Engineering

Buckling

Materials science

Applied mathematics

Superposition principle

Computer science

Symplectic geometry

Finite element method

Mathematics

GRASP

Mathematical analysis

Geometry

Composite material

Structural engineering

Programming language

Euclidean space

International Journal of Mechanical Sciences

This paper deals with the representative challenging buckling problem of a fully free plate under biaxial compression by a distinctive symplectic superposition method, which yields the benchmark analytic solutions by converting the problem to be solved into the superposition of two elaborated subproblems that are solved by the symplectic elasticity approach. The solution is advanced in the symplectic space-based Hamiltonian system rather than in the classic Euclidean space-based Lagrangian system, which shapes the main advantage of the method that a direct rigorous derivation is qualified for obtaining the analytic solutions, without any assumptions or predetermination of the solution forms. Comprehensive new analytic results for both the buckling loads and mode shapes are presented and validated by the finite element method. The fast convergence and accuracy of the method make it applicable to analytic modeling of more plate problems.

New analytic buckling solutions of rectangular thin plates with all edges free