Actual Boundary Conditions Research Articles

Advective solute transport through porous media along streamlines

Transforming the standard solute transport models into one-dimensional ones along streamlines by excluding from them diffusive and dispersive components and direct including in simulation procedures the mechanical dispersion, the predominate factor defining solute transport in day-to-day applications, permit reducing these models to ordinary differential equations of the first order, making simulations less cumbersome and more flexible and permitting analytical solutions under about any practical conditions. The models of solute transport along flux tubes and streamlines are discussed in numerous publications. Most of those models, if not all, are one-dimensional copies of the mass conservation law and do not take in consideration streamline specificity: the absence of sinks and source within flux tubes to which the streamlines belong. This makes the obtained equations either inadequate or unnecessary oversimplified by assuming the pore water velocity constant along the streamlines. The development of the solute transport equations along streamlines taking in account the above mentioned specificity is presented in Appendix 1. Appendix 2 contains development of analytical solutions to the corresponding models for spatially varying actual pore water velocities, arbitrary initial and boundary conditions, linear and non-linear (Freundlich and Langmuir isotherms) interaction of solutes with the surroundings. Calculating concentration at given points and instants, the concentrations for the involved streamlines must be summarized accordingly to mechanical dispersion. The method of weighted summarizing is suggested. The approach is illustrated by field examples.

Conceptual design of a sub-critical Pb-cooled Accelerator Driven System (ADS) fuelled by (Th-LEU)

The target of this study is to provide information on the actual boundary conditions encountered in the conceptual design of an ADS fuelled by (Th, LEU), as well as their impact on the design itself, on the performances of the system and on the possible solutions from the point of view of the choice of materials, the operating conditions, the neutron design optimization, etc. In this paper rationales and consequences of the (Th, U) fuel cycle adoption, together with the design constraints, are discussed. Identified reference core configuration and the steady state criticality results are also discussed. Stochastic approach for the neutronic evaluations has been adopted.

A complex mixed-mode crack propagation test performed with a 6-axis testing machine and full-field measurements

A new type of mixed mode crack propagation test is proposed. A single crack is initiated and propagates in a stable way up to complete failure. A combination of tensile, shear and in-plane rotation performed by a 6-axis testing machine is prescribed. The rotation creates a tension/compression gradient in the sample ensuring the stability, while the shear direction is closely related to the orientation of the crack and the tensile load is responsible for the actual propagation. The experiment is performed in an interactive manner, namely, depending on the crack tip position estimated by Digital Image Correlation (DIC) during the test, the loading is changed to bifurcate the crack. The displacements of the sample surfaces are assessed using multiple DIC measurements and displacement sensors. The displacement fields on each face of the sample give access to the crack pattern, and also to the actual boundary conditions that are crucial for a faithful numerical analysis of the test. Last, the 6 load components are recorded enabling for a complete description of the 3D mechanical behavior of the specimen.

Experimental Study and Numerical Analysis on Chloride Diffusion Coefficient of Concrete with Various Water-Cement Ratios

A rapid chloride ion diffusion coefficient measurement (RCM) was used in this study. The influence of water-cement ratios of 0.30, 0.35 and 0.40 at various ages (3, 7, 14, 28 and 56 days) on chloride ion diffusion coefficient of the concretes and pastes was studied and analyzed. The results show that, with the increase of curing ages, the chloride ion diffusion coefficient of different water-cement ratio of each specimen is decreased. In the early age, the chloride ion diffusion coefficient of the paste with the water-cement ratio of 0.40 is 2~3 times of the paste with water-cement ratio of 0.30 and 0.35, and with the increase of curing age, this difference is gradually decreased. Additionally, the chloride ion diffusion coefficient of the cement paste is 1~2 times of the concrete with same water-cement ratio at different ages. Based on the actual experiment boundary conditions, the process of chloride ions diffusion and permeability was simulated by COMSOL software, and the simulation result was analyzed to predict the permeability of concrete.

Approaches for the optimized control of solar thermally driven cooling systems

Small scale (solar-) thermally driven cooling systems suffer from two important drawbacks: firstly, the systems usually offer no means of adapting the chilling capacity to the actual load; secondly constantly running pumps and fans lead to high auxiliary electricity consumption even when the available driving and cooling water temperatures only allow a reduced chilling capacity. To solve these problems a generic approach for controlling the main parasitic electrical devices – the cooling water pump and the heat rejection fan - as a function of the actual boundary conditions was developed. Different variants of control strategies are analyzed in different system configurations under a variety of climates and load conditions by means of dynamic system simulations in TRNSYS. The most typical combinations of ab- and adsorption chillers with dry cooler and wet cooling tower are covered. The results show that capacity modulation can be realized well by this approach. Additionally electricity savings of up to 25% can be achieved for reasonably sized systems compared to a reference control strategy with fixed pump speed and fixed cooling water set temperature. Yet it becomes obvious that the concrete savings depend strongly on the system configuration and boundary conditions.

