Consider the governing equations of equilibrium of elastic plates according to the firstorder shear deformation plate theory with the von K´arm´an nonlinearity. Assume that the material of the plate...

Consider the governing equations of equilibrium of elastic plates according to the firstorder shear deformation plate theory with the von K´arm´an nonlinearity. Assume that the material of the plate is isotropic and obeys the generalized Hooke’s law. However, the elastic modulus E varies nonlinearly with the displacement gradients according to the equation

Assuming that Poisson’s ratio is constant, develop (a) the finite element model of the equations and (b) compute the tangent stiffness coefficients, T 11 ij and T 33 ij.