End Boundary Conditions Research Articles

Investigation of flow over an inclination pile under a Reynolds number of 3900 by numerical simulation

Flow over an inclination pile was studied numerically by solving the Navier–Stokes equations with large eddy simulation closure under a Reynolds number of 3900, and the inclination angles were in the range of −45° ≤ θ ≤ 45°. First, flow over a finite-length vertical pile with symmetric boundary conditions at both the upper and lower boundaries is used for verification, and the results are in good agreement with the previous results. Then, the lower boundary is set as a no-slip wall to simulate a rigid seabed, and 19 different inclination angles are numerically simulated to investigate the effects of the rigid seabed on the hydrodynamic characteristics and the wake structure of the cylindrical wake with different inclination angles. It is found that there is a significant difference between the forces on the piles, which were inclined forward and backward due to the end boundary conditions. When the pile is inclined forward, the force on the pile and the frequency of vortex shedding are lower than that of a vertical pile, which is more conducive to the stability of the structure. When the pile is inclined backward, the lower sidewall induces a strong spiral upward flow of the fluid at the lower end around the pile, which leads to the shedding of the wake vortex at a very close position to the pile. The return zone tightening phenomenon occurs at inclination angles greater than 25° backward, and this phenomenon leads to a sharp increase in the forces on the pile. Backward inclination angles greater than 30° are extremely unfavorable for structural forces.

Member capacity of cold-rolled aluminium alloy channel columns - part I: Experimental investigation

Cold-rolled aluminium alloy sections have been recently introduced in Australia as newly developed thin-walled products. To fabricate these sections, the roll-forming process used in cold-formed steel production has been employed, which has proven to be more cost-effective than the conventional extrusion process. This paper describes a series of compression tests to investigate member buckling behaviour and ultimate strengths of cold-rolled aluminium alloy 5052-36 channel columns. Twenty-eight specimens of three commercially available sections (C10030, C25025 and C40030) were tested at the University of Sydney. Two configurations of end boundary conditions were specially designed to capture flexural, flexural-torsional and local-global interaction buckling failure modes. Prior to testing, initial geometric imperfections were measured using a laser scanning method, and flat/corner coupons were tested to determine compressive and tensile strengths of the aluminium alloy material. The experimental results are compared with ultimate column strength predictions by current Australian/New Zealand, North American and European design specifications for aluminium structures. Additionally, the test results provide data for calibration of finite element models of cold-rolled aluminium structural members for use in parametric and similar studies. A companion paper describes such parametric study and the derivation of new design guidelines for member buckling of cold-rolled aluminium channel columns based on the numerical parametric data and the experimental data presented herein.

SCFs for CHS-to-CHS T- and X-type moment-loaded end connections: Proposal for formulae

The research presented in this paper is part of a series of efforts to develop design recommendations for hollow structural section (HSS) connections situated at the end of a truss (or frame) under fatigue loading. Full-sized circular hollow section (CHS)-to-CHS regular and end connections (with open chord ends and chord-end cap plates) were tested under branch in-plane bending to measure strain concentrations at the critical locations. This experimental data was then used to verify a finite element (FE) modelling approach. An FE parametric study (totaling 1120 FE models, including 560 T-type connections and 560 X-type connections) was then carried out to investigate the effects of different chord end boundary conditions (i.e., varied chord end lengths, and open versus cap-plated chord ends). The effects of branch-to-chord width (β), chord slenderness (2γ) ratios and branch-to-chord thickness (τ) were also investigated. It was found that the stress concentration factors (SCFs) in end connections are sensitive to the boundary conditions (i.e., open chord end versus with chord-end cap plate) and all three non-dimensional parameters (β, 2γ and τ). Therefore, SCF correction factors based on e/b0, β, 2γ and τ, are derived for use with existing SCF formulae in CIDECT Design Guide 8.

