Extension of MITC to higher-order beam models and shear locking analysis for compact, thin-walled, and composite structures

A class of mixed interpolated beam elements is introduced in this paper under the framework of the Carrera Unified Formulation to eliminate the detrimental effects due to shear locking. The Mixed Interpolation of Tensorial Components (MITC) method is adopted to generate locking-free displacement-based beam models using general 1D finite elements. An assumed distribution of the transverse shear strains is used for the derivation of the virtual work, and the full Gauss-Legendre quadrature is used for the numerical computation of all the components of the stiffness matrix. Linear, quadratic, and cubic beam elements are developed using the unified formulation and applied to linear static problems including compact, laminated, and thin-walled structures. A comprehensive study of how shear locking affects general beam elements when different classical integration schemes are used is presented, evidencing the outstanding capabilities of the MITC method to overcome this numerical issue. Refined beam theories based on the expansion of pure and generalized displacement variables are implemented making use of Lagrange and Legendre polynomials over the cross-sectional domain, allowing one to capture complex states of stress with a 3D-like accuracy. The numerical examples are compared to analytic, numerical solutions from the literature, and commercial software solutions, whenever it is possible. The efficiency and robustness of the proposed method demonstrated throughout all the assessments, illustrating that MITC elements are the natural choice to avoid shear locking and showing an unprecedent accuracy in the computation of transverse shear stresses for beam formulations.