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 modification of the Newmark time integration algorithm to the quaternion parameterization of rotation is presented.
COBISS.SI-ID: 5825377
We have proposed the governing equations of a composite planar beam which fully take into account the exact geometrical and material non-linearities as well as finite slip between the layers. The equations of the model are then cast into the discretized weak form by the modified principle of virtual work using the unconventional finite element technique, where strains and the interlayer normal contact traction represent the interpolated quantities. Such a complexity of the formulation results in a superb convergence and accuracy, and enables us to foresee well the mechanism of structural failure and the limit ductility of the composite structure.
COBISS.SI-ID: 6029153
We have derived a one-dimensional mathematical model and a numerical procedure for the non-linear static analysis of pre-tensioned concrete planar beams, which intends to describe quantitatively the global behaviour as well as some local phenomena in the beam, such as the tangential slip and the traction between the tendon and concrete, with accuracy sufficient for engineering design. The advantage of such a model is its extreme computational efficiency compared to the two- and three-dimensional formulations. A shear-stiff, kinematically exact planar beam theory is used to model each subcomponent of the beam. The bending moment in the tendon is neglected. Cracking of concrete is accounted for by using the smeared crack concept. Softening of material, and the related localisation of deformations, is in the numerical solution resolved by the combined use of the arc-length method and the constant strain crack band element, whose dimension is related to the fracture energy of concrete in tension. The tangential slip between the tendon and concrete is fully accounted for, yet the normal separation is not allowed. The model enables us to analyse the variation of slip and the tangential traction on tendons as well as softening of concrete in both tension and compression along the beam axis and in time. The validity of the present one-dimensional model is verified on two pre-stressed simply supported beams previously experimentally and computationally studied in literature (Rabczuk and Eibl, 2004; Rabczuk et al., 2005; Rabczuk and Belytschko, 2006). It is found out that the results of the present one-dimensional model are well in keeping with the experimental and numerical results from literature. Recalling the extreme computational efficiency of the present formulation compared to the 2D and 3D formulations, it is concluded that the proposed method of analysis could be very convenient for engineering design.
COBISS.SI-ID: 5969249
This paper presents a new finite-element formulation for the dynamic analysis of three-dimensional beams. The formulation is based on the geometrically exact three-dimensional beam theory in which the strain vectors are the only interpolated functions. The classical Newmark time integration scheme extended to the multiplicative group of spatial rotations is used and properly adapted for the strain-based formulation. The generalized-alfa method is used to enforce a numerical dissipation of higher modes. The update procedure needed in the iteration process is discussed in detail. The exact linearization of the governing equations is also presented. The performance of the formulation is demonstrated with numerical examples.
COBISS.SI-ID: 6252129
The paper discusses a possibility of using an ultrasonic wave transmission method to study the influence of superplasticizers on the formation of structure of cement pastes at early ages. When compared to mixtures without additives, lower P-wave velocity was found through superplasticized cement pastes, indicating that superplasticizers prevent formation of a solid network frame. Comparing to sulfonate naphthalene-formaldehyde superplasticizers, polycarboxylate ether (PCE) admixtures retarded the solid network frame development more intensively, resulting in a plateau on a P-wave velocity curve during the setting period. The length of the plateau is proportional to the dosage of the PCE and inversely proportional to the specific surface area of the hydration products developed, proving that the specific surface area of a solid phase affects the performance of the PCEs. Validation of ultrasonic results was made on the basis of the temperature evolution of the material in time.
COBISS.SI-ID: 6235233