关键词: Helmholtz equation, mechanical quadrature method, Newton iteration, nonlinear boundary condition

Abstract: Based on the Kantorovich approximation solution for a rectangular plate in bending, this paper deals with the solutions for the ladder plate with various boundary conditions. The deflection of the plate is expressed in a first-order displacement function w(x,y)=(x,y)v(y) where the u(x,y) in x direction is the generalized beam function. By making use of the principle of least potential energy, the variable coefficients differential equations for v(y) may he established. By solving is, these differential euqations and making use of the boundary conditions, the accurate solutions of v(y) in y direction may be obtained. Then the displacement function w(x,y) is the solution for the problem of the bending of the ladder plate with a better degree of approximation.

Key words: Helmholtz equation, mechanical quadrature method, Newton iteration, nonlinear boundary condition