Static and Dynamic Theory of Plates due to Hybrid Assumption and its Accuracies

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  • 混合型仮定による静的・動的平板理論とその精度
  • コンゴウガタ カテイ ニヨル セイテキ ドウテキ ヘイバン リロン ト ソノ セイド
  • コンゴウガタ カテイ ニ ヨル セイテキ ドウテキ ヘイバン リロン ト ソノ

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By using of mixed Hamilton's principle with Reissner's functional, the present paper derives the general higher-order static and dynamic theory of transversely isotropic elastic plate under the assumption of stress components as well as displacement ones (that is, hybrid assumption), which satisfy exactly the boundary (loading) conditions on the upper and lower surfaces of the plate. The results of this formulation include the both cases of bending and stretching behaviours of the plates. It is shown that several famous dynamic theories of plates can be derived as a special case of our result with employment of first-order terms and with some modifications. Numerical results for the statical cases of torsion of a rectangular plate with transversely isotropy and transversely loaded plate with simply supported edges under the several lower-order theories are compared with the exact solution of elasticity.

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