Actual Boundary Conditions Research Articles

Determining optimal equivalent source positions in wave superposition method by self-adaptive searching algorithm

The calculation accuracy of wave superposition method is influenced greatly by equivalent sources, their positions, and the frequency. What’s more, nonuniqueness occurs at eigenfrequencies when monopole or dipole is used as the equivalent source. Although tripole can overcome the nonuniqueness, the computational overhead is very large due to its complex expression and the accuracy is still affected greatly by the positions. A method is proposed to reduce the calculation errors. In this method, monopole, which is the simplest source, is used as the equivalent source. The upper limit frequency for a radiator under a certain meshing pattern is predicted by using the fictitious pressure generated via a reference source. Then, the optimal equivalent source positions for each frequency corresponding to the actual vibration velocity boundary condition, in which the average rate of pressure change is minimal, are determined within the upper limit frequency by a searching algorithm. Numerical simulation results of a complex structure show that the calculation errors are significantly reduced. At last, the method is verified by an experiment for a cuboid radiator. Experimental results show that the proposed method is practicable and good at accuracy.

Study on the stiffness and damping coefficients of water-lubricated rubber bearings with multiple grooves

By considering the effects of multiple grooves, rubber deformation, and actual boundary conditions, the steady elastohydrodynamic lubrication mathematical model and the dynamic Reynolds equation of water-lubricated rubber bearings are presented. The Reynolds equation is solved numerically by the finite difference method, and the stiffness and damping coefficients are calculated from the real and imaginary parts of the integrated pressure. Analysis results suggest that angular velocity, eccentricity ratio, groove configuration, and radial clearance have significant effects on the steady state and dynamic stiffness as well as damping characteristics, which also help in designing proper structure parameters of water-lubricated rubber bearings to obtain better dynamic performance.

Effect of circumferential sealant joints and metal supporting frames on the buckling behavior of glass panels subjected to in-plane shear loads

In this paper, the structural stability of adhesively supported glass panels subjected to in-plane shear walls is assessed by means of extended finite-element (FE) investigations and analytical methods. Based on past research projects, careful consideration is given to glass panels with two-side circumferential linear adhesive connections and supporting metal frames, which are frequently used in practice for facades and building envelopes. In accordance with earlier research contributions, the effects deriving from adhesive connections and supporting frames of various stiffnesses are highlighted in terms of expected Euler’s critical shear loads and ultimate buckling resistances. Further extended nonlinear incremental studies are then discussed, and the major structural effects deriving from the interaction between the glass sheets, the circumferential adhesive joints, the supporting metal frames and additional small steel supports often used to transfer the maximum compressive reaction forces to the structural background are properly highlighted. As shown, compared to classical theories of ideally simply supported or fully clamped panels under the action of in-plane shear loads, the actual boundary conditions should be carefully taken into account. At the same time, the effects deriving from multiple combinations of several geometrical and mechanical aspects should be properly assessed. In the specific case, numerically derived buckling coefficients and fitting curves of practical use are proposed for an appropriate calculation of the expected Euler’s critical load for the studied configurations. Finally, the application and validity of a normalized Eurocode-based design buckling curve recalled from literature is also assessed. Based on the rather good agreement between FE and analytical calculations, the same approach is then proposed as practical and suitable design method for the studied loading and boundary conditions.

Single crystal anisotropy and coupled stability analysis for variant reorientation in Magnetic Shape Memory Alloys

Magnetic Shape Memory Alloys (MSMAs) have been the subject of much research in recent years as potential high-actuation-energy multifunctional materials. In this work we analyze coupled magneto-mechanical stability analysis of a variant reorientation mechanism for a single crystal based on a proposed 3-D magneto-mechanically coupled constitutive equations, derived in a consistent thermodynamic way. Discrete symmetry is considered to take into account single crystal anisotropy in the modeling. Analytical results are presented to demonstrate the influence of coupling and anisotropy in the stability of such a material system. Finally, a coupled Boundary Value Problem (BVP) using finite element analysis is performed by considering actual specimen geometry and boundary conditions that are used in the experiments. The numerical simulation reveals localization zones in the solutions due to the loss of ellipticity of the coupled magneto-mechanical problem.

