Abstract
The method is proposed for solving the plates stability problems by the finite element method based on piecewise constant approximations of moments. The solution was obtained on the basis of the principles of minimum additional energy and the possible displacements. To ensure the moment fields equilibrium, the equilibrium algebraic equations of grid nodes are compiled using the possible displacements principle. Such equilibrium equations are written as a system of linear homogeneous algebraic equations. Using the Lagrange multipliers method the equilibrium algebraic equations are including to the functional. The proposed method ensures the critical stress convergence to the exact value from below, which provides reserve of the plate stability.
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