Application of the Green's function method for static analysis of nonlocal stress-driven and strain gradient elastic nanobeams

This paper focuses on the static analysis of a generally restrained Euler-Bernoulli nanobeam (GRNB), which is subjected to arbitrary distributed or concentrated loads. The small length scale effect is introduced through a strongly nonlocal integral elastic law called the stress-driven nonlocal Euler-Bernoulli beam model, and a weakly nonlocal elastic law called the strain-gradient Euler-Bernoulli beam model. The stress-driven nonlocal theory and the strain gradient elasticity theory are both employed, to formulate the differential equation governing the Euler-Bernoulli nanobeams. Both theories are ruled by a similar 6th order differential equation, with distinct higher-order boundary conditions. The paper demonstrates that the strain gradient theory can be also reformulated as a stress-driven nonlocal theory with unsymmetrical kernel, in contrast to the initial stress-driven nonlocal theory which has symmetrical exponential kernel. Additionally, some theoretical backgrounds about both nonlocal elasticity theorems are provided. Exact solutions for both nanobeam models are presented, using Green's function method. The parameters of the Green's functions are derived for each beam theory, and then utilized to establish the static displacement function of both nanobeam theories. Exact solutions are provided for the bending of both nanobeams with various end boundary conditions, that account for the small length scale effects. The paper also compares the responses of the stress-driven Euler-Bernoulli beam and the strain gradient Euler-Bernoulli beam, showing close deflections and similar effects of increasing the nonlocal parameter on beam stiffness. A major difference highlighted between the two theories is that the strain gradient theory predicts a homogeneous strain state for homogeneous stress state, as opposed to the stress-driven theory.

An open-source project for wind instrument modeling using digital waveguides

Digital waveguide methods for time-domain modeling of acoustic structures comprised of interconnected piece-wise one-dimensional cylinders, cones and toneholes have been well reported in the past. In this work, an open-source Matlab class is presented that can be used to model arbitrary wind instrument air column structures, defined by length, radii and hole geometric parameters, using digital waveguide methods. Fractional-delay filtering can be enabled or disabled, with support for both Thiran and Lagrange filter types of specified order. Thermoviscous losses can be modeling using either a discrete-time least squares or a shelf-filter fit, both of arbitrary order. Three different tonehole model options are provided (two-port, three-port or wave digital filter). End boundary conditions include closed, anechoic, ideally open, open flanged and open unflanged. The class object can be used either in single-sample iterative contexts (for example, with an attached excitation model) or with arbitrarily-sized input signals (for example, to compute a reflection function or impedance). The modeled geometry can be constructed manually by iteratively adding segments or holes, or a complete geometry can be specified in a file. This project is bundled together with a parallel and previously reported open-source project for frequency-domain transfer matrix modeling of air columns (https://github.com/garyscavone/acmt).

Hammer weight and dropping height effects on dynamic response in densely-packed geo-materials

This study aims to investigate the dynamic cone penetration index (DCPI) and dynamic responses during instrumented dynamic cone penetration test at fixed-end condition (e.g., dense layer). Several types of hammer weights and heights at fixed potential energy (45.13 N∙m) is applied on the instrumented dynamic cone penetrometer (IDCP) tests. Test results show that the instrumented dynamic cone penetration index (IDCPI) is proportional to the DCPI with various gradients lower than 1.0 due to the influence of hammer weight on drivability. Dynamic responses change with respect to the end boundary condition (e.g., dense or loose layer) and location at the head or tip. In addition, the transferred energy varies with respect to the end boundary condition, location, hammer weight and height. For layer characterization, the end boundary condition should be primarily considered as well as hammer weight and height regarding drivability.

Analytical solution for longitudinal seismic response of immersed tunnel connecting artificial islands crossing different strata

Immersed tunnels typically pass through zones with different soil properties and may be subjected to earthquake threats. This paper presents a theoretical model using two flexible joints and three tube-elements for the longitudinal seismic response analysis of immersed tunnel connecting artificial islands. According to the reaction displacement method, the governing equations for bending of the immersed tunnel are established. Based on the matrix transfer principle, the end boundary conditions and the joint continuity conditions were considered in the analytical model. The analytical solutions were verified using finite element simulation results. Results indicate that the fixed and hinged end conditions have large shear forces on both ends, while the fixed end conditions have large bending moments. The free and roller end conditions have large vertical displacements on both ends, while the hinged end conditions have large rotation angles. The free end conditions can better reflect the boundary conditions of immersed tunnel connecting artificial islands. The flexible element joints can significantly reduce the shear forces at the interface of different strata, but also produce larger deformations at the joints. However, this amount of deformations can be accommodated by the flexible joints themselves, thus minimizing the damage to the immersed tunnel under seismic loading.

