Hinged and supported plates with corners

Some solutions of minimaxmax problems for the torsional displacements of rectangular plates

“…In particular, it is convenient to know how does the gap function changes, once we perturb each of those coefficients. Taking into account (18), we have that the derivative of the coefficients , , , with respect to a perturbation of each coefficient defining can be obtained through the solution of a linear system,…”

“…We refer to [, (2.40)] for the justification of these boundary conditions, see also [] for full details on how to derive them for the rectangular plate Ω under study. The behavior of rectangular plates subject to a variety of boundary conditions is studied in []. The solution u of –– represents the vertical displacement of the plate under the action of f and, since the boundary conditions – satisfy the complementing condition [, Lemma 4.2] so that elliptic regularity applies, u is a strong solution of whenever f belongs to suitable spaces.…”

“…We refer to [24, (2.40)] for the justification of these boundary conditions, see also [8] for full details on how to derive them for the rectangular plate Ω under study. The behavior of rectangular plates subject to a variety of boundary conditions is studied in [6,10,11,18]. The solution of (20) so that elliptic regularity applies, is a strong solution of (20) whenever belongs to suitable spaces.…”

Approximation of Thin Three-Dimensional Plates with Smooth Lateral Surface by Polygonal Plates

“…We emphasize that it was the last fact that motivates the authors to study the asymptotics of a thin three-dimensional plate. Finally, as was established in [22,23], the solution to the Kirchhoff problem with linearized conditions on the edge of a polygonal plate does not satisfy the complete Signorini conditions which are unilateral constraints in their nature (the impenetrability condition and positivity of the support reaction). Thus, the cause of the Babuška paradox is purely mathematical and cannot serve as a background of physical or mechanical phenomena.…”

Thresholds for hanger slackening and cable shortening in the Melan equation for suspension bridges

“…In this section we take advantage of the results so far obtained in order to analyze the vibrating modes of a rectangular plate Ω = (0, π) × (− , ) (2 > 0 is the width of the plate and 2 π); for simplicity, we take here L = π. Specifically, we consider a partially hinged plate whose elastic energy is given by the Kirchhoff-Love functional, see [7,12] for discussions on the boundary conditions and updated derivation of the corresponding Euler-Lagrange equation. From [2] we know that the vibrating modes of the plate Ω are obtained by solving the following eigenvalue problem…”