Weak-form differential quadrature finite elements for functionally graded micro-beams with strain gradient effects

This paper proposes weak-form differential quadrature finite elements for strain gradient functionally graded (FG) Euler–Bernoulli and Timoshenko micro-beams. The elements developed both have six degrees of freedom per node and do not require shape functions. The effective material properties are assumed to change continuously along the thickness direction. To guarantee the inter-element continuity conditions, we construct sixth- and...