Dynamic Analysis of Heavy Vehicle Medium Duty Drive Shaft Using Conventional and Composite Material

The main highlight of this study is structural and modal analysis of single piece drive shaft for selection of material. Drive shaft is used for torque carrying from vehicle transmission to rear wheel differential system. Heavy vehicle medium duty transmission drive shaft was selected as research object. Conventional materials (Steel SM45 C, Stainless Steel) and composite materials (HS carbon epoxy, E Glass Polyester Resin Composite) were selected for the analysis. Single piece composite material drive shaft has advantage over conventional two-piece steel drive shaft. It has higher specific strength, longer life, less weight, high critical speed and higher torque carrying capacity. The main criteria for drive shaft failure are strength and weight. Maximum modal frequency obtained is 919 Hz. Various harmful vibration modes (lateral vibration and torsional vibration) were identified and maximum deflection region was specified. For single-piece drive shaft the natural bending frequency should be higher because it is subjected to torsion and shear stress. Single piece drive shaft was modelled using Solid Edge and Pro-E. Finite Element Analysis was used for structural and modal analysis with actual running boundary condition like frictional support, torque and moment. FEA simulation results were validated with experimental literature results.

Theoretical analysis and finite element method simulations on dynamic sensitivity of hemisphere-shaped electrostatic sensors

Electrostatic sensors are key components of electrostatic monitoring systems. Their sensitivity characteristics have a direct influence on monitoring accuracy. In previous studies, spatial sensitivity, which is called static sensitivity here, was used to describe the sensitivity characteristics. However, it only reflects a basic relationship between static charged particles and induced charges on an electrostatic sensor’s probe. Besides, as a three-dimensional defined parameter, it is difficult to build a unified model if actual boundary conditions are considered. Thus, it is not quite proper for applications that detect moving particles. To solve this problem, dynamic sensitivity is proposed in this article. As for a hemisphere-shaped electrostatic sensor, first, a more accurate model of static sensitivity is built. Based on it, dynamic sensitivity is defined and modeled analytically. Then, a calibration method is proposed to improve the model’s accuracy under actual boundary conditions. In the end, finite element method simulations are done for validations. The results demonstrate that dynamic sensitivity reflects a relationship between moving charged particles and the actual output signals of a sensor, thus it is direct and practical for moving particles. And the theoretical results are highly consistent with the simulated ones. Moreover, the dynamic sensitivity indicates localized sensing characteristics of hemisphere-shaped electrostatic sensors.

Magnetization and transport characteristics of layered high-temperature superconductors with different anisotropy parameters

The magnetization of a layered high-temperature superconductor with different anisotropy parameters has been calculated using the Monte Carlo method in the framework of a modified three-dimensional Lawrence–Doniach model with actual boundary conditions. The penetration of a magnetic flux into a bulk sample from the boundary has been simulated, and the curves of magnetization reversal of a high-temperature superconductor by an external magnetic field have been calculated for different anisotropy parameters γ and types of defects in the sample. It has been found that there are significant differences in the magnetization curves and transport properties of superconductors with different anisotropy parameters γ. The influence of tilted columnar defects on the critical current has been analyzed. A decreasing dependence of the critical current on the tilt angle of defects with respect to the c axis has been obtained. It has been shown that, as the anisotropy parameter increases, this dependence weakens and, for a specific value of γ, disappears. An explanation of the mechanism responsible for the disappearance of the dependence has been proposed.

Mixed Convolved Action Variational Methods for Poroelasticity

Although Lagrangian and Hamiltonian analytical mechanics represent perhaps the most remarkable expressions of the dynamics of a mechanical system, these approaches also come with limitations. In particular, there is inherent difficulty to represent dissipative processes, and the restrictions placed on end point variations are not consistent with the definition of initial value problems. The present work on the time-domain response of poroelastic media extends the recent formulations of the mixed convolved action (MCA). The action in this proposed approach is formed by replacing the inner product in Hamilton's principle with a time convolution. As a result, dissipative processes can be represented in a natural way and the required constraints on the variations are consistent with the actual initial and boundary conditions of the problem. The variational formulation developed here employs temporal impulses of velocity, effective stress, pore pressure, and pore fluid mass flux as primary variables in this mixed approach, which also uses convolution operators and fractional calculus to achieve the desired characteristics. The resulting MCA is formulated directly in the time domain to develop a new stationary principle for poroelasticity, which applies to dynamic poroelastic and quasi-static consolidation problems alike. By discretizing the MCA using the finite element method over both space and time, new computational mechanics formulations are developed. Here, this formulation is implemented for the two-dimensional case, and several numerical examples of dynamic poroelasticity are presented to validate the approach.