A Study On Flight Vibration Environmental Test of Unmanned Aerial Vehicle using Dual Electric Vibration Exciters

Analysis of dynamic characteristics and flight vibration test for unmanned aerial vehicles was studied by using dummy test body. The FEM model for dummy test body was supplemented by results of modal and random vibration test. The free end boundary condition to simulate flight environments was made by test setup using bungee cable. Prior to the flight vibration test using a dual electric vibration exciters, the test procedure to calculate quantitative vibration level was studied by using military specification. The actual test was successfully done by using the analysis and pretest results. From the analysis results, it was possible to determine the feasibility of the test by predicting the excitation force of the flight vibration test and to get the response of any point which could not be measured by the test. The results of this study will much contribute to the Test and Evaluation of unmanned aerial vehicles.

Flügge shell theory and solution for the vibration analysis of a thin elastic cylindrical panel of varying curvature

In this paper, the free vibration behavior of isotropic and orthotropic cylindrical shell panels with variable curvature subjected to certain ends boundary conditions is analyzed by the transfer matrix technique and solved by the Romberg integration approach. Flügge’s shell theory is employed to model the governing three-dimensional equations of vibration and Fourier’s approach is used to deform the displacement fields as trigonometric functions in the longitudinal direction. As a result of a semi-analytical procedure is conducted, the coupled governing equations of panel problem can be written in a matrix partial differential equation of first order with variable coefficients and reduced from the two-dimensional problem to one-dimensional one which is solved numerically as an initial-value problem. The proposed model is applied to get the natural frequencies and mode shapes for the vibration behavior of two-side simply-supported cylindrical panels with simply-supported, free-free, clamped-free and clamped-clamped ends boundary conditions lying at their curved edges. The sensitivity of the vibration behavior to the variety of curvature, panel parameters and material orthotropy of shell is studied.

Three-Dimensional Vibration Model of Cylindrical Shells via Carrera Unified Formulation.

In this paper, we present a novel and unified model for studying the vibration of cylindrical shells based on the three-dimensional (3D) elastic theory and the Carrera Unified Formulation. Our approach represents a significant advancement in the field, as it enables us to accurately predict the vibrational behavior of cylindrical shells under arbitrary boundary conditions. To accomplish this, we expand the axial, circumferential, and radial displacements of the shell using Chebyshev polynomials and Taylor series, thereby reducing the dimensionality of the expansion and ensuring the precision and rigor of our results. In addition, we introduce three groups of artificial boundary surface springs to simulate the general end boundary conditions of the cylindrical shell and coupling springs to strongly couple the two surfaces of the cylindrical shell φ = 0 and φ = 2π to ensure continuity of displacements on these faces. Using the energy function of the entire cylindrical shell model, we obtain the characteristic equation of the system by finding the partial derivatives of the unknown coefficients of displacement in the energy function. By solving this equation, we can directly obtain the vibration characteristics of the cylindrical shell. We demonstrate the convergence, accuracy, and reliability of our approach by comparing our computational results with existing results in the literature and finite element results. Finally, we present simulation results of the frequency features of cylindrical shells with various geometrical and boundary parameters in the form of tables and figures. Overall, we believe that our novel approach has the potential to greatly enhance our understanding of cylindrical shells and pave the way for further advancements in the field of structural engineering. Our comprehensive model and simulation results contribute to the ongoing efforts to develop efficient and reliable techniques for analyzing the vibrational behavior of cylindrical shells.

