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Research Papers

Ultimate Carrying Capacity of Elastic-Plastic Plates on a Pasternak Foundation

[+] Author and Article Information
L. Lanzoni

DIEF—Dipartimento di Ingegneria “Enzo Ferrari”,
Università di Modena e Reggio Emilia,
Via Vignolese 905,
Modena 41125, Italy;
DET—Dipartimento di Economia e Tecnologia,
Università di San Marino,
Salita alla Rocca 44,
Republic of San Marino,
San Marino 47890, Italy

E. Radi

DISMI—Dipartimento di Scienze e
Metodi dell'Ingegneria,
Università di Modena e Reggio Emilia,
Via Amendola 2,
Reggio Emilia 42122, Italy
e-mail: eradi@unimore.it

A. Nobili

DIEF—Dipartimento di Ingegneria “Enzo Ferrari”
Università di Modena e Reggio Emilia,
Via Vignolese 905,
Modena 41125, Italy

Manuscript received September 27, 2013; final manuscript received December 4, 2013; accepted manuscript posted December 10, 2013; published online January 8, 2014. Assoc. Editor: Nick Aravas.

J. Appl. Mech 81(5), 051013 (Jan 08, 2014) (9 pages) Paper No: JAM-13-1407; doi: 10.1115/1.4026190 History: Received September 27, 2013; Revised December 04, 2013; Accepted December 10, 2013

In the present work, the problem of an infinite elastic perfectly plastic plate under axisymmetrical loading conditions resting on a bilateral Pasternak elastic foundation is considered. The plate is assumed thin, thus making it possible to neglect the shear deformation according to the classical Kirchhoff theory. Yielding is governed by the Johansen's yield criterion with associative flow rule. A uniformly distributed load is applied on a circular area on the top of the plate. As the load is increased, a circular elastic-plastic region spreads out starting from the center of the loaded area, whereas the outer unbounded region behaves elastically. Depending on the size of the loaded area, a further increase of the load may originate two or three different elastic-plastic regions, corresponding to different yield loci. A closed form solution of the governing equations for each region is found for a special value of the ratio between Pasternak soil moduli. The performed analysis allows us to estimate the elastic-plastic behavior of the plate up to the onset of collapse, here defined by the formation of a plastic mechanism within the plate. The corresponding collapse load and the sizes of the elastic-plastic regions are thus found by imposing the boundary and continuity conditions between the different regions. The influence of the soil moduli, plate bending stiffness, and size of the loaded area on the ultimate bearing capacity of the plate is then investigated in detail.

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Figures

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Fig. 2

(a) Johansen's yield locus for elastic-plastic plates and corresponding flow rule, and (b) positive bending moments and shear force per unit length

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Fig. 1

Sketch of the plastic mechanism (a) for b < c and (b) for c < b. The loaded region 0≤r≤a has been highlighted; (0) plastic corner region r ≤ d, (1) elastic-plastic region under load d≤r≤a, (2) unloaded elastic-plastic region, and (3) elastic outer region; (4) annular elastic-plastic region

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Fig. 9

(a) Dimensionless ultimate load versus the amplitude a of the loaded area for μ = 0.5, 1; (b) dimensionless loci c/L, b/L, and d/L versus the amplitude a of the loaded area for μ = 0.5, 1

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Fig. 3

Dimensionless plate deflection versus the radial coordinate for different amplitude a of the loaded area for (a) μ = 1 and (b) μ = 0.5

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Fig. 5

Dimensionless radial bending moment versus the radial coordinate for different amplitude a of the loaded area for (a) μ = 1 and (b) μ = 0.5

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Fig. 6

Dimensionless circumferential bending moment versus the radial coordinate for different amplitude a of the loaded area for (a) μ = 1 and (b) μ = 0.5

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Fig. 7

Dimensionless shear force versus the radial coordinate for different amplitude a of the loaded area for (a) μ = 1 and (b) μ = 0.5

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Fig. 8

Dimensionless reacting soil pressure versus the radial coordinate for different amplitude a of the loaded area for (a) μ = 1 and (b) μ = 0.5

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Fig. 4

Dimensionless rotation of the plate cross section versus the radial coordinate for different amplitude a of the loaded area for (a) μ = 1 and (b) μ = 0.5

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