Ultimate load of composite floors in fire with flexible supporting edge beams

A number of previous analytical studies have been conducted to predict the enhanced load-bearing capacity of a concrete slab due to tensile membrane action. These analytical approaches are based on an implicit assumption that the vertical supports along the slab panel boundaries during a fire do not deform. In reality, the edge beams do deflect even though they are fire-protected, and this assumption may not be valid. This may render any approaches based on this assumption to be unconservative when there is significant deflection of protected edge beams. This work looks at the actual boundary condition where the protected edge beams do deflect, and the slab still bends in synclastic curvature. The authors propose a semi-analytical model which can predict the load-bearing capacity of composite beam–slab floor systems enhanced by tensile membrane action under fire conditions, but weakened by deflection of protected edge beams. The novelty is that the slab enhancement factor actually takes account of the deflections of protected edge beams. The new model can consider the beam–slab interaction under fire conditions and give information of the edge beams. Validations with the test results show that the new model gives fairly accurate and conservative predictions of the load-bearing capacity of composite beam–slab systems.

Investigation of seasonal thermal flow in a real dam reservoir using 3-D numerical modeling

Abstract Investigations indicate that correct estimation of seasonal thermal stratification in a dam reservoir is very important for the dam reservoir water quality modeling and water management problems. The main aim of this study is to develop a hydrodynamics model of an actual dam reservoir in three dimensions for simulating a real dam reservoir flows for different seasons. The model is developed using nonlinear and unsteady continuity, momentum, energy and k-ε turbulence model equations. In order to include the Coriolis force effect on the flow in a dam reservoir, Coriolis force parameter is also added the model equations. Those equations are constructed using actual dimensions, shape, boundary and initial conditions of the dam and reservoir. Temperature profiles and flow visualizations are used to evaluate flow conditions in the reservoir. Reservoir flow’s process and parameters are determined all over the reservoir. The mathematical model developed is capable of simulating the flow and thermal characteristics of the reservoir system for seasonal heat exchanges. Model simulations results obtained are compared with field measurements obtained from gauging stations for flows in different seasons. The results show a good agreement with the field measurements.

A design method of bending deflection on hyper-static leaf spring

A group of leaf springs which provides the flexible support of stator is designed to satisfy the requirement of low vibration motor at megawatt (MW) level. Spring steel 65Mn is chosen as the material of the leaf spring. The size of the leaf spring is obtained by calculation and load analysis according to a deflection formula. The deflection and stiffness of the single leaf spring is calculated with both theoretical method and finite element analysis (FEA). A deflection test platform is established based on actual force and boundary condition to verify the deflection and stiffness of the leaf spring. The results show that the maximal deflection of the three pieces of 1.2 mm leaf spring group is 0.71 mm and the stiffness of the leaf spring group is 364 N/mm, which satisfies the requirements of the motor. The design method is also applicable for other MW power level motors.

Substructural Identification of Flexural Rigidity for Beam-Like Structures

This study proposes a novel substructural identification method based on the Bernoulli-Euler beam theory with a single variable optimization scheme to estimate the flexural rigidity of a beam-like structure such as a bridge deck, which is one of the major structural integrity indices of a structure. In ordinary bridges, the boundary condition of a superstructure can be significantly altered by aging and environmental variations, and the actual boundary conditions are generally unknown or difficult to be estimated correctly. To efficiently bypass the problems related to boundary conditions, a substructural identification method is proposed to evaluate the flexural rigidity regardless of the actual boundary conditions by isolating an identification region within the internal substructure. The proposed method is very simple and effective as it utilizes the single variable optimization based on the transfer function formulated utilizing Bernoulli Euler beam theory for the inverse analysis to obtain the flexural rigidity. This novel method is also rigorously investigated by applying it for estimating the flexural rigidity of a simply supported beam model with different boundary conditions, a concrete plate-girder bridge model with different length of an internal substructure, a cantilever-type wind turbine tower structure with different type of excitation, and a steel box-girder bridge model with internal structural damages.

