An incautious use of the well-known Galërkin’s technique to find approximate solutions of a differential problem may lead to apparently wrong results. Examples are based on an inverse approach to investigate buckling of compressed axisymmetric circular plates, a subject that is common in courses on mechanics of structures and stability of structural elements. We discuss how the mistake may originate and show how it is possible to recover the expected results, thus providing a means for the students to cross-check their outputs.
GalerkinBV.Sterzhni i plastiny. Ryady v nekotorykh voprosakh uprugogo ravnovesiya sterzhnei i plastin (rods and plates series occurring in some problems of elastic equilibrium of rods and plates). Vestnik Inzhenerov i Tekhnikov1915;
19: 897–908. Petrograd (in Russian). (English Translation: 63-18925, Clearinghouse Fed. Sci. Tech. Info).
2.
RepinS.One hundred years of the Galerkin method. Comput Meth Appl Math2017;
17: 351–357.
3.
RutaGElishakoffI.Towards the resolution of the Smith-Herrmann paradox. Acta Mechanica2004;
173: 89–105.
4.
De BellisMLRutaGCElishakoffI.Influence of wieghardt foundation on the dynamic stability of a pipe conveying fluid. Arch Appl Mech (Ingenieur-Archiv)2010;
80: 785–801.
5.
ElishakoffIRutaGStavskyY.A novel formulation leading to closed-form solutions for buckling of circular plates. Acta Mech2006;
185: 81–88.
