Abstract: In this paper, new principles of minimum potential/stationary complementary energy of thin plates and shallow shells for large deflection are proposed by means of Legender transformation. And based on these new principles, new three-variable generalized variational principles of thin plate/shallow shell for large deflections are establisted by applying Lagrange multiplier method to relax all constraint conditions including generalized stress-generalized strain relation. And the relations between them and previous generalized varitional principles are discussed.

Key words: Elastic mechanics, Large deflection, Shallow shell, Thin plate, Variational method