement diseases.