Post Tensioned CFRP tubes for improved energy absorption

Thin-walled tubes made of CFRP (Carbon fiber reinforced Polymer) are being increasingly used as CC (Crush Cans) due to their higher specific energy absorption capacity in the automotive domain for absorbing impact energy during a frontal crash. Finite element analysis (FEA) based computational methods have matured over the years with increased accuracy and acceptable correlation with experimental results. FEA-based computational studies when used appropriately can reduce the number of physical tests and prototypes required besides accelerating the overall cycle design time. The present work proposes an FEA based design validation approach for the evaluation of post-tensioned crush can design that can absorb more impact energy compared to a normal CFRP thin tube. The FEM based method uses a combination of multiple simulation techniques to predict the behavior of a post-tensioned tube. The post-tensioning in the present work has been proposed in the form of internal pressure for the thin tube. It was found that a safe value of pressure, when applied as a post-tensioning load, can improve the energy absorption capacity without increasing the weight of the tube.

Steady-State Navier–Stokes Equations in Thin Tube Structure with the Bernoulli Pressure Inflow Boundary Conditions: Asymptotic Analysis

Steady-state Navier–Stokes equations in a thin tube structure with the Bernoulli pressure inflow–outflow boundary conditions and no-slip boundary conditions at the lateral boundary are considered. Applying the Leray–Schauder fixed point theorem, we prove the existence and uniqueness of a weak solution. An asymptotic approximation of a weak solution is constructed and justified by an error estimate.

Decayless Kink Oscillations Excited by Random Driving: Motion in Transitional Layer

In this article we study the plasma motion in the transitional layer of a coronal loop randomly driven at one of its footpoints in the thin-tube and thin-boundary-layer (TTTB) approximation. We introduce the average of the square of a random function with respect to time. This average can be considered as the square of the oscillation amplitude of this quantity. Then we calculate the oscillation amplitudes of the radial and azimuthal plasma displacement as well as the perturbation of the magnetic pressure. We find that the amplitudes of the plasma radial displacement and the magnetic-pressure perturbation do not change across the transitional layer. The amplitude of the plasma radial displacement is of the same order as the driver amplitude. The amplitude of the magnetic-pressure perturbation is of the order of the driver amplitude times the ratio of the loop radius to the loop length squared. The amplitude of the plasma azimuthal displacement is of the order of the driver amplitude times $\text{Re}^{1/6}$ Re 1 / 6 , where Re is the Reynolds number. It has a peak at the position in the transitional layer where the local Alfvén frequency coincides with the fundamental frequency of the loop kink oscillation. The ratio of the amplitude near this position and far from it is of the order of $\ell$ ℓ , where $\ell$ ℓ is the ratio of thickness of the transitional layer to the loop radius. We calculate the dependence of the plasma azimuthal displacement on the radial distance in the transitional layer in a particular case where the density profile in this layer is linear.

Fatigue Variability of Alloy 625 Thin-Tube Brazed Specimens

As an advanced heat exchanger for aero-turbine applications, a tubular-type heat exchanger was developed. To ensure the optimum performance of the heat exchanger, it is necessary to assess the structural integrity of the tubes, considering the assembly processes such as brazing. In this study, fatigue tests at room temperature and 1000 K were performed for 0.135 mm-thick alloy 625 tubes (outer diameter of 1.5 mm), which were brazed to the grip of the fatigue specimen. The variability in fatigue life was investigated by analyzing the locations of the fatigue failure, fracture surfaces, and microstructures of the brazed joint and tube. At room temperature, the specimens failed near the brazed joint for high σmax values, while both brazed joint failure and tube side failure were observed for low σmax values. The largest variability in fatigue life under the same test conditions was found when one specimen failed in the brazed joint, while the other specimen failed in the middle of the tube. The specimen with brazed joint failure showed multiple crack initiations circumferentially near the surface of the filler metal layer and growth of cracks in the tube, resulting in a short fatigue life. At 1000 K, all the specimens exhibited failure in the middle of the tube. In this case, the short-life specimen showed crack initiation and growth along the grains with large through thickness in addition to multiple crack initiations at the carbides inside the tube. The results suggest that the variability in the fatigue life of the alloy 625 thin-tube brazed specimen is affected by the presence of the brazed joint, as well as the spatial distribution of the grain size and carbides.

