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Abstract

The load carrying capacity and collapse scenarios for an infinite elastic-plastic plate resting on a twoparameter elastic foundation uniformly loaded on a small circular footprint are investigated in a general framework of stiffness and yield parameters. The present work extends the study already presented for a specific value of the Pasternak modulus and it allows the investigation of the influence of the stiffness property of the underlying soil and the amplitude of the loaded region on the load carrying capacity of the plate and the corresponding collapse mechanism. Moreover, the present analysis allows for the evaluation of the transverse deflection, slope, radial and circumferential bending moments, shearing force within the plate and the reactive pressure of the elastic subgrade at the onset of the plastic collapse together with their dependence on the foundation moduli. The effect of the ratio between negative and positive yield moments is also investigated. The amplitude and assembly of plastic regions at the onset of the plastic collapse are discussed in some detail. 459 460 LUCA LANZONI, ANDREA NOBILI, ENRICO RADI AND ANDREA SORZIA book of Timoshenko and Woinowsky-Krieger [1959]. The axisymmetric flexure of an infinite elastic plate resting on an incompressible elastic half-space is considered by Selvadurai [1977] by making use of the potential functions and Hankel transforms. The problem of an elastic plate supported by an elastic twoparameter subgrade is studied in [Wen-da and Shu 1987] in order to model the circular foundation of a cooling hyperbolic tower. Results are compared with a numerical solution obtained through a FE package. The mechanical interaction between an infinite cracked Kirchhoff plate resting on a two-parameter elastic subgrade can be found in [Nobili et al. 2014[Nobili et al. , 2015. A full-field solution is obtained therein by means of the Wiener-Hopf method and the influence of the subgrade parameters on the stress intensity factors at the crack tip are evaluated in detail.Recently, Shukla et al. [2011] have obtained the solution of a circular plate supported by a tensionless Pasternak-type subgrade by using the strain energy approach and assuming a power series expansion for the transverse deflection of the plate. Variational boundary conditions for a beam resting on a twoparameter tensionless elastic foundation have been developed in [Nobili 2012]. Shell-and plate-like elements in contact with elastic media have been adopted as a reliable model to study micro-or nanostructures in the framework of modern microelectronics based on the use of special composite materials. As an example, Ru [2001] studied the critical loading for a double-walled carbon nanotube embedded in an elastic matrix. There, the nanotube is modeled as a thin elastic cylindrical shell supported by a Winkler subgrade, which accounts for the van der Waals forces. Likewise, in order to investigate the vibrations of carbon nanotubes, Liew et al. [2006] consider a plate embedded into a Pasternak elastic medium a...