Buckling and postbuckling analysis of rectangular plates resting on elastic foundations with the use of the spectral method

Hybrid control of vibrations of a smart von Kármán plate

“…The operators H, B, P and F take different forms depending on the boundary conditions. The expressions for them and for A 1,2 and A 2,N can be found in [25] and [26]. The convergence of the method is investigated in [26].…”

Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review

“…According to the results of [38], if the compressive loading factor λ is greater than the Euler critical value λ E (the first eigenvalue of the linearized problem for the nonlinear equation in Equation ( 6) with the fixed tensile loading (λ = λ f ), then the plate buckles up and there exist at least three solutions to Equations (2) and ( 6): (w, ψ), (−w, ψ) for w = 0 and ψ = 0, and (0, 0). Otherwise, the plate is not deformed and it remains flat.…”

“…There are few devoted to the investigation of the two phenomena buckling and contact together in the nonlinear cases. Nevertheless, one can mention the articles of Yu and Wang [63], Bielski and Telega [64], Shen [65], Borisovich et al [34], Muradova et al [40], and Muradova and Stavroulakis [37,38]. The works by Borisovich et al [34] and Muradova et al [40] are devoted to the exploration of stability of a rectangular, isotropic plate on the linear Winkler-type foundation.…”

“…In [40], an application of the contact model to the problem from biomechanics and the numerical treatment of it are presented. Buckling and postbuckling analysis of the simply supported plate with the nonlinear foundation of the type in Equation ( 10) is studied in the work [65] and also in [37,38]. In the paper of Holanda and Goncalves [66], the buckling and postbuckling behavior of plates laterally constrained by a tensionless foundation and subjected to in-plane compressive forces are investigated.…”

“…The classical linear and nonlinear plate equations are the main keys for creating various plate models, including delamination of composite plates (Vasiliev and Morozov [27], Stavroulakis and Panagiotopoulos [28], Storakers and Andersson [29], Xue et al [30], and Haghani et al [31]), contact problems (Ohtake et al [32,33], Borisovich et al [34], and Malekzadeh and Setoodeh [35], Muradova and Stavroulakis [36][37][38][39], Muradova et al [40], Fichera [41]), analysis of buckled plates (Ciarlet and Rabier [3], Caloz and Rappaz [42], Matkowsky; Putnick [43], Chien et al [44], Chien et al [45], Muradova [46][47][48], Dossou and Pierre [49]), etc.…”