Levy solution and state-space approach for hygro-thermo-magnetic bending of a cross-ply laminated plate on Kerr foundation under various loadings

For the first time, Levy-type solution model and the state-space concept are employed to investigate the hygrothermal bending response of a cross-ply laminated plate on a three-parameter Kerr foundation subjected to a 2D magnetic field. The displacement field is established based on Shimpi’s two-variable plate theory. Based on Maxwell’s equations, the magnetic body force (Lorentz force) is established. In the present analysis, two opposite edges of the plate are simply supported. While, the other two edges have arbitrary boundary conditions. For more generality and reality, the mechanical load, temperature and moisture that are applied to the upper surface of the plate are assumed to be uniformly, linearly, exponentially, and sinusoidally varied. The principle of virtual displacements is employed to derive the governing partial differential equations based on the present theory, including Lorentz magnetic force. Levy procedure is employed to obtain the nonhomogeneous ordinary differential equations. The matrix method is utilized to get the homogeneous solution. While, the particular solution is obtained by employing the method of undetermined coefficients. The effects of Kerr foundation, loading type, boundary conditions, side-to-thickness ratio, plate aspect ratio, magnetic parameter, temperature, and moisture on deflection and stresses of Levy plate are investigated. It is noted that the magnetic field and hygrothermal loads reduce the structure’s strength, which leads to an increment in the deflection and stresses.