Geometrically Nonlinear Aeroelastic Flutter Characteristic of Laminated Composite Shell Panels Under Supersonic Flow

The nonlinear aeroelastic flutter characteristics of laminated composite curved (flat and cylindrical) panels are reported in this paper by obtaining the finite element (FE) solutions under the supersonic flow. The panel model has been derived from the third-order shear deformation theory framework including full geometrical nonlinearity via Green–Lagrange strain. In contrast, the flutter due to aerodynamic loading is included via the first-order piston theory. The current predicted solution accuracy and their validations have been demonstrated by relating the free vibration frequency, coalescence frequency, and critical aerodynamic pressure with the available numerical data. The initial free vibration eigenvalue responses are compared with in-house experimental values. Finally, a few numerical examples are presented by varying parameters like the effect of fiber orientation, flow angle, end boundary conditions, aspect ratio, modular ratio, thickness ratio, and amplitude ratio on the supersonic flutter boundaries of shell panels. The critical aerodyanamic pressure for simply supported cross-ply flat panels increases by 42.85% when the amplitude ratio increases from 0 to 0.75.

Shear vibration modes of granular structures: Continuous and discrete approaches

AbstractThis work is dedicated to the study of shear vibration modes of one‐dimensional granular microstructured beams using a discrete Cosserat model. The dynamic response of the one‐dimensional granular beam (discrete beam) is investigated for various boundary conditions, through the analytical resolution of an exact discrete eigenvalue problem. For an infinite number of grains, the dynamic behavior of the discrete problem converges towards a Bresse–Timoshenko continuum beam model. First, the effective modeling parameters, the constitutive equations and the governing equations of motion are derived in a difference form. For simply supported granular beams, the appearance of pure shear modes of vibration is highlighted (vibration modes without deflection), a phenomenon which is already known in the free vibration of a continuous Bresse–Timoshenko beam problem. The eigenfrequencies of these pure shear modes for the discrete granular beam coincide with the critical frequencies of the discrete system. These pure shear modes may appear for granular beams composed of few grains, which give a physical support of a phenomenon well studied in the literature from a continuum beam model. The eigenfrequencies of the discrete granular beam are also calculated for various boundary conditions, including clamped, hinge and free end boundary conditions. Based on the discrete element method (DEM), several numerical simulations of dynamic tests in some representative examples have been performed. The responses of the numerical approach are accurately compared against the exact results of the analytical solutions based on the difference eigenvalue problem, which illustrates the relevance of the proposed approach.

An analytical method for free vibration analysis of multi-layered transversely isotropic cylindrical shells

This work presents an effective analytical method based on displacement potential functions (DPF) for solving 3-D free vibration problem of thick and multi-layered transversely isotropic cylindrical shells with simply supported end boundary conditions. By using the DPF method, the three-dimensional elasticity equations are simplified and decoupled into two linear partial differential equations of fourth and second order as governing differential equations. These equations are analytically solved using the separation of variables method in terms of fields that exactly satisfy end boundary conditions and the continuity of a closed cylinder in the hoop direction. One of the advantages of the present work is the analysis of thick cylindrical shells using an exact method without any approximations and simplifying assumptions in the distribution of stress or strain along the thickness of the shells. The analysis is extended to multi-layered cylindrical shells by applying appropriate boundary conditions at the interfacial surfaces of the layers. Numerical comparisons to other analytical works shows the accuracy of the present work and also due to the lack of study for multi-layered transversely isotropic cylindrical shells, 3-D finite element analysis has been performed for comparison. In addition, various more involved problems are studied and solved analytically for single and multi-layered shells of transversely isotropic material and the effect of various parameters such as shell dimensions, mechanical properties, number of layers and other parameters on shell behavior are evaluated. The results of the present study can be used as benchmark solutions for other studies.

