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A Pasternak foundation is a two-parameter foundation model used to analyze the behavior of laterally loaded beams embedded in semi-infinite media.
The load-displacement relationship of the foundation is assumed to be p0 = Kwxw ‒ Kp (w,xx + w,yy), where p0 is the force per unit area, Kw (N/m3) is the Winkler foundation stiffness, Kp (N/m) is shearing layer stiffness of the foundation, w is the displacement and a comma denotes partial differentiation with respect to the corresponding coordinates.
From:
A.M. Najafov (1), A.H. Sofiyev (2), D. Hui (3), Z. Karaca (4), V. Kalpakci (5) and M. Ozcelik (6)
(1) Institute for Machine Elements and Lifting-and-Shifting Machines of Azerbaijan Technical University, Baku, Azerbaijan
(2) Department of Civil Engineering, Engineering Faculty, Suleyman Demirel University, Isparta, Turkey
(3) Department of Mechanical Engineering, University of New Orleans, New Orleans, USA
(4) Department of Civil Engineering, Ondokuz Mayis University, Samsun, Turkey
(5) Department of Civil Engineering, Hasan Kalyoncu University, Gaziantep, Turkey
(6) Department of Geological Engineering, Suleyman Demirel University, Isparta, Turkey
“Stability of EG cylindrical shells with shear stresses on a Pasternak foundation”, Steel and Composite Structures, Vol. 17, No. 4 (2014) 453-470, DOI: http://dx.doi.org/10.12989/scs.2014.17.4.453
ABSTRACT: This article is the result of an investigation on the influence of a Pasternak elastic foundation on the stability of exponentially graded (EG) cylindrical shells under hydrostatic pressure, based on the first-order shear deformation theory (FOSDT) considering the shear stresses. The shear stresses shape function is distributed parabolic manner through the shell thickness. The governing equations of EG orthotropic cylindrical shells resting on the Pasternak elastic foundation on the basis of FOSDT are derived in the framework of Donnell-type shell theory. The novelty of present work is to achieve closed-form solutions for critical hydrostatic pressures of EG orthotropic cylindrical shells resting on Pasternak elastic foundation based on FOSDT. The expressions for critical hydrostatic pressures of EG orthotropic cylindrical shells with and without an elastic foundation based on CST are obtained, in special cases. Finally, the effects of Pasternak foundation, shear stresses, orthotropy and heterogeneity on critical hydrostatic pressures, based on FOSDT are investigated.
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