Application of Mathematica to the Rayleigh–Ritz method for plane elasticity problems

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Ioakimidis, Nikolaos
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Abstract
The classical Rayleigh–Ritz method for plane isotropic elasticity problems governed by the well-known biharmonic equation (satisfied by the Airy stress function) is revisited. The modern and powerful computer algebra system Mathematica was employed for the symbolic/numerical approximate solution of the biharmonic equation. A related simple procedure was prepared and the classical problem of a rectangular elastic region loaded by a parabolic tensile loading was chosen as an example of the application of the approach. The available symbolic/numerical results in the literature and additional more complicated analogous results were directly derived by using the aforementioned procedure. Further related possibilities and generalizations are also discussed in brief.
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Rayleigh–Ritz method, Plane elasticity, Isotropic elasticity, Biharmonic equation, Airy stress function, Symbolic computations, Numerical computations, Approximate solutions, Computer algebra, Mathematica
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