Predicting elemental stiffness matrix of FG nanoplates using Gaussian Process Regression based surrogate model in framework of layerwise model

Abstract

The accuracy of predicting the behaviour of structure using finite element (FE) depends widely on the precision of the evaluation of the stiffness matrix. In the present article, an attempt has been made to evaluate the stiffness matrix of functionally graded (FG) nanoplate using Gaussian process regression (GPR) based surrogate model in the framework of the layerwise theory. The stiffness matrix comprises various matrix terms corresponding to the membrane, membrane-bending, bending-membrane, and bending and shear. Following two different methodologies are adopted for predicting the stiffness matrix at the elemental level, one in which the final elemental stiffness matrix is evaluated, and the second one in which all the matrix terms as stated are evaluated separately using the GPR surrogate model and then are added to get the final stiffness matrix at the elemental level. The effectiveness of both approaches has been worked out by comparing the present results with those available in the literature. Both the proposed methodologies can predict the behaviour of FG nanoplates with good accuracy. However, the second one is found to be outstanding.