Finite Element Mathematical Model Research Articles

Susceptibility of Clay Core to Cracks in Rockfill Dams by Finite Element Modeling

The behaviour of the core of rockfill dam with slanting clay core was investigated with the Jebba main dam, Nigeria as a case study. The stress-deformation behavior of the dam was studied using the finite element mathematical modeling technique. The actual fill properties were utilized and two loading scenarios-no water and full reservoir operations-were investigated. At full reservoir, the actual seepage line, as recorded over the years was used. The linear total stress analysis using the finite element method of analysis was employed to analyze the dam section. Following the finite element mathematical modeling and computer simulations of the models, deformations and stresses distributions were determined. The results showed that the observed longitudinal cracks at the Jebba main dam crest are as a result of potential cracks in the dam core section. The cracks observed at the crest, from analysis, commenced from the dam’s core upstream face, downstream face and core crest. This may have resulted from probable hydraulic fracturing and tensile stresses developments in these regions. The results also showed likely loss of integrity of core due to cracks. However, total collapse may not be experienced but dam performance may be impaired and alarming visible cracks may not be ruled out over time.

ESTIMATION OF PARAMETERS OF A TANK WAGON FOR RAILWAYS OF INDIA

On the basis of the developed design documentation a tank-car structure finite element mathematical model is created, and the analysis of stresses in elements of frameless tank-car for oil transportation on the Indian railways at various operational loading is carried out. The results of calculations are compared with the data of prototype tests.

Study of Ocular Transport of Drugs Released from an Intravitreal Implant Using Magnetic Resonance Imaging

Ensuring optimum delivery of therapeutic agents in the eye requires detailed information about the transport mechanisms and elimination pathways available. This knowledge can guide the development of new drug delivery devices. In this study, we investigated the movement of a drug surrogate, Gd-DTPA (Magnevist) released from a polymer-based implant in rabbit vitreous using T1-weighted magnetic resonance imaging (MRI). Intensity values in the MRI data were converted to concentration by comparison with calibration samples. Concentration profiles approaching pseudosteady state showed gradients from the implant toward the retinal surface, suggesting that diffusion was occurring into the retinal-choroidal-scleral (RCS) membrane. Gd-DTPA concentration varied from high values near the implant to lower values distal to the implant. Such regional concentration differences throughout the vitreous may have clinical significance when attempting to treat ubiquitous eye diseases using a single positional implant. We developed a finite element mathematical model of the rabbit eye and compared the MRI experimental concentration data with simulation concentration profiles. The model utilized a diffusion coefficient of Gd-DTPA in the vitreous of 2.8 x 10(-6) cm2 s(-1) and yielded a diffusion coefficient for Gd-DTPA through the simulated composite posterior membrane (representing the retina-choroidsclera membrane) of 6.0 x 10(-8) cm2 s(-1). Since the model membrane was 0.03-cm thick, this resulted in an effective membrane permeability of 2.0 x 10(-6) cm s(-1). Convective movement of Gd-DTPA was shown to have minimal effect on the concentration profiles since the Peclet number was 0.09 for this system.

Sensitivity Analysis of a Microslip Friction Model

Real physical systems subjected to dynamic environments all display nonlinear behavior, yet they are most frequently modeled in a linear framework. The main reasons are, first, that it is convenient and efficient to solve linear equations, and second, that the system behavior can often be accurately approximated using linear governing equations. Experience shows that much of the nonlinearity of system behavior arises from the dynamic action of mechanical joints in systems. When the linear framework is used, the stiffness of joints is modeled as linear, and the damping is modeled as linear and viscous. To model mechanical joints otherwise requires a nonlinear framework and mathematical finite element model that accommodates transient time domain analysis. This study investigates a particular mechanical joint energy dissipation model: the Iwan model for energy dissipation caused by microslip friction. The sensitivity of energy dissipation in a system due to variation of model parameters is studied. The results of a combined numerical/experimental example that uses a model calibrated to a sequence of experiments are presented.