End boundary effects on wakes dynamics of inclined circular cylinders

We perform direct numerical simulations to characterize the three-dimensional wake dynamics of long inclined circular cylinders with inhomogeneous end boundary conditions. Three Reynolds numbers, Re=100, 200 and 300, corresponding to the regimes of laminar flow, mode A* wake, and mode B wake, respectively, are considered to reveal the roles of the intrinsic secondary instabilities and the extrinsic end boundary effects in shaping the three-dimensional flows. At Re=100, the end boundary effects are felt over the entire cylinder span by inducing oblique vortex shedding, which is associated with stronger spanwise flow in the wake than a parallel shedding. The Strouhal number of the oblique shedding is related to that of the parallel shedding of straight cylinder by the cosine law, considering the combined inclination angle and oblique angle. At Re=200, the intrinsic secondary instability results in large-scale vortex dislocation, precluding the propagation of the end boundary effects towards further span. Nevertheless, for the inclined cases, oblique shedding is still observed within limited span from the upstream end boundary. The oblique vortices feature intact and straight vortex cores, and are related to the two-dimensional flow at Re=200 (that are void of vortex dislocations) from the viewpoint of cosine law. Further along the span, the oblique vortices destabilizes with the formation of small-scale vortices, and the flow transitions to the typical mode A* wake. At Re=300, the highly three-dimensional flow near the end boundary creates disturbances that travel along the cylinder span, creating vortex dislocations for cases with low inclination angles. For high inclination angle, oblique vortex shedding is again observed over the cylinder span, and is not disrupted by vortex dislocations of either intrinsic or extrinsic causes. The present study offers renewed insights into the three-dimensional wake dynamics of inclined cylinders, and lays the foundation for the designs of long flexible engineering structures and related flow control techniques.

A Study on the Flight Vibration Environmental Specification of Unmanned Flying Vehicle using Random Vibration Test and Analysis Methods

In this study, analysis of dynamic characteristics and flight vibration was performed to unmanned aerial vehicles. The analysis model was supplemented by performing a dynamic characteristic test and a random vibration test using manufactured dummy aerial vehicle. For the dynamic characteristic test, a bungee cable was used to implement the free end boundary condition. Prior to the flight vibration test using a multiple electric shaker, a random vibration test was performed to predict the excitation force during the actual flight vibration test. It was judged that the actual test could be predicted more accurately by supplementing the analysis model from the test results. In addition, it was possible to determine the feasibility of the test by predicting the excitation force of the flight vibration test.

3-D analytical solution of non-homogeneous transversely isotropic thick closed cylindrical shells

This paper presents an effective analytical method based on displacement potential functions (DPF) for solving 3D static problem of thick and multilayer transversely isotropic cylindrical shells with simply supported end boundary conditions. By using the DPF method, the three-dimensional elasticity equations are simplified and decoupled into two linear partial differential equations of fourth and second order as governing differential equations. The governing equations are solved by the separation of variable method in terms of fields that exactly satisfy end boundary conditions and the continuity of a closed cylinder in the hoop direction. The analysis covers a straightforward solution process for handling problems on multilayered cylindrical shells of transversely isotropic material, adopting all boundary and continuity conditions. Extensive sets of general radial loads located on the inner and outer faces of the cylindrical shell may be stated and examined with in a systematic manner. Comparisons are performed to other existing analytical results for one and multilayered cylindrical shells, and show excellent agreement for different materials, thicknesses and aspect ratios of the shell. In addition, various more involved problems are studied and solved analytically for single and three-layered shells of transversely isotropic material with different sets of radial loading functions at the outer and inner shell surfaces. The results of the present study can be used as benchmark solutions for other studies.

Soil Thermal Response to Temperature Cycles and End Boundary Conditions of Energy Piles

This paper explores the influence of building cover and pile toe boundary conditions on ground temperature distributions surrounding energy piles. Experimental and numerical studies were conducted on two isolated cast-in-place energy piles installed in dense unsaturated sand, one exposed to the atmosphere at the ground surface (diameter=0.6 m and length=16.1 m) and the other installed under a six-story building (diameter=0.6 m and length=10 m). Investigations were conducted for monotonic heating and daily cyclic temperature changes of the piles ranging between 10°C and 35°C. The changes in ground temperature decreased as radial distance increased from the edge of both piles. Cyclic temperatures in both piles induced lower ground temperature changes and decreased the radial thermal influence zone compared with monotonic heating. However, the radial thermal zone in cyclic operating mode can be influenced by different ratios of heating to cooling times and hence should be selected carefully to avoid unexpected ground temperature changes. Atmospheric effects were observed up to a depth of 2 m for the energy pile exposed to the atmosphere. The insulation provided by the building footprint slightly decreased the impacts of ground-atmosphere interaction on the soil temperature distribution with depth near the surface compared to the energy pile exposed to the atmosphere. The ground temperature variations were dominant along the length of the heat exchanger loops for both piles. However, they were negligible near the pile toe below the heat exchanger loops for both piles.