Propagation of Ultrasonic Guided Waves in Composite Multi-Wire Ropes.

Multi-wire ropes are widely used as load-carrying constructional elements in bridges, cranes, elevators, etc. Structural integrity of such ropes can be inspected by using non-destructive ultrasonic techniques. The objective of this work was to investigate propagation of ultrasonic guided waves (UGW) along composite multi-wire ropes in the cases of various types of acoustic contacts between neighboring wires and the plastic core. The modes of UGW propagating along the multi-wire ropes were identified using modelling, the dispersion curves were calculated using analytical and semi-analytical finite element (SAFE) techniques. In order to investigate the effects of UGW propagation, the two types of the acoustic contact between neighboring wires were simulated using the 3D finite element method (FE) as well. The key question of investigation was estimation of the actual boundary conditions between neighboring wires (solid or slip) and the real depth of penetration of UGW into the overall cross-section of the rope. Therefore, in order to verify the results of FE modelling, the guided wave penetration into strands of multi-wire rope was investigated experimentally. The performed modelling and experimental investigation enabled us to select optimal parameters of UGW to be used for non-destructive testing.

Mode selection for reduced order modeling of mechanical systems excited at resonance

Welding, food cutting, atomizing, cleaning and deagglomerating are just a few common uses for ultrasonic resonators, which are carefully designed to operate excited in resonance. Finite element analysis is nearly always adopted for predicting and improving resonator performances. Large number of small elements are usually needed to guarantee accuracy. As a consequence, models have typically very large dimensions, and hence considerable computational and ill conditioning problems arise. Model reduction techniques can be extremely useful to keep model dimensions to a minimum. In this paper a new ranking method, called Interior Mode Ranking (IMR), is introduced for the selection of the interior normal modes in the Craig Bampton reduction technique, which is one of the most popular model reduction methods, often available in commercial finite element software packages. The IMR method allows ranking the interior modes analytically by comparing the contributions provided by the interior modes of the subsystem with constrained boundary conditions to the dynamics of interest of the complete system (with actual boundary conditions). The method is general and can be applied to any resonator in the reduction at the system level. Here it is employed to obtain an accurate reduced-order model of an ultrasonic welding bar horn. The results achieved by the method are compared with those yielded by other ranking techniques. The comparison shows that the IMR method outperforms the other ranking techniques and leads to accurate representations of the excited modes.

TECHNOLOGY EVALUATION OF STRUCTURAL AND VIBRATIONAL CHARACTERISTIC OF COMPOSITE DRIVE SHAFT FOR AUTOMOBILE USING FEM

In vehicle drive shaft is one of the most important component. It transmits torque from the engine to the differential gear of a rear wheel drive vehicle. Generally the drive shaft is made up of steel alloy but the use of conventional steel has disadvantages such as low specific stiffness and strength and high weight. Nowadays this steel drive shaft is replaced by composite material drive shaft. This advanced composite such as graphite, Kevlar, carbon, glass with suitable resin have advantage of higher specific strength, less weight, high damping capacity, longer life, high critical speed and greater torque carrying capacity and can results in considerable amount of weight reduction as compared to steel shaft. The main objective of this research work is to study the structural and vibrational behavior of composite material drive shaft assembly as compared to conventional steel drive shaft. Heavy duty vehicle transmission drive shaft has been used for the project. The conventional material steel SM45C and three composite materials HS carbon epoxy, E-glass epoxy, HM carbon epoxy have been used for drive shaft study so as to determine the suitable composite replacement in order to optimize the performance and design. The drive shaft was modelled using the CREO 3.0 cad software and finite element analysis were done using ansys 14.0 FEA as an analysis tool for numerical simulation to find the dynamic vibration response of composite material drive. The simulation result determines the total deformation, Equivalent Von misses stress, Maximum shear stress, natural frequencies and mode shapes under actual boundary conditions. The result concluded that HS carbon epoxy composite material is suited more for composite drive shaft application as compared to other composite materials.