Constitutive data and friction measurements of powders using instrumented die

An instrumented die has been developed to measure friction and constitutive data on powders during compaction. Such data is useful for quality assurance and as input data for computer models of die compaction. The measurement system consists of a die with radial stress sensors, punch force measurement, and a displacement transducer to measure punch displacement. The outputs of these sensors enable simultaneous measurement of density, die wall friction coefficient, and the triaxial stresses acting on the powder during the course of compaction.The die system has been tested at three industrial sites on automated and manual presses measuring ferrous, ceramic, and tungsten carbide powders at applied stresses of up to 650 MPa and speeds of up to 26 mm s-1. Sensor outputs were sufficiently noise free to permit the recording of useful data down to stresses less than 1 MPa. Typically the run to run reproducibility of friction coefficients was better than ± 0·005, depending on the type of powder and the applied stress. Variations in constitutive data were usually better than ± 4%, again depending on material and the stress. Die wall friction coefficients are found generally to decrease with increasing density and stress.It has been possible to discriminate between different grades and batches of the same material using the frictional and constitutive data. Constitutive data for all types of powder can be accurately represented by an analytical relationship involving four adjustable parameters. This parametric form of data is suitable as input to finite element mathematical models.

A two-dimensional computational model to simulate suspended sediment transport and bed changes

This article presents a two-dimensional finite element mathematical model to simulate suspended sediment transport in coastal regions. Sediment transport is formulated in terms of a hydrodynamic model plus a convection- diffusion equation with source and sink terms representing the erosion and deposition processes. Test problems treating the evolution of a hypothetical dredged trench in a channel, perpendicular to the main flow direction, are used to evaluate the sensitivity of the model to empirical parameters. The model was calibrated, validated and later applied to predict the circulation patterns and bottom bed evolution in Puerto Miranda oil terminal, located in the Maracaibo Strait, Venezuela. Results show that the model is able to predict the bed evolution of the dredged access channels to the terminal. Notwithstanding the complexity of the sediment transport phenomena that occur in dredged trenches, the relatively simple model proposed herein is capable of giving useful results in practical problems.

Study on the influence of thermal stress in the firing of a ceramic body

Considering the thermophysical and mechanical parameters tested, a three-dimensional finite element mathematical model of the temperature and thermal stress fields in the firing of ceramic bodies, and the surface temperature field measured by infrared thermal imaging under the first boundary condition, the influence of thermal stress on the firing of ceramic body is studied in this paper. © 1999 Scripta Technica, Heat Trans Asian Res, 28(7): 620–625, 1999

Study on the influence of thermal stress in the firing of a ceramic body

Considering the thermophysical and mechanical parameters tested, a three-dimensional finite element mathematical model of the temperature and thermal stress fields in the firing of ceramic bodies, and the surface temperature field measured by infrared thermal imaging under the first boundary condition, the influence of thermal stress on the firing of ceramic body is studied in this paper. © 1999 Scripta Technica, Heat Trans Asian Res, 28(7): 620–625, 1999

Study on the influence of thermal stress in the firing of a ceramic body

Considering the thermophysical and mechanical parameters tested, a three-dimensional finite element mathematical model of the temperature and thermal stress fields in the firing of ceramic bodies, and the surface temperature field measured by infrared thermal imaging under the first boundary condition, the influence of thermal stress on the firing of ceramic body is studied in this paper. © 1999 Scripta Technica, Heat Trans Asian Res, 28(7): 620–625, 1999

Growth of lithium triborate crystals. I. Mathematical model

A finite element mathematical model for the top seeded solution growth of Li 2O·3B 2O 3 (LBO) crystals, grown from a melt containing the flux MoO 3, is presented. The model is used to calculate the thermal fields and fluid flow in the melt during growth. The thermal boundary conditions used in the model are estimated from temperature measurements made in the melt. The phase diagram of the LBO MoO 3 system is determined experimentally using differential thermal analysis. The physical parameters required in the model are obtained from the literature, when available. Values of the melt viscosity, as a function of the MoO 3 concentration, are determined experimentally. The temperature fields and fluid flow in the melt, particularly below the growing crystal, are calculated for a range of crystal rotations, crucible rotations, crucible sizes, and melt viscosities. The results show that the most effective means of producing fluid flow in this system is by crucible rotation. Fluid flow immediately below the crystal interface determines the movement of the MoO 3 flux rejected by the crystal, away from the interface. This flow is primarily dependent on crucible rotation. If the concentration of MoO 3 at the interface reaches the eutectic composition, MoO 3-rich phases form, terminating the growth of a satisfactory quality LBO crystal.

A finite-element facial model for simulating plastic surgery.