A comprehensive study on numerical analysis of contaminant migration process in compacted clay liner and underlying aquifer for MSW landfill

For the study of MSW landfills in which the lining system is composed of a compacted clay liner (CCL), a two-layer strata model is presented to reproduce the system which consists of a CCL and an underlying aquifer. Considering all types of mechanisms including advection, hydrodynamic dispersion and sorption of soil skeleton, one-dimensional differential equation is formulated for describing the migration behaviour of contaminant in the CCL and aquifer. Together with the actual initial and boundary conditions, the resulting initial boundary value issue is numerically solved by various effective procedures. Based on abundant numerical computations by varying various relevant parameters, the effects of the production modes of contaminant source, hydraulic conductivity and dispersion as well as various sorption behaviours of the CCL, the equilibrium and linear sorption of the aquifer as well as biochemical degradation on the migration behaviour of contaminants in both the CCL and aquifer are systematically examined. It is shown that an independent mechanism in addition to hydrodynamic dispersion and advection, the sorption of soil skeleton plays a much important role in controlling the migration behaviour of contaminants. The sorption model and its parameters should be carefully chosen in the numerical analysis of contaminants migration and design of MSW landfill. Moreover, both coefficients of hydraulic conductivity and dispersion of the CCL should be duly determined according to the actual condition. Compared with the sorption effect of the CCL, the influence of sorption of aquifer on the migration behaviour of contaminants can be overlooked.

Supercurrent Generation by Spin-twisting Itinerant Motion of Electrons: Re-derivation of the ac Josephson Effect Including the Current Flow Through the Leads Connected to Josephson Junction

Based on a new supercurrent generation mechanism proposed for the cuprate superconductivity (as reported by Koizumi (J. Supercond. Nov. Magn. 24:1997, 2011); Hidekata and Koizumi (J. Supercond. Nov. Magn. 24:2253, 2011); Koizumi et al. (J. Supercond. Nov. Magn. 27:121, 2014); Koizumi et al. (J. Supercond. Nov. Magn. 2014), we re-derive the ac Josephson effect including the current flow through the leads connected to the Josephson junction and the impressed electromotive force. It is noted that the actual experimental boundary condition where the Josephson frequency 2e V 0/h (h is Planck’s constant, e is the absolute value of electron charge, and V 0 is the dc voltage across the Josephson junction) is measured differently from the one assumed by Josephson, and 2e V 0/h is obtained by the electron tunneling instead of the Cooper pair tunneling. It is also indicated that the standard textbook description for the Josephson relation, “if a dc voltage V 0 is applied, the time-variation of ϕ occurs” (as reported by Feynman et al. (1965); Ashcroft and Mermin (1976); Kittel (1986); Tinkham (1996) (ϕ is related to the tunneling current as J s = J c sinϕ) should be rephrased, “if the time-variation of ϕ is introduced, a voltage difference V 0 appears.” We show that by adding the Rashba spin-orbit interaction to the Bardeen, Cooper, and Schrieffer (BCS) Hamiltonian, the spin-twisting itinerant motion of electrons is stabilized in the BCS superconductors; thus, it is suggested that the present, new supercurrent generation mechanism is also relevant to the BCS superconductors, i.e., the true origin of the supercurrent generation in the BCS superconductors may also be the spin-twisting itinerant motion of electrons.

DIC identification and X-FEM simulation of fatigue crack growth based on the Williams’ series

A unified Digital Image Correlation (DIC)/eXtended Finite Element Method (X-FEM) framework based on the Williams’ series for fatigue crack growth identification and simulation is proposed. Williams’ series are used for post-processing the displacement measured by digital image correlation. It gives access to the change of stress intensity factors and crack length with the number of cycles. A Paris’ crack propagation law is subsequently identified and further validated by simulating the experiment. The simulation uses measured displacements as Dirichlet boundary conditions and a direct estimation of stress intensity factors based on a coupling between a finite element model and the analytical Williams’ solutions. It is shown that the use of actual boundary conditions is crucial. The use of the Williams’ formalism is further investigated on an elasto-plastic simulation to validate the extraction of nonlinear features in the crack tip vicinity.