Semi-empirical calculation for design of flexural mode silicon mechanical resonator with variable cross section

This paper newly proposes a semi-empirical calculation for design of electrostatically driven flexural mode silicon (Si) mechanical resonators with a variable cross section which is applicable to a feasibility study of their development without finite element analysis (FEA). In the design for Si mechanical resonators with a variable cross section, a mode function describing a shape of vibration is simply assumed to be a static deflection function, and a resonant frequency is derived by applying the Rayleigh-Ritz method. The static deflection function, which reflects an effect of stress concentration generated by a variation of cross section, is semi-empirically formulated using some FEA results. This research adopts a clamped–clamped beam Si mechanical resonator which a wide rectangular bar located at the center is supported by same two narrow rectangular bars clamped to anchors. The resonant frequencies of the Si mechanical resonators are calculated within a mean absolute percentage error of 3% from the FEA results. In order to confirm the applicability of the semi-empirical formula, twenty different sizes of clamped–clamped beam Si mechanical resonators having the first-mode resonant frequency of 5–20MHz are designed and fabricated from a silicon-on-insulator (SOI) wafer, and their vibration characteristics in a vacuum environment are measured by a network analyzer. From the comparison with the measured resonant frequency of each Si mechanical resonator, the mean and maximum absolute percentage errors of the semi-empirical calculation are 28.6 and 51.3%, respectively, which are not negligible errors for the feasibility study. The fabricated Si mechanical resonators are different from an ideal clamped–clamped beam due to undercuts of the insulator layer under the anchors. The resonant frequency of each Si mechanical resonator is analyzed by the FEA model taking into account the effect of the undercuts. The mean and maximum absolute percentage errors of the FEA results from the measured ones are reduced to 9.61 and 19.9%, respectively. These results show that the large errors of the semi-empirical calculation are mainly caused by the undercuts, i.e., flexural stiffness degradation at both clamped ends. Under the condition that the FEA results obtained from FEA models precisely imitating actual geometry and boundary condition are used in the semi-empirical calculation, this is adequately applicable to the feasibility study for developing the Si mechanical resonator with a variable cross section.

Finite element modeling of cold-formed steel channels with solid and slotted webs in shear

This paper presents finite element models of cold-formed steel channels with solid and slotted webs subjected to shear. The models were created in ANSYS and validated against test data. The effects of boundary conditions on the elastic shear buckling load and the ultimate shear strength were numerically investigated on the models with the test setup and realistic boundary conditions. The obtained results showed that the elastic shear buckling loads and the ultimate shear strengths of the slotted channels were affected considerably more by the boundary conditions when compared with the solid channels. Therefore, the actual boundary conditions should be considered in further parametric studies of the slotted channels.

Numerical simulation and experimental verification of heating performance of an integrally water-heated tool

Design and manufacturing of composite tooling are crucial in producing cost effective composite components with high quality. Aimed at identifying the optimal design of integrally heated tools in terms of their thermal performance, a number of design variables were investigated numerically in a previous study. Statistical analysis of the simulation results revealed that a parallel layout of heating channels can significantly improve the heating performance, and channel separation should be determined according to the production requirement. In the present work, an integrally water-heated tool is manufactured according to the optimal design after some geometry amendments. Thermal properties of the constituent materials of the produced tool are also measured. A numerical model of the tool geometry is simulated with actual material properties and boundary conditions to calculate the response variables of temperature uniformity and heating rate. The numerical results are verified by experimental testing, using a thermal camera and thermocouples. Good agreement between the simulation and the experimental results confirmed the suitability of numerical simulation in predicting the thermal performance of integrally heated tooling and the validity of the boundary conditions.

New method for solving the bending problem of rectangular plates with mixed boundary conditions

A new method is used to solve the rectangular plate bending problem with mixed boundary conditions. The method overcomes the complicated derivation of the classical solution by Fourth-order differential problem into integrating question. Under uniform loading rectangular plate bending problem with one side fixed the opposite side half simply supported half fixed the other two sides free rectangular plate, one side simply supported the opposite side half simply supported half fixed the other two sides free rectangular plate is systematically solved. According to the actual boundary conditions of the rectangular plate, the corresponding characteristic equation can easily be set up. It is presented deflection curve equation and the numerical calculation. By compared the results of the equation to the finite element program, we are able to demonstrate the correctness of the method. So the method not only has certain theoretical value, but also can be directly applied to engineering practice.

Finite element modeling of light propagation in turbid media under illumination of a continuous-wave beam.

