Free vibrations and bending of laminated thin plates with distorted domains in gradient elasticity: an isoparametric finite element formulation based on Hermite mapping

The paper aims to extend the isoparametric mapping based on the Hermite interpolating polynomials as developed by the authors in their previous work [1] to distorted domains with curved edges. To this end, parabolic, circu- lar, elliptic, and annular configurations are investigated with respect to both static and dynamic responses. The theoretical framework is based on a non- local version of the Kirchhoff theory for laminated composite thin plates, where nonlocal effects are characterized by strain gradient theory. This peculiar formulation requires the interpolation of higher-order derivatives of displacements for both the membrane and bending degrees of freedom. Consequently, higher-order Hermite functions are employed to approximate the primary variables, according to the principles of conforming and non- conforming approaches. However, significant challenges arise when analyz- ing distorted domains, particularly in defining an appropriate isoparametric mapping procedure. The results are presented graphically to illustrate the convergence behavior of the numerical approach as the number of elements increases. Pairs of graphs compare the outcomes derived from classical and nonlocal elasticity theories. In addition, influence of nonlocal effects on the implementation of boundary conditions is discussed.