Vol.:(0123456789) 1 3 Journal of the Brazilian Society of Mechanical Sciences and Engineering (2019) 41:501 https://doi.org/10.1007/s40430-019-2000-8 TECHNICAL PAPER Stochastic impact responses analysis of functionally graded plates P. K. Karsh 1,2  · R. R. Kumar 2,3  · S. Dey 2 Received: 27 March 2019 / Accepted: 8 October 2019 © The Brazilian Society of Mechanical Sciences and Engineering 2019 Abstract The present paper portrays the mapping for stochasticity in low-velocity impact responses of functionally graded material (FGM) plates by employing multivariate adaptive regression splines (MARS) surrogate model in conjunction with fnite element (FE) approach. The unavoidable stochastic variabilities (caused due to numerous errors involved in manufacturing processes) in material properties of FGM plates are considered in order to map the efect of elemental variabilities on global response of the structure. The material properties of FGM plates are considered to follow the rule of mixture in conjunction to power law. The Newmark’s time integration scheme and modifed Hertzian contact law are employed to solve the time- dependent equation. The present FE formulation is based on an eight noded isoparametric element in which each element has fve degrees of freedom. The efects of variability in temperature and power-law exponent on stochastic low-velocity impact responses are also portrayed. The maximum contact force, plate and impactor displacement are considered as the response parameters. The present MARS model is coupled with the fnite element to achieve the higher efciency with adequate accuracy as compared to the FE-based full-scale Monte Carlo simulation. The statistical results illustrate that the stochasticity in material properties signifcantly infuences the low-velocity impact responses of FGM plates. Keywords Monte Carlo simulation · Functionally graded materials · Low-velocity impact · Multivariate adaptive regression splines · Stochastic analysis 1 Introduction Functionally graded materials (FGM) are the special type of materials in which volume fractions of constituents materials are varied throughout the depth to obtain the required func- tional property in a single material. For high-temperature application such as thermal barrier, the mixture of metal and ceramic is used to form functionally graded materi- als. The top of the plate is ceramic rich, while the bottom is metal-rich, and in between two surfaces we can control the volume fraction of constituent materials by using rule of mixture. The ceramic materials have the low thermal conductivity which provides high-temperature resistance, while metal gives tensile strength. Due to unique properties of FGMs, it has wide applications in many sectors such as aerospace, automobile, medical, sports, and marine [1]. The basic diference between composite and functionally graded materials is the absence of an interface joint inside the FGM plates. The composite is the layered structure, while FGM have continuous distribution of material without any inter- face. The composite mainly fails due to the delamination at the interface of two laminates due to mismatch of mechani- cal properties. Another problem of the composite is crack formation at the interface, which weakens the plate. The internal residual stress in the composite laminate interface is developed due to the diference in the thermal expan- sion coefcients of fbre and matrix. The above lacuna of composite materials is negligible in the functionally graded materials. During the service life, many times the FGMs are subjected to low-velocity impact loading which causes dam- age and failure of structures. So, it is essential to carry out Technical Editor: José Roberto de França Arruda. * P. K. Karsh pradeepkarsh@gmail.com * R. R. Kumar ravinits2014@gmail.com 1 Department of Mechanical Engineering, Parul Institute of Engineering and Technology, Vadodara, India 2 Department of Mechanical Engineering, National Institute of Technology Silchar, Silchar, India 3 Department of Mechanical Engineering, Chandigarh Engineering College, Mohali, India