Geometrically nonlinear analysis of thin-walled laminated composite beams

Abstract

The use of thin-walled composite beams in Engineering has attracted great interest in recent years. Composite beams and other structural elements tend to have thin walls due to the high strength of the material. Other important aspect is that, even without reaching large strains and without overcoming the elastic limit of the material, such as beams present geometric nonlinear behavior due to their high slenderness, leading to large displacements and rotations. In this paper, a three-dimensional frame finite element for geometric nonlinear analysis of thin-walled laminated composite beams is presented. The finite element uses the Total Lagrangian formulation in order to allow the treatment of large displacements, but with moderated rotations. The constitutive matrix of the laminated beams is evaluated through a suitable thin-walled beam theory. In this theory, the effects of the couplings for several layups are considered, but the effects of the warping and transverse shear are neglected. Comparisons with numerical experiments demonstrate the very good accuracy of the proposed finite element.

Corotational elements for thin-walled laminated composite beams with large 3D rotations

“…Similar conclusions have also been drawn using shell elements [19]. Some recent works have successfully applied a 4 × 4 constitutive matrix to linear analysis, as well as nonlinear analysis restricted to moderate rotations, of laminated beams [20]. The corotational formulation has been successfully adopted for analysis of beams and shells subjected to large rotations, provided that the strains remain small [21].…”

“…can be found in Refs. [20,29,35]. One can demonstrate that = P P 2 and that the matrix has six zero eigenvalues, whose corresponding eigenvectors are the rigid body modes of the finite element.…”

A conjugate modal force strategy for instability analysis of thin-walled structures: an unconstrained vector positional finite element approach

“…These methods, applied in instability analysis, received a lot of contributions in the last years, as for example, Silvestre et al (2019), Basaglia et al (2019) and Manta et al (2020) for GBT and Mirzaei et al (2015), Poorveis et al (2019) and Shahmohammadi et al (2019) for FSM. Some interesting works using classical Finite Element Method (FEM) and solving stability problems may be cited (Mororo et al, 2015;Pastor and Roure, 2009;Ren et al, 2006). Among them, applications related to the stability of thin-walled structures are present, for example, in Anbarasu and Sukumar (2014), Ghumare and Sayyad (2017) and Soares et al (2019).…”

On the role of large cross-sectional deformations in the nonlinear analysis of composite thin-walled structures

“…Obst and Kapania [14] developed a 1D higher-order beam model with a parabolic shear distribution. Mororó et al [15] developed a three-dimensional frame FE for geometrical nonlinear analysis of thin-walled laminated composite beams is presented. Simo and Vu-Quoc [16,17] developed spatial beam FEs, based on strain measures derived from the principle of virtual work.…”