Keywords: plate bending analogy, complex analysis, torsion, plate, Saint Venant beam, Prandtl function..

The use of complex analysis for studying two-dimensional potential problems is an efficient tool and increasingly used for numerical analysis of problems related to systems governed by the Laplace equation. Two main advantages are reached by use of complex analysis: a technical one and a physical one. Technically, it is possible to characterize the solution for two conjugate functions at once; physically, the real and the imaginary part are orthogonal functions and have a general meaning of potential and stream functions, in one word complex analysis allows a binocular view of an engineering problem.

This aspect has been stressed for solving beams under torsion actions. In this regard the solution may be evaluated as a complex potential function whose real part is the warping function, and the imaginary part is related to the stress function, this highlights the effective binocular aspect. Moreover taking into account the analogy between the bending of simply supported plates loaded by uniformly distributed edge moments and the torsion of a beam, in this paper, it will be shown how to evaluate the deflection of the aforementioned plate performing line integrals only. Additionally in this paper an innovative formulation for evaluating the deflection function of a simply supported plate loaded by uniformly distributed edge moments is introduced. This innovative formulation implemented through a few lines of Mathematica software leads to reliable solutions for all cases and to an exact solution for some cases.

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