Buckling Instability Wave Inequality Constraints

Shells especially cylindrical shells as a kind of structure are often used in architecture , shipping, airplane and astro-carrying machines. The pipings under ground. tunnels and pressure vessels usually have thin underlayer. When it bucks, the buckling of model is different from other shells because it is constrained by the cavum. In this paper, in the cylindrical shell's axis direction, it is discreted by the finite strips and on the circumference the straight lines. The problem of the constrained generalized eigenvalues is transferred to a quadratic programming problem. Consequently the solution method of generalized eigenvalue equations which possess linear complementary conditions is presented. The inverse iteration method for solving the minimum of the generalized eigenvalues is developed in this paper. At every step of iterations, the linear complementary equations are solved by Newton non-smooth algorithm. The numerical results show that the method proposed by this paper is effective. The buckling critical load of the constrained cylindrical shell is almost the same, and is independent of the length of the cylindrical shell, which is completely different from free (unconstrained) cylindrical shell.It is also proved that the geometrical relationships used in this paper approach to Koiter-Standers theory of cylindrical shell, when the length of the straight beam element on the circumference approaches zero.In the theory of elasticity , the basic equations are classified as the displacement equation > the stress equation and the mixed formulation. It is pointed out in this paper that the mixed formulation here is also the Hamiltonian representation of elasticity field. The importance of the mixed formulation and a method of constructing the Hamilton canonical equations are also stated. A method of the buckling critical load for laminated beam and laminated plate under Hamilton system is presented on this basis. Using the theory of geometrically nonlinear, a equation to calculate the buckling critical load of elasticity field is presented. The theory of elasticity based on Hamilton system is developed.