CAPS (Computer-Aided Plastic Surgery) is a prototype computer program that uses a three-dimensional graphic model of a human face and incorporates a finite-element mathematical model of the physical properties of the soft tissue. This program can estimate the biomechanic consequences of ablation and rearrangement of tissue. The results of two hypothetical surgeries on the face are presented: A surgeon could use this program as a sketch pad to predict and compare the outcome of facial plastic procedures on a patient-specific model. The relation of this program to previous work is discussed, and directions for research and possible applications are addressed.

52732 X-ray and acoustic measurements yield stiffnesses : Madras, E.I.; Kline, R.A. Journal of the Acoustical Society of America, Vol. 93, No. 6, pp. 3522–3523 (Jun. 1993)

Analytical technique combines ultrasonic scanning measurements of local velocity of sound in specimen of material with x-ray computed tomographic measurements of local mass density to compute local stiffness of material. Stiffnesses at various locations in specimen then used in finite-element mathematical model of elastic behavior of specimen to compute local stresses, local strains, and overall deformations. Technique enhances value of quantitative nondestructive x-ray and ultrasonic measurements. Especially useful in characterization of carbon/carbon composites and other advanced materials not homogeneous and for which customary simplifying assumption of constant density and/or constant stiffness not valid.

X-ray and acoustic measurements yield stiffnesses

Analytical technique combines ultrasonic scanning measurements of local velocity of sound in specimen of material with x-ray computed tomographic measurements of local mass density to compute local stiffness of material. Stiffnesses at various locations in specimen then used in finite-element mathematical model of elastic behavior of specimen to compute local stresses, local strains, and overall deformations. Technique enhances value of quantitative nondestructive x-ray and ultrasonic measurements. Especially useful in characterization of carbon/carbon composites and other advanced materials not homogeneous and for which customary simplifying assumption of constant density and/or constant stiffness not valid.

Conductivity mapping to determine interwell fluid saturation

Experimental work indicated that the concept of the focused current logging tool can be extended to well-to-well potential measurements to determine the interwell fluid saturation distribution. A model reservoir 8 ft in diameter with 20 in. of sand between two layers of shale was saturated with 80, 000 ppm of sodium chloride. Eleven wells (cased with finemesh plastic) were located throughout the reservoir and a scaled nine-electrode laterolog was used to provide the focused current. Electrical potentials measured at each well were used to map the isopotential lines. The uniform saline solution was then changed at one well by injecting fresh water and isopotential maps of the saturation abnormality were made. Dissipation of the saturation abnormality with respect to time, due to counter-current diffusion, also was tracked. A finite-element mathematical model using Poisson's and Archie's equations was prepared. The exact dimensions of the model reservoir and the experimental input data were used in the computer program. Using these data, the computer program produced maps of isopotential lines which were within 3% accuracy of the measured data. The results indicate that this could be developed into a technique to measure the interwell saturation distribution in reservoirs. It also could be used for location of saturation anomalies and discontinuities, caused by geological structure changes, between wells.

Geochemical modelling in rapidly subsiding basins

Geochemical modelling in rapidly subsiding basins presents some puzzling questions. In trying to clarify them, two African basins related to different domains were studied. The high Tertiary and Quaternary sedimentation rate is a common feature of the two basins. In each of them present heat flow values were computed in different wells on the basis of temperature, stratigraphic and petrophysical data using a one dimensional finite element mathematical model. The resulting distributions show in some cases irregular patterns, which are examined in detail to outline their possible causes. Extrapolation of the present thermal regime to the past generally gives computed maturity values considerably higher than those obtained experimentally. The experimental data include vitrinite reflectance values, Rock-Eval pyrolysis results, sterane and hopane isomerization and sterane aromatization. Hypotheses about thermal history are made in order to explain the areal maturity distribution. They are checked comparing computed maturity values and experimental ones. By combining experimental data and results of the modelling exercise we conclude that the high sedimentation rate, independent of the tectonic domain in which it occurs, can induce noticeable and peculiar thermal anomalies.

A Theory of Substructure Modal Synthesis

A theory is presented for representing the displacements of a substructure finite-element mathematical model with a reduced number of degrees of freedom. A first or second-order approximation is used for the substructure’s modal coordinates associated with significantly larger or smaller eigenvalues than the system eigenvalues of excitation. The derived representations of the substructure displacements are capable of employing any type of substructure natural mode; free-free, cantilever or hybrid mode, and of retaining the dynamic behavior of any frequency range. It is shown that the present representations compute the system eigenvalues of interest with satisfactory accuracy, and it appears that the second-order approximation methods compute the system eigenvalues with greater accuracy than the first-order methods.