Spatially resolved spectroscopy provides a means for measuring the optical properties of biological tissues, based on analytical solutions to diffusion approximation for semi-infinite media under the normal illumination of an infinitely small light beam. The method is, however, prone to error in measurement because the actual boundary condition and light beam often deviate from that used in deriving the analytical solutions. It is therefore important to quantify the effect of different boundary conditions and light beams on spatially resolved diffuse reflectance in order to improve the measurement accuracy of the technique. This research was aimed at using finite element method (FEM) to model light propagation in turbid media, subjected to normal illumination by a continuous-wave beam of infinitely small or finite size. Three types of boundary conditions [i.e., partial current (PCBC), extrapolated (EBC), and zero (ZBC)] were evaluated and compared against Monte Carlo (MC) simulations, since MC could provide accurate fluence rate and diffuse reflectance. The effect of beam size was also investigated. Overall results showed that FEM provided results as accurate as those of the analytical method when an appropriate boundary condition was applied. ZBC did not give satisfactory results in most cases. FEM-PCBC yielded a better fluence rate at the boundary than did FEM-EBC, while they were almost identical in predicting diffuse reflectance. Results further showed that FEM coupled with EBC effectively simulated spatially resolved diffuse reflectance under the illumination of a finite size beam. A large beam introduced more error, especially within the region of illumination. Research also confirmed an earlier finding that a light beam of less than 1 mm diameter should be used for estimation of optical parameters. FEM is effective for modeling light propagation in biological tissues and can be used for improving the optical property measurement by the spatially resolved technique.

New equivalent parameters for thermal characterization of opaque building envelope components under dynamic conditions

As reported in the scientific literature and mentioned in building energy performance legislation, the thermal inertia of the opaque building envelope can have a significant positive impact on the reduction of summer indoor overheating, of space cooling peak load and of electricity consumption.At the early stages of the envelope design, there is a need to use simplified as well as effective parameters to correctly characterize the thermal performance of the opaque envelope under dynamic conditions.In this work, a new methodology to describe the dynamic thermal behavior of opaque components is proposed. The approach is based on the harmonic parameters specified in ISO 13786 but it also takes into account realistic boundary conditions for different orientations and solar absorptance values. New equivalent thermal parameters are determined by means of dynamic simulations. The use of these parameters to assess the conduction heat flow rate by means of a simplified model is validated through a comparison with the results of a dynamic simulation.The method presented in the article represents an improvement with respect to the parameters usually applied at the early design stage to thermally characterize the opaque envelope of the building under dynamic conditions. In fact, it allows simplified but reliable performance parameters referring to actual boundary conditions to be obtained. The application potential of the proposed methodology lies in the drawing-up of catalogues and technical standards that supply the values of the new equivalent thermal parameters for different technical solutions.

Manufacturing error sensitivity analysis and optimal design method of cable-network antenna structures

Inevitable manufacturing errors and inconsistency between assumed and actual boundary conditions can affect the shape precision and cable tensions of a cable-network antenna, and even result in failure of the structure in service. In this paper, an analytical sensitivity analysis method of the shape precision and cable tensions with respect to the parameters carrying uncertainty was studied. Based on the sensitivity analysis, an optimal design procedure was proposed to alleviate the effects of the parameters that carry uncertainty. The validity of the calculated sensitivities is examined by those computed by a finite difference method. Comparison with a traditional design method shows that the presented design procedure can remarkably reduce the influence of the uncertainties on the antenna performance. Moreover, the results suggest that especially slender front net cables, thick tension ties, relatively slender boundary cables and high tension level can improve the ability of cable-network antenna structures to resist the effects of the uncertainties on the antenna performance.

Evaluation of the free–free resonant frequency method to determine stiffness moduli of cement-treated soil

The objective of this research is to validate the free–free resonant frequency method and its interpretation to determine the small-strain stiffness moduli of cement-treated soil. In this testing method, a cylindrical soil specimen is laid on top of a soft foam layer to approach fully free boundary conditions. Next, an accelerometer is placed in contact with one end of the specimen to measure vibrations, while the other end is impacted with a light hammer. Then, the small-strain moduli can be evaluated from the density, the dimensions and the fundamental frequency of the vibrations. Factors that could affect the interpretation include the actual boundary conditions of the sample, the interference of the accelerometer on the vibrational response of the sample and the aspect ratio of the sample given by the ratio diameter to length. In order to verify the reliability of the measurements, the free–free resonant frequency method was compared with a more robust technique like the laser Doppler vibrometer. Furthermore, the impact of the sample’s aspect ratio was investigated through a numerical modal analysis from which correction factors were also proposed to improve the reliability of the interpretations.