Arabian Journal for Science and Engineering https://doi.org/10.1007/s13369-018-3142-1 RESEARCH ARTICLE - CIVIL ENGINEERING Transient Hygrothermal Analysis of FG Sandwich Plates Lying on a visco-Pasternak Foundation via a Simple and Accurate Plate Theory Mohammed Sobhy 1,2 · M. S. Alotebi 3 Received: 14 August 2017 / Accepted: 6 February 2018 © King Fahd University of Petroleum & Minerals 2018 Abstract Based on a new four-unknown shear deformation theory, the hygrothermal bending response of functionally graded (FG) sandwich plates lying on visco-Pasternak foundation is investigated in this work. The present sandwich plate is composed of a homogeneous ceramic core covered by two FG layers. The properties of face layers are graded according to a power law distribution in terms of volume fraction. The governing equations are derived from Hamilton principle containing the hygrothermal effects employing the suggested theory. This theory includes only four unknown functions and accounts for quasi-parabolic distribution of transverse shear stress. In addition, it satisfies the free traction conditions at the top and bottom surfaces of the plate. By varying the thickness of the core, several types of FGM sandwich plates are obtained and studied. By comparing the present results with those available in the literature, the present theory is validated. Parametric studies are executed to demonstrate the effects of humidity, temperature rise, foundation coefficients, core thickness, and power law index on the bending of FGM sandwich plates. Keywords FG sandwich plates · Four-unknown shear deformation theory · Hygrothermal analysis · Viscoelastic foundation · Bending 1 Introduction Traditional sandwich structures are composed of three differ- ent homogeneous layers bonded together to obtain enhanced mechanical and thermal properties, namely a core layer is covered by two face sheets. However, a sudden change in material properties occurs at the interfaces of the sandwich plate. To overcome this problem, Zenkour [1] introduced an FGM sandwich plates. He assumed that the core layer is com- posed of fully homogeneous ceramic, while the face layers are made of FGMs. The material properties of FGMs [2] are varied smoothly through the thickness according to a power law distribution as a function of the volume fractions B Mohammed Sobhy msobhy2011@gmail.com; msobhy@kfu.edu.sa 1 Department of Mathematics and Statistics, Faculty of Science, King Faisal University, P.O. Box 400, Hofuf 31982, Saudi Arabia 2 Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt 3 Department of Mathematics, Faculty of Arts and Science at Nairiyah, Hafr Al Batin University, P.O. Box 1803, Hafr Al Batin 31991, Saudi Arabia of the constituents. Another type of FGM sandwich plate is developed using an FGM core and homogeneous face sheets [3,4]. Such structures have become even more attractive for the industries and engineering applications, such as aircraft and space vehicles, ships, and boats. Anderson [3] introduced an analytical 3-D solution for an FGM sandwich plate subjected to transverse loading by a rigid sphere and obtained the stresses and displacements with varying the core stiffness. In this investigation, the sand- wich plate is composed of orthotropic face layers and an isotropic FGM core with varying properties exponentially in the thickness direction. The governing equations are deduced by employing Reissner functional. Thermo-elastic analysis of a sandwich plate made of orthotropic stiff face sheets bonded to a soft FGM core was presented by Das et al. [5]. Kashtalyan and Menshykova [6] introduced 3-D elastic- ity analysis for static bending of sandwich plates with FGM core subjected to transverse loading. Free vibration of sand- wich cylindrical plates with FG core based on power law distribution was studied by Aragh et al. [7] using the differ- ential quadrature method to solve the governing differential equations. Dozio [8] presented an advanced 2-D Ritz-based model to study the natural frequencies of sandwich panels 123