Theoretical and experimental study of the Lamb wave eigenmodes of vibration in terms of the transducer thickness-to-width ratio

In order to improve ultrasonic systems, like imagers, it is more probably necessary to get a better understanding of the transducer behavior, rather than refine the associated electronic parts. For the completion of this study of transducer behavior, the mathematical finite element model may be used, and then the transducer vibration may be analyzed at a particular frequency. Here, the simpler method of modal analysis has been chosen, since it gives a clearer physical insight. It is shown that a Lamb waves model describes well the propagating modes along the three principal directions of the transducer. Among these modes, those which resonate along the width W have been observed experimentally. The particular interest in these modes arise from the fact that they induce severe distortions in the acoustic radiation pattern and must therefore be suppressed. Moreover, the modes which resonate along the thickness t must be retained, since their contribution to the radiation pattern is essential. Then an optimal geometry may be found for a transducer operating at a given nominal frequency.

Deflection and stress analysis of a 42-m diam primary mirror of an altazimuth-mounted telescope

Large finite-element mathematical models are developed to calculate the deformations induced by the supports of a 4.2-m aperture 3.2-focal ratio primary mirror of an optical telescope. It is supported axially on three rings of pneumatic cylinders and radially by a system of transverse level weights, an arrangement only possible in a telescope that uses an altazimuth mounting. The stress distributions in the mirror when lifted by a central lifter and when resting on its axial flotation system are shown. A comparison is made between the results using classical flat-plate theory and the finite-element models.

Quantification of bone stresses during remodeling

An experiment to quantitate the effect of compressive stress upon bone remodeling rate was devised. Remodeling herein is described as the renewal process of bone separate from initial formation. A finite element mathematical model of the rabbit calvarium was devised. Actual rabbit calvaria were stressed utilizing a load cell monitored lever type loading device. They were periodically stained with fluorescing bone seeking dyes. Upon necropsy, histologic sections were prepared and the growth rate at known locations in the stressed area was measured by planimetry. Observed bone formation was subdivided into lamellar and fibrous. Lamellar bone formation (remodeling) rate remained above control levels until stresses of approximately 360 psi were reached; above this level remodeling rate fell to or below control. Fibrous bone exhibited higher formation rates which decreased with increasing stress but remained above control. At stresses approaching 1000 psi the technique could not measure formation rates due to the confused fibrous bone formation.

Hydrologic Characteristics and Response of Fractured Till and Clay Confining a Shallow Aquifer

Fractures in glacial till and glaciolacustrine clay were observed in excavations up to 20 ft (6.1 m) in depth and in drill cores at the Whiteshell Nuclear Research Establishment (WNRE) in southeastern Manitoba. The fractures are characteristically coated with carbonate and oxide precipitates, which indicate groundwater movement through the fractures. The fractures impart an effective bulk hydraulic conductivity to the clay–loam till and lacustrine clay, as evidenced by tritium tracer experiments and piezometer responses in the till and clay to pumping of an underlying sandy aquifer.The intergranular hydraulic conductivity of clay–loam till and glaciolacustrine clay in the Interior Plains, as determined from laboratory consolidation test data, is in the range of 2 × 10−10 to 9 × 10−11 ft s−1 (6 × 10−9 to 2.7 × 10−9 cm s−1). The bulk hydraulic conductivity of the fractured clay–loam till at WNRE, as determined from finite-element mathematical modeling, is about 6 × 10−9 ft s−1 (1.8 × 10−7 cm s−1). The model value represents the effective hydraulic conductivity imparted to the till by the fractures.Seven pumping tests, ranging in duration from 8.75 to 120 h were conducted on the sandy aquifer and drawdown data in the aquifer were analyzed to obtain the hydraulic conductivity and storativity of the aquifers.A 32 day pumping test on the aquifer showed that many of the piezometers in the till and clay respond quickly and strongly to the aquifer drawdown, while others show no noticeable response. The responding piezometers intersect open fractures whereas the others do not. Analysis of the piezometer drawdowns during the long-term pumping test using the Neuman and Witherspoon ‘ratio’ method indicates that the rapid piezometer drawdowns in the confining layers can be accounted for by assigning specific storativity values in the range of 1 × 10−5 to 5 × 10−6 ft−1 (3 × 10−5 to 1.5 × 10−5 m−1) to the clay–loam till and lacustrine clay. These values are typical of fractured rock. If intergranular specific storage values are used, the calculated piezometer drawdowns are very small or negligible.