ABSTRACT
For decoulping the system, the variable substitution defined as follow:
subsititute Eq. (7), Eq. (8) and Eq. (9) into the coupling equations, and get two independent equations just including the new variable as followed:
where α, β, γ and (m1, m2) are the constant coefficients decided by Cij , Dij and mi. In next step
work, taking an orthotropic rectangular plate with four simple edges as an example, solve Eq. (10) and Eq. (11) respectively. The boundary condition expressions are:
Through the solutions of Eq. (10) and Eq. (11), the final exact solution of the generalized displacements for the orthotropic plates are obtained as followed:
The exact solution of the rectangular plate with the boundary condition SSSS is calculated in a numerical example, which is considered that a = b = 4 m, h = 0.8, E = 343 MPa, q = 2.0 × 106 N and υ= 0.3, and the calculating result is shown in Fig. 1.
