THE U-TRANSFORMATION-FINITE ELEMENT METHOD FOR RECTANGULAR THIN-PLATE BENDING PROBLEMS
The U-Transformation-Finite Element method for a rectangular thin plate is extended in this paper. The stiffness matrix is converted to a cyclic matrix by establishing an equivalent system for the rectangular thin plate with simply-supported boundary conditions or clamped boundary conditions, and their combination. Then the finite element matrix equation is uncoupled by adopting U-transformation, resulting in the calculation which can be performed in one element. The series of solution to deflections of the central point for the square plate, subjected to a concentrated force acted at the center of the plate and to a uniform bending moment acted on the two opposite edges, is given out. It could give an explicit expression of the error estimation and control the computational accuracy. Calculation examples for several different boundary conditions show that the present result has high efficiency and precision compared with existing results.