Refined Beam Theory for Geometrically Nonlinear Pre-Twisted Structures

• Published in: Aerospace Vol. 9; no. 7; p. 360
• Main Authors: Hu, Yi, Zhao, Yong, Liang, Haopeng
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.07.2022
• Subjects: Beam theory (structures); Carrera unified formulation; Deformation; Deformation effects; Finite element method; finite untwist; Flexing; geometrical nonlinearity; large displacement; local mapping; Mathematical analysis; Mathematical models; Matrices (mathematics); Mechanical properties; Nonlinearity; Polynomials; refined beam theory; Stiffening; Tensors
• ISSN: 2226-4310; 2226-4310
• DOI: 10.3390/aerospace9070360

This paper proposes a novel fully nonlinear refined beam element for pre-twisted structures undergoing large deformation and finite untwisting. The present model is constructed in the twisted basis to account for the effects of geometrical nonlinearity and initial twist. Cross-sectional deformation is allowed by introducing Lagrange polynomials in the framework of a Carrera unified formulation. The principle of virtual work is applied to obtain the Green–Lagrange strain tensor and second Piola–Kirchhoff stress tensor. In the nonlinear governing formulation, expressions are given for secant and tangent matrices with linear, nonlinear, and geometrically stiffening contributions. The developed beam model could detect the coupled axial, torsional, and flexure deformations, as well as the local deformations around the point of application of the force. The maximum difference between the present deformation results and those of shell/solid finite element simulations is 6%. Compared to traditional beam theories and finite element models, the proposed method significantly reduces the computational complexity and cost by implementing constant beam elements in the twisted basis.