Critical Aspects of the Cracked Brazilian-disc test Explored by the Method of Caustics

Some critical aspects of the cracked Brazilian-disc test are explored in the light of recently introduced analytic solutions for the stress- and displacement-fields developed in a centrally cracked cylindrical disc under uniform pressure (acting along two finite arcs of its periphery symmetric with respect to the disc's center). The study is focused to the reliable determination of the respective Stress Intensity Factors (SIFs) and also to the role of the actual boundary conditions along the disc-jaw contact arc (assuming that the disc is compressed between the curved jaws of the device suggested by the International Society for Rock Mechanics (ISRM) for the standardized implementation of the Brazilian-disc test). The crack is assumed relatively short with respect to the disc's radius. The results of the analytic approach concerning the SIFs and the length of the disc-jaw contact arc are compared to the respective ones obtained experimentally using the method of Caustics. The agreement is satisfactory at least for load levels for which the linearity assumption is not violated. Taking advantage of the insight gained additional issues related to the validity of the test as a mean to determine mode-I fracture toughness are critically discussed revealing that quite a few questions are still open although the test is standardized by ISRM almost since 20 years.

MODAL CHARACTERISTIC ANALYSIS OF THE APR1400 NUCLEAR REACTOR INTERNALS FOR SEISMIC ANALYSIS

Reactor internals are sensitive to dynamic loads such as earthquakes and flow induced vibration. Thus, it is essential to identify the dynamic characteristics to evaluate the seismic integrity of the structures. However, a full-sized system is too large to perform modal experiments, making it difficult to extract data on its modal characteristics. In this research, we constructed a finite element model of the APR1400 reactor internals to identify their modal characteristics. The commercial reactor was selected to reflect the actual boundary conditions. Our FE model was constructed based on scale-similarity analysis and fluid-structure interaction investigations using a fabricated scaled-down model.

The Comparison of the Probabilistic Calculation of Course of Temperatures in Peripheral Construction with Actual Measured Data

This article deals with probabilistic calculation of the behavior of the peripheral wallof the wooden passive house in terms of the temperatures inside the structure in the winter. The probabilistic calculation was made for the actual boundary conditions, ie. actually measured exterior and interior temperature. The results of the probabilistic calculation are ultimately compared with the results of experimental measurements of temperature inside the structure, ie. the actual behavior of the structure.

On the oxidative ageing mechanism and its effect on asphalt mixtures morphology

This paper investigates the influence of mixture morphologies and microstructures on oxidative ageing of asphalt mixtures. For this, an oxidative ageing mechanism based on a diffusion–reaction process was developed. Previously, most asphalt oxidative ageing modeling research focused on unidirectional diffusion of continuous oxygen flow through bitumen films, which is far from the actual boundary conditions in asphalt mixtures. For this reason in the current study, a finite element (FE) analysis has been conducted in which 3D mixture morphology was considered. Mixture morphology is the combination of mineral aggregate packing, porosity, air-void distribution and their interconnectivity. One dense and one open graded field asphalt mixture core were scanned with a computerized tomography X-ray scanner. In the analyses, the developed oxidative ageing model was implemented. The FE analysis showed that the effect of the air-void distribution, their interconnectivity and the mineral aggregate packing has a significant effect on the resulting age hardening of the overall mixture. Furthermore, from the microstructural investigation done in this research, strong indications were found that, depending on the bitumen and its conditioning, water soluble thin films are formed due to ageing. This means that ageing and moisture damage are strongly interlinked and this should thus be considered in the design of the asphaltic materials and the prediction of their long term performance.

Analysis of the Thermal Behavior of a Ball Screw Based on Simulation and Experimental Investigation

Thermal expansion of ball screw system affects the machining accuracy of machine tools significantly. The objective of this paper is to analyze the thermal behavior and predict the temperature variation pattern of a ball screw based on finite element analysis and experimental investigation. Wireless temperature sensors are used to monitor the temperature variation of the ball screw system under different thermal conditions during both the warm-up and cooldown phases, so as to investigate its temperature variation pattern. Then an exponential algorithm is proposed to analyze and predict the temperature variation of the ball screw based on finite element analysis, and the actual thermal boundary conditions of the ball screw system are exactly defined according to the proposed algorithm and the experimental results. Finally, it was found that the simulation based on the thermal boundary conditions identified herein could match quite well with the experimental results.

