Abstract
The general theory of elastic stability for discrete conservative systems is applied to the post-buckling of a circular plate using the kinematically-admissible finite-element procedure and a corresponding continuum perturbation analysis is written down for comparison. The energy functional for moderately large deflections is first established, with a careful discussion of the precise mode of compressive loading. The calculus of variations is then used to generate the differential equations of equilibrium, and a continuum perturbation scheme employing the two basic displacement functions is developed as far as the second load derivative. The finite-element study is then made on the basis of the transformed energy functional, and the results are observed to converge rapidly to those of the exact continuum analysis, twelve elements being necessary for accurate results. The perturbation patterns of the finite-element and continuum schemes are seen to be essentially identical, and it is felt that the finite-element perturbation approach is a viable method for more complex practical problems of elastic post-buckling.
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