Original Article Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory Hadjira Hellal 1 , Mohamed Bourada 1 , Habib Hebali 1,2 , Fouad Bourada 1,3 , Abdelouahed Tounsi 1,4 , Abdelmoumen A Bousahla 5,6 and SR Mahmoud 7 Abstract A new simple “four-variable shear deformation” plate model is proposed in this work to demonstrate the hygro-thermal environment effects on dynamic and buckling of functionally graded material “sandwich plates” supported by “Winkler–Pasternak” elastic foundations. Equations of motion are obtained from Hamilton’s principle 1 Civil Engineering Department, Faculty of Technology, Material and Hydrology Laboratory, University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria 2 Universite ´ Ibn Khaldoun, Tiaret, Algeria 3 De ´partement des Sciences et de la Technologie, Centre Universitaire de Tissemsilt, Ben Hamouda, Algeria 4 Civil and Environmental Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia 5 Laboratoire de Mode ´lisation et Simulation Multi-e ´chelle, Universite ´ de Sidi Bel Abbe ´s, Sidi Bel Abbe ´s, Algeria 6 Centre Universitaire de Relizane, Relizane, Algeria 7 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia Corresponding author: Fouad Bourada, Civil Engineering Department, University of Sidi Bel Abbes, Sidi Bel Abbes 22000, Algeria. Email: bouradafouad@yahoo.fr Journal of Sandwich Structures & Materials 0(0) 1–38 ! The Author(s) 2019 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/1099636219845841 journals.sagepub.com/home/jsm