Finite element solution of vibrations and buckling of laminated thin plates in hygro-thermal environment based on strain gradient theory

The paper aims to develop a finite element methodology to deal with vibrations and buckling of laminated thin plates subjected to thermal and hygroscopic effects, once a second-order strain gradient theory is included to overcome the limitations of conventional elasticity and to capture nonlocal phenomena. The numerical scheme takes advantage of Hermite approximation for both membrane and bending primary variables, since the strain gradient introduces higher-order derivatives of the nodal displacements. Its versatility is proven by dealing with general lamination schemes and arbitrary boundary conditions. The analyzed configurations cannot be solved analytically.