Perivascular pumping in the mouse brain: Improved boundary conditions reconcile theory, simulation, and experiment

Cerebrospinal fluid (CSF) flows through the perivascular spaces (PVSs) surrounding cerebral arteries. Revealing the mechanisms driving that flow could bring improved understanding of brain waste transport and insights for disorders including Alzheimer’s disease and stroke. In vivo velocity measurements of CSF in surface PVSs in mice have been used to argue that flow is driven primarily by the pulsatile motion of artery walls — perivascular pumping. However, fluid dynamics theory and simulation have predicted that perivascular pumping produces flows differing from in vivo observations starkly, particularly in the phase and relative amplitude of flow oscillation. We show that coupling theoretical and simulated flows to more realistic end boundary conditions, using resistance and compliance values measured in mice instead of using periodic boundaries, results in velocities that match observations more closely in phase and relative amplitude of oscillation, while preserving the existing agreement in mean flow speed. This quantitative agreement among theory, simulation, and in vivo measurement further supports the idea that perivascular pumping is an important CSF driver in physiological conditions.

MODAL FREQUENCY ANALYSES OF THE VARIABLE STIFFNESS MECHANISM DESIGN OF THE SOFT ROBOTIC SYSTEM

In this study, mechanism design and numerical analysis are investigated and directly simulated through additively manufacturing materials of the thermoplastic polyurethane TPU and ABS. Systematic motion planning of humanoid arm systems improved concerning the designed soft robotic arm-like variable stiffness system through the completed novel methodology for the analysis. Soft robotics variable stiffness for mechanism design is a novel research area. Additionally, the humanoid arm-like variable stiffness mechanism herein is taken as a case study in this technology. The variable stiffness types for soft robotics are inflatable robotic technology, smart materials technology, mechanism technology, and a combination of them. The variable stiffness mechanism has a novel design opportunity via the boundary conditions and the orientation of the initial conditions for soft robotics. The relation between the boundary conditions and variable stiffness is not investigated sufficiently. The novel field of study completed herein, the soft robotics variable stiffness, is a fundamental investigation for further development in the mechanism design. Variable stiffness mechanisms can transmit the translational and rotational motions into required directions with required displacements and applied forces on the multibody systems. The stiffness for the fixed-free structural constraint boundary condition of the specified initial condition orientation is 8 Nm/rd compared to the stiffness value of the 65.6 Nm/rd fixed-fixed end boundary condition.

A symplectic analytical approach for free vibration of orthotropic cylindrical shells with stepped thickness under arbitrary boundary conditions

Exact analytical solutions for free vibration of isotropic and orthotropic cylindrical shells with uniform and stepped thickness subject to general boundary conditions are presented by means of a symplectic analytical approach. The Reissner shell theory is adopted to formulate a theoretical model. By introducing a Hamiltonian system, the governing higher order partial differential equation is reduced to a set of ordinary differential equations which can be analytically solved by separating the variables. Applying the end boundary and interface continuous conditions, a set of analytical characteristic frequency equations are obtained, and exact solutions can be determined. To ensure accuracy and validity of the symplectic method, the analytical solutions for uniform and stepped cylindrical shells with isotropic or orthotropic material properties and with arbitrary boundary conditions are compared with available published data and FEM solution. A set of comprehensive new result for orthotropic stepped cylindrical shells under classical and elastic restraints are presented. Some typical mode shapes for various examples are illustrated. In addition, the effects of boundary conditions and orthotropic properties on vibration frequency are analyzed. The result shows that the fundamental frequency is higher for a boundary with more constraints.