In this paper, we present an original energy-preserving numerical formulation for velocity-based geometrically exact three-dimensional beams. We employ the algebra of quaternions as a suitable tool to express the governing equations and relate rotations with their derivatives, while the finite-element discretization is based on interpolation of velocities in a fixed frame and angular velocities in a moving frame description. The proposed time discretization of governing equations directly relates the energy conservation constraint with the time-discrete kinematic compatibility equations. We show that a suitable choice of primary unknowns together with a convenient choice of the frame of reference for quantities and equations is beneficial for the conservation of energy and enables admissible approximations in a simple manner and without any additional effort. The result of this study is simple and efficient, yet accurate and robust numerical model.
COBISS.SI-ID: 8601953
In this paper, we present a coupled dynamic analysis of a moving particle on a deformable three-dimensional frame. The presented numerical model is capable of considering arbitrary curved and twisted initial geometry of the beam and takes into account geometric non-linearity of the structure. Coupled with dynamic equations of the structure, the equations of moving particle are solved. The moving particle represents the dynamic load and varies the mass distribution of the structure and at the same time its path is adapting due to deformability of the structure. A coupled geometrically non-linear behaviour of beam and particle is studied. The equation of motion of the particle is added to the system of the beam dynamic equations and an additional unknown representing the coordinate of the curvilinear path of the particle is introduced. The specially designed finite-element formulation of the three-dimensional beam based on the weak form of consistency conditions is employed where only the boundary conditions are affected by the contact forces.
COBISS.SI-ID: 8198753
We present a novel consistent singularity-free strain-based finite element formulation for the analysis of three-dimensional frame-like structures. Our model is based on a geometrically exact finite-strain beam theory, quaternion parametrization of spatial rotations, assumption that the strain measures are constant along the length of the element and a proper choice of basis for the translational strain vector representation. As it is common for strain-based elements, the present formulation does not suffer from shear locking and allows incorporation of wide range of constitutive models including the models considering strain softening. A comparison of our results with the results from the literature and a commercial finite element analysis software demonstrates the advantages of the proposed formulation, especially when the structure is subjected to larger shear deformations. This stems from the fact that our model ensures a mathematically consistent updating procedure for all the quantities describing the beam.
COBISS.SI-ID: 9081185
To perform geodetic measurements of displacements of the ground and manmade constructions, stabilised reference points are needed from which control points on the object or its surroundings could be measured. Reference points are most commonly stabilised with reinforced concrete pillars; however, they are not always constructed in an appropriate manner. The influence of temperature variation within a pillar on the position of the fixed screw for forced centring is not negligible and should be considered when performing precise measurements. In this research paper, the displacement of a pillar was calculated as a result of the temperature changes in the pillar, and then an experiment was performed in which the pillar was heated from one side, and the horizontal displacement of the fixed screw for forced centring was measured.
COBISS.SI-ID: 8872545