Review article

The application of Legendre polynomials as approximating functions to study the stability of shell structures is investigated. The shells in question are square in plan, made of steel and have an articulated fixed support. As a mathematical model for studying the stress-strain state of shells, the functional of the total potential energy of deformation is used, taking into account transverse shifts (Timoshenko-Reisner model). The stability of three structures of different geometries for different sets of approximating functions has been investigated. The results obtained are compared with similar results obtained using the trigonometric basis. The convergence of the bases for the considered structures is analyzed.