Contents lists available at ScienceDirect Thin–Walled Structures journal homepage: www.elsevier.com/locate/tws Full length article Axisymmetric post-buckling behavior of saturated porous circular plates M.R. Feyzi, A.R. Khorshidvand ⁎ Department of Mechanical Engineering, Islamic Azad University, South Tehran Branch, 11365/4435 Tehran, Iran ARTICLE INFO Keywords: Post-buckling Porous material Circular plate Shooting method ABSTRACT This study aimed to investigate axisymmetric post-buckling behavior of a circular plate made of porous material under uniformly distributed radial compression with simply supported and clamped boundary conditions. Pores are saturated with fluid and plate properties vary continuously in the thickness direction. Governing equations are obtained based on classical plate theory and applying Sanders nonlinear strain-displacement relation. Shooting numerical method is used to solve the governing equations of problem. Effects of porosity coefficient, pore distribution, pore fluid compressibility, thickness change and boundary conditions on the post-buckling behavior of the plate are investigated. The results obtained for post-bucking of homogeneous/isotropic plates and critical buckling load of porous plates are compared with the results of other researchers. 1. Introduction Porous materials are composed of two components; a solid matrix and fluid within matrix pores that can be liquid or gas. Porous materials exist in nature such as stone, wood and bone and may be made artificially such as metal, ceramic and polymer foams and they are used as structural components in various industries such as aerospace, transportation, building, etc. Biot [1] who is the pioneer in developing the theory of poroelas- ticity, studied buckling of a fluid-saturated porous slab under axial compression and showed that critical buckling load is proportional to pore compressibility. Magnucki and Stasiewicz [2] investigated buck- ling of a simply supported porous beam and showed porosity effect on the strength and buckling load of the beam. Buckling and bending of a rectangular porous plate with varying properties across the thickness and under in-plane compression and transverse pressure were studied by Magnucki et al. [3]. Magnucka-Blandzi [4] examined buckling of a circular porous plate and showed that the critical load linearly decrease with increase porosity of the plate; he also studied dynamic stability of a circular plate made of metal foam and showed porosity effect on critical loads with numerical results [5]. He continued his research in this field and investigated rectangular sandwich plate with metal foam core and simply supported boundary condition. In this study, he considered the middle plane of the plate as symmetry plane and by numerical method obtained critical buckling loads for a set of sandwich plates [6]. Jasion et al. [7] obtained global and local buckling for sandwich beam and plate with metal foam core by experimental, numerical and analytical methods, and compared the obtained results. Wen [8] obtained an analytical solution for saturated porous plate with an incompressible fluid and showed that there is a significant interac- tion between the solid and flow. Closed-form solution for buckling of porous circular plate saturated with fluid and with three different types of pore distribution in thickness direction including nonlinear nonsym- metric, nonlinear symmetric and monotonous and based on classical plate theory (CPT) under mechanical and thermal loads was obtained by Jabbari et al. [9,10]. Buckling of porous circular plates integrated with piezoelectric layers was investigated under mechanical and thermal loads and based on CPT by [11–13] and under thermal load and based on first-order shear deformation plate theory by [14]. Buckling analysis of porous plates with functional properties is similar to functionally graded material (FGM) plates to some extent. Woo and Meguid [15] obtained an analytical solution in terms of Fourier series for the coupled large deflection of FG plates and shallow shells under transverse mechanical loads and a temperature field. Closed-form solution for the critical buckling temperature of a rectan- gular FG plate was obtained under different types of thermal loads and based on classical and higher-order shear deformation plate theories by Javaheri and Eslami [16,17]. They showed that classical plate theory overestimates buckling temperatures. They also examined Buckling of FG Plates under in-plane Compression and based on CPT [18]. Najafizadeh and Eslami [19] presented buckling of a circular plate with functional properties under uniform radial compression. Ma and Wang [20] investigated axisymmetric post-buckling of an FG circular plate under uniformly distributed radial compressive load. They also [21] studied bending and thermal post-buckling of an FG circular plate based on classical nonlinear von Karman plate theory. The governing http://dx.doi.org/10.1016/j.tws.2016.11.026 Received 10 June 2016; Received in revised form 24 November 2016; Accepted 30 November 2016 ⁎ Corresponding author. E-mail address: ar_khorshidvand@azad.ac.ir (A.R. Khorshidvand). Thin-Walled Structures 112 (2017) 149–158 0263-8231/ © 2016 Elsevier Ltd. All rights reserved. MARK