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

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Ioakimidis, Nikolaos
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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.
Rayleigh–Ritz method, Plane elasticity, Isotropic elasticity, Biharmonic equation, Airy stress function, Symbolic computations, Numerical computations, Approximate solutions, Computer algebra, Mathematica