An Approach to Bayesian Optimization for Design Feasibility Check on Discontinuous Black-Box Functions

The paper presents a novel approach to applying Bayesian Optimization (BO) in predicting an unknown constraint boundary, also representing the discontinuity of an unknown function, for a feasibility check on the design space, thereby representing a classification tool to discern between a feasible and infeasible region. Bayesian optimization is a low-cost black-box global optimization tool in the Sequential Design Methods where one learns and updates knowledge from prior evaluated designs, and proceeds to the selection of new designs for future evaluation. However, BO is best suited to problems with the assumption of a continuous objective function and does not guarantee true convergence when having a discontinuous design space. This is because of the insufficient knowledge of the BO about the nature of the discontinuity of the unknown true function. In this paper, we have proposed to predict the location of the discontinuity using a BO algorithm on an artificially projected continuous design space from the original discontinuous design space. The proposed approach has been implemented in a thin tube design with the risk of creep-fatigue failure under constant loading of temperature and pressure. The stated risk depends on the location of the designs in terms of safe and unsafe regions, where the discontinuities lie at the transition between those regions; therefore, the discontinuity has also been treated as an unknown creep-fatigue failure constraint. The proposed BO algorithm has been trained to maximize sampling toward the unknown transition region, to act as a high accuracy classifier between safe and unsafe designs with minimal training cost. The converged solution has been validated for different design parameters with classification error rate and function evaluations at an average of <1% and ∼150, respectively. Finally, the performance of our proposed approach in terms of training cost and classification accuracy of thin tube design is shown to be better than the existing machine learning (ML) algorithms such as Support Vector Machine (SVM), Random Forest (RF), and Boosting.

Excitation of decayless kink oscillations by random motion

We study kink oscillations of a straight magnetic tube with a transitional region at its boundary. The tube is homogeneous in the axial direction. The plasma density monotonically decreases in the transitional region from its value inside the tube to that in the surrounding plasma. The plasma motion is described by the linear magnetohydrodynamic equations in the cold plasma approximation. We use the ideal equations inside the tube and in the surrounding plasma, but take viscosity into account in the transitional region. We also use the thin tube and thin transitional or boundary layer (TTTB) approximation. Kink oscillations are assumed to be driven by a driver at the tube footpoint. We derive the equation describing the displacement in the fundamental mode and overtones. We use this equation to study kink oscillations both in the case of harmonic as well as random driving. In the case of random driving we assume that the driver is described by a stationary random function. The displacements in the fundamental mode and overtones are also described by stationary random functions. We derive the relation between the power spectra of the fundamental mode and all overtones and the power spectrum of the driver. We suggest a new method of obtaining information on the internal structure of coronal magnetic loops based on the shape of graphs of the power spectrum of the fundamental mode.

Modelling and Analysis of Complex Viscous Fluid in Thin Elastic Tubes

Cardiovascular disease is a major threat to human health. The study on the pathogenesis and prevention of cardiovascular disease has received special attention. In this paper, we have contributed to the derivation of a mathematical model for the nonlinear waves in an artery. From the Navier–Stokes equations and continuity equation, the vorticity equation satisfied by the blood flow is established. And based on the multiscale analysis and perturbation method, a new model of the Boussinesq equation with viscous term is derived to describe the propagation of a viscous fluid through a thin tube. In order to be more consistent with the flow of the fluid, the time-fractional Boussinesq equation with viscous term is deduced by employing the semi-inverse method and the fractional variational principle. Moreover, the approximate analytical solution of the fractional equation is obtained, and the effect of viscosity on the amplitude and width of the wave is studied. Finally, the effects of the fractional order parameters and vessel radius on blood flow volume are discussed and analyzed.