In the latter case, the integrability of the field R( (r) (r)) is ensured if rot (R( (r) (r))) 0 and on all internal contours of the cross section of the beam the following conditions. The last problem admits solution for any datum. This result may be motivated by making recourse to an analogy with an elastostatic problem ( Romano, 2002 ). The condition for existence and uniqueness, to within a constant, of the solution C 2 ( R) of the Laplace-Neumann problem is that the integral of the normal derivative of the function, over the boundary, vanishes. Two analogies with elastostatics show that these problems admit an unique solution, to within a constant, for any datum ( Romano, 2002 ).įor particular positions and geometries of the holes of multiply connected cross sections or in the case of pure torsion the evaluation of the elastic shear stresses may be alternatively carried out formulating a Poisson-Dirichlets problem. Scienza Delle Costruzioni Gambarotta Free Form To.Scienza Delle Costruzioni Gambarotta Plus The Gradient.
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