The rotational quaternions represent a unique four-dimensional parametrization of rotations in the three-dimensional Euclidean space. In the present paper, they are used as the basic rotational parameters in formulating the finite-element approach of geometrically exact beam-like structures. The classical concept of parameterizing the rotation matrix by the rotational vector is completely abandoned so that the only rotational parameters are the rotational quaternions representing both rotations and rotational strains in the beam. The space discretization based on the collocation method is used and the adjustment of the Newmark time integration algorithm to the quaternion parameterizations of rotation is presented.
COBISS.SI-ID: 5825377
A new mathematical model and its finite element formulation for the non-linear analysis of mechanical behaviour of a two-layer timber planar beam is presented. It is assumed that non-linear material can differ from layer to layer; the slip and uplift laws are non-linear; the kinematics is linear. The theory is validated by the experimental results of full-scale laboratory tests. It is found out that the type of the slip law strongly dictates the deformability of the composite beam.
COBISS.SI-ID: 4917089
The paper presents an analysis of the effect of boundary conditions and axial deformation on the buckling loads of the geometrically perfect elastic two-layer composite columns with interlayer slip between the layers. It is shown that the boundary conditions of such composite columns are interrelated in both longitudinal and transverse directions. The parametric analyses reveal that the influence of longitudinal boundary conditions on buckling load can be significant. In contrast, the influence of axial deformation is negligible.
COBISS.SI-ID: 5069153
Failure of concrete under compression results in a localized region of softened material subject to high strain. The paper attempts to find out the error of the numerical method for the mechanical analysis of planar reinforced-concrete beams subject to temperature increase simulating typical fire conditions at high temperatures, if the strain softening in concrete is considered, while employing continuous finite elements. The results are confronted with the formulation using constant-strain crack band elements in the localized regions combined with the continuous elements everywhere else. The width of the crack band is, in principle, temperature- and stress-state dependent. In the paper we assume the crack band elements of constant width throughout the analysis, which may be a valid assumption at high temperatures, as indicated by some data given in literature. Results of the analyses of a two-story, two-bay reinforced concrete frame, designed strictly in accordance with the European standards, and subject to self weight, dead and service loads and, additionally, to the increasing fire-like thermal load, are presented. The use of solely continuous finite elements, yet accounting for strain softening of material where it occurs, yields spatially oscillating results for strains around the localized region. This usually yields a totally false result or loss of convergence of the global Newton method. The width of the localized band tends to zero with the growing density of the finite-element mesh, with the results being highly mesh sensitive. The finite-element meshes where constant-strain crack band elements in the localized regions are combined with the continuous elements everywhere else yield, on the other hand, a computationally stable and accurate post-instability response for a wide range of crack band element widths. Its critical point is, however, obtaining a reliable estimate of the width of the crack band element at high temperatures. This will require extensive experimental testing with hot concrete in compression.
COBISS.SI-ID: 5905761
In the paper a new setup for measuring a setting and hardening process of cementitious materials, using a non-destructive ultrasonic shear wave reflection technique, and designed with the objective to be easily used in situ, is described. Using the setup, the measurements can be performed by slighlyt deepening a measuring head into a paste in a mold or by placing the paste into a mold fixed on a measuring head. To test the proposed methodology, cement pastes with different compositions were prepared and exposed to different curing temperatures. Significant differences in the evolution of a change of a shear wave reflection coefficient Δr in time were observed, indicating the ability of the method to monitor setting process of cement pastes. Moreover, some interesting phenomena in the solidification process of materials can be identified. A linear relationship between development of the Δr and penetration resistance dP values in time was found, allowing development of a simplified procedure to determine both initial and final setting times of the material. This presents a significant contribution to the development of new advanced non-destructive techniques to evaluate early age properties of cementitious materials and expands the range of applicability of ultrasonic methods to a high degree.
COBISS.SI-ID: 6202721