PSI - Issue 41

Efstathios E. Theotokoglou et al. / Procedia Structural Integrity 41 (2022) 361–371 Efstathios E.Theotokoglou/ Structural Integrity Procedia 00 (2022) 000–000

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1. Introduction Functionally graded materials (FGMs) are nonhomogeneous materials at the microscopic level, which have a gradation in their structure and composition with the properties of the material varying along one or more directions (Gupta & Talha, (2015)), (Garg, et al., (2021)), (Çömez, (2014)). This changing microstructure differentiates FGMs from conventional composites which fail from delamination (Gupta & Talha, (2015)) (Trinh, et al., (2016)). In sandwich structure, the abrupt change of properties (mechanical thermal) from one layer to another creates stress concentration at the interface (Şimşek & Al-shujairi, (2016)), (Gouasmi, et al., (2015)). FGMs can be used to eliminate the stress concentration at the interface of the layers (Gupta & Talha, (2015)). Delamination can be eliminated in sandwich structures using FGM because these materials have a uniform change in their properties from one surface to another (Şimşek & Al-shujairi, (2016)) (Trinh, et al., (2016)). The applications of these materials are in: Aerospace, Automotive, Biomedical-Medical, Optoelectronics-electronics, Machinery, Energy, Military-Defense, Marine (Gupta & Talha, (2015)), (Saleh, et al., (2020)), (Manu, et al., (2021)), (Çömez, (2014)), (Sayyad & Ghugal, (2018)). In other studies in the field of sandwich FGM structures, Shodja, et al. (2007) derived an exact solution for thermoelastic problem for a two dimensional thick composite with homogeneous and FGM layers. In (Avhad & Sayyad, (2020)) the authors present a semi analytical Navier type solutions of a fifth order shear and normal deformation theory for a sandwich FGM curved beams. In (Nirmala, et al., (2005)) an analytical expression for thermoelastic stresses in a sandwich beam with FGM core and homogeneous top and bottom layers is presented. In (Şimşek & Al-shujairi, (2016)) the authors used Timoshenko beam theory to study the static free and forced vibration of a sandwich FGM beam. In (Pandey & Pradyumna, (2017)) the authors presented an analysis of FGM sandwich beam subjected to thermal shock using Finite element method. In (Tran, et al., (2019)) the authors present a static bending analysis at high temperature and thermal buckling of sandwich FGM beam based on third-order shear deformation theory and finite elements, they assumed temperature-dependent material properties. In this work the study of a sandwich beam with metal core and FGM face sheets and a sandwich beam with ceramic core and FGM face sheets has been performed. We also confronted the problem of the beam with ceramic core and metal face sheets and with metal core and ceramic face sheets in order to compare them with the other configurations. The load was a distributed load on the upper face sheet of the beam. In this study 8-node two dimensional quadrilateral isoparametric element is used. Nomenclature σ ij stress tensor C ijkl elastic moduli ε kl strain tensor u k displacement vector [J] Jacobian matrix [k] stiffness matrix [B] strain-displacement matrix [D] constitutive matrix N i shape functions P material property V volume fraction p volume fraction index x m position vector υ displacement in y axis u displacement in x axis E Young's modulus v {d} Poisson ratio nodal displacement s