Análise não linear geométrica de vigas laminadas de parede fina

Abstract

The use of thin walled laminate beams in Aeronautical, Civil, Mechanical and Naval Enginee- ring is increasing in the last years. This is due to their high stiffness/weight and strength/weight ratios. Composite beams and other structural elements tend to have thin walls due to the elevated strength of the material. Other important aspect is that, even without reaching large strains and without overcoming the elastic limit of the material, such beams present geometric nonlinear behavior due to high their slenderness, leading to large displacements and rotations. Depen- ding on the composite layup, the beams of composite materials can present several couplings between generalized stresses and strains, requiring a more complex analysis procedure when compared to isotropic beams. In this work, two three-dimensional space frame finite elements that can be used to analyze composite thin-walled beams subjected to geometric non-linearity were developed. The cross-section properties of the beams are evaluated through suitable thin walled beam theories, where the effects of the warping and transverse shear are neglected. Such theories yield a 4x4 constitutive matrix for the laminate and different levels of coupling between generalized stresses and strains can be considered. Depending of such couplings, the constitu- tive matrix can either be full or diagonal. The element independent corotational approach was used in order to consider large displacaments and rigid body rotations in space. In the local coordinate system, two elements are used, one based on the linear strain theory and the other on the Total Lagrangian formulation. The mathematical treatment of the large rotations in the space is performed by means of the rotation tensor (Rodrigues’s formula) in conjunction with the concept of the pseudovector. The computational implementations of the two finite elements proposed in this work were done in the open source software FAST ( Finite Element Analysis Tool ). The methodology used follows the classical steps used in computational methods, in- cluding formulation, implementation, verification and validation of results. Such verification is accomplished through shell and solid three-dimensional finite element models developed in the ABAQUS commercial software. The validation is performed by means of comparison with the experimental results found in literature. Regarding the evaluation of cross-sectional properties, one can observe a good agreement between the laminated beam theories adopted in this work and numerical and experimental results for all composite layups and load conditions conside- red. In the case of space frame elements, a good agreement is obtained between the results of finite elements proposed in this work and the analytical and computational results available in the literature. It is also observed that the element based on the Lagrangian formulation is more efficient than the element based on the linear theory regarding the ability to provide a satisfatory response with a less refined mesh