A class of higher-order C0 composite and sandwich beam elements based on the Refined Zigzag Theory

Based on the Refined Zigzag Theory (RZT), a class of efficient higher-order C0-continuous beam elements is formulated and numerically assessed. The attention is mainly on the choice of shape functions that allow for free shear locking effects in slender beams. For this purpose, interdependent/anisoparametric interpolations are adopted to approximate the four independent kinematic variables. To achieve simpler (with a reduced number of nodal dofs) elements, a constraint condition on the axial variation of the effective transverse shear strain is adopted, which consists in reducing the polynomial degree of the shear strain measure (or, equivalently, the shear force), by one order. The issues investigated for the assessment are (i) shear locking, i.e., strategies for formulating shear-locking free C0 refined zigzag beam elements, (ii) computational efficiency, and (iii) predictive capability and accuracy. Accuracy and predictive capabilities of the proposed class of higher-order beam elements are numerically assessed by analyzing cantilevered beams over a range of loading conditions, lamination sequences, heterogeneous material properties, and slenderness ratios. It is concluded that the constraint condition on the transverse shear strain gives rise to a remarkably accurate class of higher-order C0 constrained refined zigzag beam elements, which offer the best compromise between computational efficiency and accuracy.