The Cattaneo telegraph equation for temperature with moving time-harmonic source is studied on the line and the half-line domain. The Laplace and Fourier transforms are used. Expressions which show the wave fronts and elucidate the Doppler effect are obtained. Several particular cases of the considered problem including the heat conduction equation and the wave equation are investigated. The quasi-steady-state solutions are also examined for the case of non-moving time-harmonic source and time-harmonic boundary condition for temperature.

In Part I, a novel hypoelastic framework for soft-tissues was presented. One of the hallmarks of this new theory is that the well-known exponential behavior of soft-tissues arises consistently and spontaneously from the integration of a rate based formulation. In Part II, we examine the application of this framework to the problem of biaxial kinematics, which are common in experimental soft-tissue characterization. We confine our attention to an isotropic formulation in order to highlight the distinction between non-linearity and anisotropy. In order to provide a sound foundation for the membrane extension of our earlier hypoelastic framework, the kinematics and kinetics of in-plane biaxial extension are revisited, and some enhancements are provided. Specifically, the conventional stress-to-traction mapping for this boundary value problem is shown to violate the conservation of angular momentum. In response, we provide a corrected mapping. In addition, a novel means for applying loads to in-plane biaxial experiments is proposed. An isotropic, isochoric, hypoelastic, constitutive model is applied to an in-plane biaxial experiment done on glutaraldehyde treated bovine pericardium. The experiment is comprised of eight protocols that radially probe the biaxial plane. Considering its simplicity (two adjustable parameters) the model does a reasonably good job of describing the non-linear normal responses observed in these experimental data, which are more prevalent than are the anisotropic responses exhibited by this tissue.

It is well known in planar kinematics of rigid bodies that the acceleration of the material point coinciding with the instantaneous center of rotation (or pole) is perpendicular to the so-called pole changing velocity. In the present paper, the concept of pole changing velocity is generalized to spatial motions. Using this result, the acceleration of the material points along the instantaneous screw axis can be expressed in a straightforward way, without the tools of advanced differential geometry.

A shear deformable beam moving along a straight path is considered as an idealization of the problem of stationary operation of a belt drive. The partial contact with a traveling surface results in the shear deformation of the beam. The tangential contact force grows near the end of the contact zone. Assuming perfect adhesion of the lower fiber of the beam to the traveling surface (no slip), we analytically demonstrate the necessity of accounting for concentrated contact forces and jump conditions, which is important for modeling the belt-pulley interaction. Along with dynamic effects, we further consider a frictional model with zones of stick and slip contact and demonstrate its convergence to the results with perfect adhesion at growing maximal friction force.

We investigate rate-independent stress paths under constant rate of strain within the hypoplasticity theory of Kolymbas type. For a particular simplified hypoplastic constitutive model, the exact solution of the corresponding system of nonlinear ordinary differential equations is obtained in analytical form. On its basis, the behaviour of stress paths is examined in dependence of the direction of the proportional strain paths and material parameters of the model.

A review is presented of measurement techniques to characterise dispersed multiphase flows, which are not accessible by means of conventional optical techniques. The main issues that limit the accuracy and effectiveness of optical techniques are briefly discussed: cross-talk, a reduced signal-to-noise ratio, and (biased) data drop-out. Extensions to the standard optical techniques include the use of fluorescent tracers, refractive index matching, ballistic imaging, structured illumination, and optical coherence tomography. As the first non-optical technique, a brief discussion of electrical capacitance tomography is given. While truly non-invasive, it suffers from a low resolving power. Ultrasound-based techniques have rapidly evolved from Doppler-based profiling to recent 2D approaches using feature tracking. The latter is also suitable for time-resolved flow studies. Magnetic resonance velocimetry can provide time-averaged velocity fields in 3D for the continuous phase. Finally, X-ray imaging is demonstrated to be an important tool to quantify local gas fractions. While potentially very powerful, the impact of the techniques will depend on the development of acquisition and measurement protocols for fluid mechanics, rather than for clinical imaging. This requires systematic development, aided by careful validation experiments. As theoretical predictions for multiphase flows are sparse, it is important to formulate standardised 'benchmark' flows to enable this validation.

In this paper, the significance of application-oriented fundamental research on concrete and reinforced concrete structures for progress regarding practical applications to structural design is addressed based on four examples. They were treated in a joint research project of Vienna University of Technology and Tongji University. The first topic refers to sudden heating or cooling of concrete structures, the second one to high-dynamic strength of specimens made of cementitious materials, the third one to structural analysis of segmental tunnel rings used in mechanized tunneling, and the fourth one to serviceability and ultimate limit states of concrete hinges used in integral bridge construction. The first two topics deal with exceptional load cases. Results from the fundamental research call for improvements of state-of-the-art simulation approaches used in civil engineering design. The last two topics refer to reinforced concrete hinges used in mechanized tunneling and integral bridge construction, respectively. Integrative research has led to progress regarding the verification of serviceability and ultimate limit states. In all four examples, results from fundamental research are used to scrutinize state-of-the-art approaches used in practical structural design of civil engineering structures. This allows for identifying interesting directions for the future development of design guidelines and standards.

A simplified model of the belt motion with small strains is proposed. The main purpose of the modeling is to show the effects arising when the line of action of friction forces is shifted to the belt's middle axis. The prestressed shearable model of the belt is used in this study. The differential equations of the steady state motion are integrated and combined together with the boundary conditions into two nonlinear systems of algebraic equations corresponding to the different cases of the belt behavior: presence and absence of a sliding segment. The nonlinearity results from the fact that the boundaries of the contact segments are a priori unknown. The case without sliding requires introduction of a concentrated force at the point where the belt leaves the pulley. Considerable effects of the assumptions of contact characterization on the simulation results are demonstrated.

