Abstract: In this paper, a new highcr-ortler theory to luminated plate and shells is presemed and then symmetric and antisymmetric cross-ply laminated plates, cyliadric bending and heading of spherical shells are also studied. In order to examine the accuracy of the theory, several particular examples have been calculated. The numerical results are in good agreement with the exact solution, which shews the theory is possessed of higher accuracy and is easy to solve a problem with few unknowns.

Key words: minimax theorem, variational method, dissipation rate, upper bound, game theory, turbulence