Analytical solutions for multilayered composite cylinders with harmonic quadratic eigenstrain in arbitrary layers

The eigenstrain problem of multilayered hollow and solid composite cylinders working in a constant magnetic field is investigated analytically in this paper. Each layer of the composite cylinder can undergo a harmonic and spatially varying eigenstrain. The eigenstrain is assumed to be a quadratic polynomial function of the radial coordinate. The closed-form elastic solutions are obtained by solving the inhomogeneous governing Bessel differential equations. Then, the effects of eigenstrain distribution, angular frequency and the intensity of the magnetic field on the radial displacement, radial stress, hoop stress, and axial stress are presented graphically.