Consider the governing equations of equilibrium of elastic plates according to the first order shear deformation plate theory with the von K´arm´an nonlinearity. Assume that the plate is made of two...

Consider the governing equations of equilibrium of elastic plates according to the first order shear deformation plate theory with the von K´arm´an nonlinearity. Assume that the plate is made of two homogeneous isotropic materials that are combined according to the following power-law distribution

where E1 and E2 are moduli of the two materials that are being mixed, h is the total thickness of the plate, and n is the power-law index that dictates the volume fraction f(z) of material 1. Develop the displacement finite element model of the functionally graded plate and determine the tangent stiffness coefficients.