Time-varying positioning error modeling and compensation for ball screw systems based on simulation and experimental analysis

Thermal expansion of ball screw systems affects the machining accuracy of machine tools significantly. This paper intends to provide a comprehensive error compensation method for the time-varying positioning error of machine tools. To confirm the thermal deformation mechanism of ball screw systems, experiments have been designed to study the thermal behaviors of a ball screw system under varying temperature conditions. An exponential algorithm is proposed to predict the temperature variation pattern of the ball screw based on finite element analysis, and the actual thermal boundary conditions of the ball screw system are exactly defined according to the proposed algorithm and the experimental results. Then, a comprehensive compensation model is established based on the decomposition of the initial geometric error and thermal error components. Finally, a real-time error compensation system is developed for machine tools based on the function of external machine original coordinate shift and fast Ethernet data interaction, and satisfactory results have been achieved for the compensation experiments on a machining center.

Anodic bonding using SOI wafer for fabrication of capacitive micromachined ultrasonic transducers

In medical ultrasound imaging, mostly piezoelectric crystals are used as ultrasonic transducers. Capacitive micromachined ultrasonic transducers (CMUTs) introduced around 1994 have been shown to be a good alternative to conventional piezoelectric transducers in various aspects, such as sensitivity, transduction efficiency or bandwidth. This paper focuses on a fabrication process for CMUTs using anodic bonding of a silicon on insulator wafer on a glass wafer. The processing steps are described leading to a good control of the mechanical response of the membrane. This technology makes possible the fabrication of large membranes and can extend the frequency range of CMUTs to lower frequencies of operation. Silicon membranes having radii of 50, 70, 100 and 150 µm and a 1.5 µm thickness are fabricated and electromechanically characterized using an auto-balanced bridge impedance analyzer. Resonant frequencies from 0.6 to 2.3 MHz and an electromechanical coupling coefficient around 55% are reported. The effects of residual stress in the membranes and uncontrolled clamping conditions are clearly responsible for the discrepancies between experimental and theoretical values of the first resonance frequency. The residual stress in the membranes is determined to be between 90 and 110 MPa. The actual boundary conditions are between the clamped condition and the simply supported condition and can be modeled with a torsional stiffness of 2.10−7 Nm rad–1 in the numerical model.

Atlas-based transfer of boundary conditions for biomechanical simulation.

An environment composed of different types of living tissues (such as the abdominal cavity) reveals a high complexity of boundary conditions, which are the attachments (e.g. connective tissues, ligaments) connecting different anatomical structures. Together with the material properties, the boundary conditions have a significant influence on the mechanical response of the organs, however corresponding correct mechanical modeling remains a challenging task, as the connective structures are difficult to identify in certain standard imaging modalities. In this paper, we present a method for automatic modeling of boundary conditions in deformable anatomical structures, which is an important step in patient-specific biomechanical simulations. The method is based on a statistical atlas which gathers data defining the connective structures attached to the organ of interest. In order to transfer the information stored in the atlas to a specific patient, the atlas is registered to the patient data using a physics-based technique and the resulting boundary conditions are defined according to the mean position and variance available in the atlas. The method is evaluated using abdominal scans of ten patients. The results show that the atlas provides a sufficient information about the boundary conditions which can be reliably transferred to a specific patient. The boundary conditions obtained by the atlas-based transfer show a good match both with actual segmented boundary conditions and in terms of mechanical response of deformable organs.

Analysis of the low-frequency magnetoelectric performance in three-phase laminate composites with Fe-based nanocrystalline ribbon

The theoretical analysis of magnetoelectric (ME) performance in three-phase Terfenol-D/PZT/FeCuNbSiB (MPF) laminate composite is presented in this paper. The ME couplings at low frequency for ideal and less than ideal interface couplings are studied, respectively, and our analysis predicts that (i) the ME voltage coefficient for ideal interface coupling increases with the increasing layers (n) of Fe-based nanocrystalline ribbon FeCuNbSiB (Fe73.5Cu1Nb3Si13.5B9) while the sizes of PZT (Pb(Zr1−xTix)O3) and Terfenol-D (Tb1−xDyxFe2−y) are kept constant, and then it tends to be a constant when the layers of FeCuNbSiB are >100; (ii) by introducing the interface coupling factor k and considering the degradation of d33m,f with n, the ME voltage coefficient for a less than ideal interface condition is predicted. As the FeCuNbSiB layer increases, it first increases and reaches to a maximum value, and then slowly decreases. Various MPF laminates are fabricated and tested. It is found that the theoretical predictions for the consideration of actual boundary conditions at the interface are in agreement with the experimental observations. This study plays a guiding role for the design of MPF composite in real applications.