Executive Summary : | A non-linear multiphysics model of magneto-electro-elastic (MEE) structures will be developed using the mathematical methodology Variational Asymptotic Method (VAM). 3D nonlinear MEE modeling is divided into two parts, i.e., 1D nonlinear normal analysis (analytical) and 2D nonlinear reference surface analysis (numerical analysis). The main contributions of this research lie in the 1D normal (through-the-thickness) analysis which derives an asymptotically accurate electro-magnetic-elastic 2D constitutive law, 3D warping functions, and 3D recovery relations for MEE plates. The geometric nonlinearity is addressed by considering finite deformations (displacements and rotations), while material nonlinearity is accounted for by finite strains through strain energy density. 3D magneto-electro-elastic energy density is divided into different orders of magnitudes using VAM. Minimization of these asymptotic orders of 3D MEE density with respect to unknown warping functions subjected to global constraints provides the warping functions in terms of 2D variables. substitution of these unknowns into the 3D functional and integration along the thickness provide 2D MEE energy. The double derivative of this 2D MEE energy with respect to 2D strains provides the dimensionally reduced (2D) magneto-electro-elastic nonlinear constitutive law. Recovery relations are derived to provide 3D components like displacements, stresses, strains, electric potential, magnetic potential, and fluxes. Validation of the proposed work will be done with benchmark problems, including multifunctional coupling and load conditions and comparison with exact solutions. Application of VAM to MEE structures reduces the computational cost and increases the accuracy. MEE structures have great potential in absorbing vibrations of the aircraft landing gear and converting them into electric energy for sustainable development. |
Co-PI: | Dr. Ankit Gupta, shiv Nadar Institution Of Eminence, Greater Noida, Uttar Pradesh-201314, Dr. Yamini sudha sistla, shiv Nadar Institution Of Eminence, Greater Noida, Uttar Pradesh-201314 |