New analytical solutions for the static deflection of anisotropic composite beams resting on variable stiffness elastic foundations are obtained by the means of the Homotopy Analysis Method (HAM). The method provides a closed-form series solution for the problem described by a non-homogeneous system of coupled ordinary differential equations with constant coefficients and one variable coefficient reflecting variable stiffness elastic foundation. Analytical solutions are obtained based on two different algorithms, namely conventional HAM and iterative HAM (iHAM). To investigate the computational efficiency and convergence of HAM solutions, the preliminary studies are performed for a composite beam without elastic foundation under the action of transverse uniformly distributed loads considering three different types of stacking sequence which provide different levels and types of anisotropy. It is shown that applying the iterative approach results in better convergence of the solution compared with conventional HAM for the same level of accuracy. Then, analytical solutions are developed for composite beams on elastic foundations. New analytical results based on HAM are presented for the static deflection of composite beams resting on variable stiffness elastic foundations. Results are compared to those reported in the literature and those obtained by the Chebyshev Collocation Method in order to verify the validity and accuracy of the method. Numerical experiments reveal the accuracy and efficiency of the Homotopy Analysis Method in static beam problems.

The vertices of two specific eigenvectors, obtained from a novel linear eigenvalue problem, describe two curves on the surface of an -dimensional unit hypersphere. denotes the number of degrees of freedom in the framework of structural analysis by the Finite Element Method. The radii of curvature of these two curves are 0 and 1. They correlate with pure stretching and pure bending, respectively, of structures. The two coefficient matrices of the eigenvalue problem are the tangent stiffness matrix at the load level considered and the one at the onset of loading. The goals of this paper are to report on the numerical verification of the aforesaid geometric-mechanical synergism and to summarize current attempts of its extension to combinations of stretching and bending of structures.

Under external loads trees exhibit complex oscillatory behaviour: their canopies twist and band. The great complexity of this oscillatory behaviour consists to an important degree of torsional oscillations. Using a system of ordinary differential fractional-order equations, free and forced main eigen-modes of fractional-type torsional oscillations of a hybrid discrete biodynamical system of complex structures were done. The biodynamical system considered here corresponds to a tree trunk with branches and is in the form of a visco-elastic cantilever of complex structure. Visco-elasticity corresponds to different ages of a tree. We set up a new model of torsional oscillations of a complex discrete, biodynamical system, using the Kelvin-Voigt visco-elastic model involving a fractional-order time derivative. The analytical expressions describing the characteristic properties of its fractional-type oscillations are determined. Based on mathematical and qualitative analogies, this concept represents a new model of torsional oscillations of a light cantilever that takes into account visco-elastic, dissipative properties of the material. Rigid discs are attached to the cantilever. Expressions for kinetic energy, deformation work and a generalized function of the fractional-type energy dissipation of this biodynamical system are defined. Independent main eigen-modes of the fractional type for free and forced torsional oscillations were determined for a special class of such systems, using formulas for the transformation of independent generalized angle coordinates to the principal main eigen-coordinates of the system. The forms of their approximate analytical solutions are shown. In the general case for inhomogeneous biodynamical systems of fractional type, there are no independent main fractional-type eigen-modes of torsional oscillations. The system behaves as a nonlinear system. A new constitutive relation between coupling of torsion loading to a visco-elastic fractional-type cantilever with fractional-type dissipation of cantilever mechanical energy and angle of torsion deformation is determined using a fractional-order derivative. The main advantages of the proposed model are the possibility to analyse torsional oscillations of more complex structures and the possibility to analyse complex cantilevers with different cross-sectional diameters.

This paper presents a novel approach of modeling of three-layer beam. Such composites are usually known as sandwich structures if the modulus of elasticity of the core is much smaller than those of the faces. In the present approach, the faces are modeled as Bernoulli-Euler beams, the core as a Timoshenko beam. Taking into account the kinematic and dynamic interface conditions, which means that the perfect bonding assumptions hold for the displacement and each layer is subjected to continuous traction stresses across the interface, a sixth-order differential equation is derived for the bending deflection, and a second-order system for the axial displacement. No restrictions are imposed on the elastic properties of the middle layer, and hence the developed theory also yields accurate results for hard cores. The presented refined theory is compared to analytical models from the literature and to finite element calculations for various benchmark examples. Special focus is laid the boundary conditions and the core stiffness. A parametric study varying the Young modulus of the core shows that the present sandwich model agrees very well with the target solutions obtained from finite element calculations under plane stress assumptions, in particular concerning the transverse deflection, the shear stress distribution and the interfacial normal stress.

The present contribution focuses on shape control of thick beam-type structures. First the governing equations of a multi-layered beam are derived by taking advantage of the Timoshenko assumptions and the constitutive relations of piezoelectric materials. The deflection curves are explicitly given for a piezoelectric cantilever subjected to a polynomial distribution of the vertical load and the applied electric voltage. In order to find a solution for the optimal shape control voltage an objective function, which depends on the quadratic deflection curve over the beam length, is minimized. Finally several benchmark examples are given for thick beams and the outcome is compared to finite element results and previously derived shape control results from the scientific literature that hold for thin piezoelectric beams. The presented shape control method shows a better agreement with the numerical outcome than the analytical shape control results within the Bernoulli-Euler theory, but the desired voltage distribution only slightly differs from the outcome for thin beams. Furthermore it is found that for a given total thickness-to-length ratio piezoelectric bimorph structures may be more difficult to be perfectly controlled than three-layer beams with thin piezoelectric layers. This is due to higher order piezoelectric effects which are not considered by the present theory (e.g. the thickness deformation caused by the thickness piezoelectric coupling constant).