  Based on Lagrange and Hermite interpolation two novel versions of weak form
quadrature element are proposed for a non-classical Euler-Bernoulli beam
theory. By extending these concept two new plate elements are formulated using
Lagrange-Lagrange and mixed Lagrange-Hermite interpolations for a non-classical
Kirchhoff plate theory. The non-classical theories are governed by sixth order
partial differential equation and have deflection, slope and curvature as de-
grees of freedom. A novel and generalize way is proposed herein to implement
these degrees of freedom in a simple and efficient manner. A new procedure to
compute the modified weighting coefficient matri- ces for beam and plate
elements is presented. The proposed elements have displacement as the only
degree of freedom in the element do- main and displacement, slope and curvature
at the boundaries. The Gauss-Lobatto-Legender quadrature points are considered
as element nodes and also used for numerical integration of the element
matrices. The framework for computing the stiffness matrices at the integra-
tion points is analogous to the conventional finite element method. Numerical
examples on free vibration analysis of gradient beams and plates are presented
to demonstrate the efficiency and accuracy of the proposed elements.
