A Stochastic Investigation of Effect of Temperature on Natural Frequencies of Functionally Graded Plates
The present paper deals with thermal uncertainty quantification in the free vibration of functionally graded materials (FGMs) cantilever plate by using the finite element method coupled with multivariate adaptive regression splines surrogate (MARS) model. The combined effects of uncertainty in material properties on the natural frequency are examined. The power law is employed for gradation of material properties across the depth of FGM plate, while the Touloukian model is used to evaluate temperature effects on the material properties. In finite element analysis (FEA), eight noded iso-parametric elements are considered with each element having five degrees of freedoms. In MARS, Sobol sampling is employed to train the model, which results in better convergence and accuracy. The results of MARS model are validated with Monte Carlo simulation results. The results reveal that MARS model can achieve a significant level of accuracy without compromising the accuracy of results.
KeywordsFinite element method Monte Carlo simulation Multivariate adaptive regression splines Free vibration Thermal uncertainty Functionally graded plates
P. K. Karsh received financial support from the MHRD, Government of India, during this research work.
- 4.Dey S, Mukhopadhyay T, Adhikari S (2018) Uncertainty quantification in laminated composites: a meta-model based approach. CRC Press, Taylor & Francis Group, Boca Raton. ISBN 9781498784450Google Scholar
- 8.Mukhopadhyay T (2017) Mechanics of quasi-periodic lattices. Ph.D. thesis, Swansea UniversityGoogle Scholar
- 24.Mukhopadhyay T, Mahata A, Adhikari S, Asle Zaeem M (2017) Effective mechanical properties of multilayer nano-heterostructures. Sci Rep 7:15818Google Scholar
- 31.Meirovitch L (1992) Dynamics and control of structures. Wiley, NYGoogle Scholar
- 32.Touloukian YS (1967) Thermophysical properties of high temperature solid materials. McMillan, New YorkGoogle Scholar
- 45.Hastie T, Tibshirani R, Friedman J (2009) Unsupervised learning. In: The elements of statistical learning. Springer, New YorkGoogle Scholar
- 47.Mukhopadhyay T (2017) A multivariate adaptive regression splines based damage identification methodology for web core composite bridges including the effect of noise. J Sandwich Struct Mater 1099636216682533Google Scholar