scholarly journals Displacement modes of a thin-walled beam model with deformable cross sections

2019 ◽  
Vol 141 ◽  
pp. 576-592 ◽  
Author(s):  
Anders Bau Hansen ◽  
Jeppe Jönsson
2021 ◽  
pp. 1-23
Author(s):  
M. Talele ◽  
M. van Tooren ◽  
A. Elham

Abstract An efficient, fully coupled beam model is developed to analyse laminated composite thin-walled structures with arbitrary cross-sections. The Euler–Lagrangian equations are derived from the kinematic relationships for a One-Dimensional (1D) beam representing Three-Dimensional (3D) deformations that take into account the cross-sectional stiffness of the composite structure. The formulation of the cross-sectional stiffness includes all the deformation effects and related elastic couplings. To circumvent the problem of shear locking, exact solutions to the approximating Partial Differential Equations (PDEs) are obtained symbolically instead of by numerical integration. The developed locking-free composite beam element results in an exact stiffness matrix and has super-convergent characteristics. The beam model is tested for different types of layup, and the results are validated by comparison with experimental results from literature.


Author(s):  
Seher Durmaz ◽  
Metin O. Kaya

In this study, accounting for large displacements a geometrically nonlinear theory, which is valid for laminated thin-walled composite beams of open and closed cross sections, is developed. The beam model incorporates a number of non-classical effects such as material anisotropy, transverse shear deformation and warping restraint. Moreover, the directionality property of thin-walled composite beams produces a wide range of elastic couplings. In this respect, symmetric lay-up configuration i.e. Circumferentially Asymmetric Stiffness (CAS) is adapted to this model to generate coupled motion of flapwise bending-torsion-flapwise transverse shear. Initially, free vibration analyses are carried out for the linear model of the shearable and the non-shearable thin-walled composite beams. Similar to the linear model, the displacement-based nonlinear equations are derived by the variational formulation, considering the geometric non-linearity in the von Karman sense. Finally, the static and the dynamic analyses for the nonlinear beam model are carried out addressing the effects of transverse shear, fiber-orientation and sweep angle on the nonlinear frequencies and the static response of the beam.


2018 ◽  
Vol 8 (10) ◽  
pp. 1847 ◽  
Author(s):  
Lei Zhang ◽  
Weidong Zhu ◽  
Aimin Ji ◽  
Liping Peng

In this paper, a simplified approach to identify sectional deformation modes of prismatic cross-sections is presented and utilized in the establishment of a higher-order beam model for the dynamic analyses of thin-walled structures. The model considers the displacement field through a linear superposition of a set of basis functions whose amplitudes vary along the beam axis. These basis functions, which describe basis deformation modes, are approximated from nodal displacements on the discretized cross-section midline, with interpolation polynomials. Their amplitudes acting in the object vibration shapes are extracted through a modal analysis. A procedure similar to combining like terms is then implemented to superpose basis deformation modes, with equal or opposite amplitude, to produce primary deformation modes. The final set of the sectional deformation modes are assembled with primary deformation modes, excluding the ones constituting conventional modes. The derived sectional deformation modes, hierarchically organized and physically meaningful, are used to update the basis functions in the higher-order beam model. Numerical examples have also been presented and the comparison with ANSYS shell model showed its accuracy, efficiency, and applicability in reproducing three-dimensional behaviors of thin-walled structures.


Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3468
Author(s):  
Zbigniew Kolakowski ◽  
Andrzej Teter

The phenomena that occur during compression of hybrid thin-walled columns with open cross-sections in the elastic range are discussed. Nonlinear buckling problems were solved within Koiter’s approximation theory. A multimodal approach was assumed to investigate an effect of symmetrical and anti-symmetrical buckling modes on the ultimate load-carrying capacity. Detailed simulations were carried out for freely supported columns with a C-section and a top-hat type section of medium lengths. The columns under analysis were made of two layers of isotropic materials characterized by various mechanical properties. The results attained were verified with the finite element method (FEM). The boundary conditions applied in the FEM allowed us to confirm the eigensolutions obtained within Koiter’s theory with very high accuracy. Nonlinear solutions comply within these two approaches for low and medium overloads. To trace the correctness of the solutions, the Riks algorithm, which allows for investigating unsteady paths, was used in the FEM. The results for the ultimate load-carrying capacity obtained within the FEM are higher than those attained with Koiter’s approximation method, but the leap takes place on the identical equilibrium path as the one determined from Koiter’s theory.


1995 ◽  
Vol 55 (6) ◽  
pp. 1045-1054 ◽  
Author(s):  
H. Shakourzadeh ◽  
Y.Q. Guo ◽  
J.-L. Batoz
Keyword(s):  

2014 ◽  
Vol 1019 ◽  
pp. 96-102
Author(s):  
Ali Taherkhani ◽  
Ali Alavi Nia

In this study, the energy absorption capacity and crush strength of cylindrical thin-walled structures is investigated using nonlinear Finite Elements code LS-DYNA. For the thin-walled structure, Aluminum A6063 is used and its behaviour is modeled using power-law equation. In order to better investigate the performance of tubes, the simulation was also carried out on structures with other types of cross-sections such as triangle, square, rectangle, and hexagonal, and their results, namely, energy absorption, crush strength, peak load, and the displacement at the end of tubes was compared to each other. It was seen that the circular cross-section has the highest energy absorption capacity and crush strength, while they are the lowest for the triangular cross-section. It was concluded that increasing the number of sides increases the energy absorption capacity and the crush strength. On the other hand, by comparing the results between the square and rectangular cross-sections, it can be found out that eliminating the symmetry of the cross-section decreases the energy absorption capacity and the crush strength. The crush behaviour of the structure was also studied by changing the mass and the velocity of the striker, simultaneously while its total kinetic energy is kept constant. It was seen that the energy absorption of the structure is more sensitive to the striker velocity than its mass.


AIAA Journal ◽  
2001 ◽  
Vol 39 (12) ◽  
pp. 2422-2424 ◽  
Author(s):  
Zhanming Qin ◽  
Liviu Librescu

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