Arbitrary Material Properties Research Articles

Analysis of MRI antenna loaded by an elliptical subject

AbstractPreviously, the authors developed a computer code for obtaining the current distribution on the MRI antenna loaded by a man model with an arbitrary geometry and material properties by incorporating the impedance method into Richmond's method. By this method, the relation between the position of the feeding point and the sensitivity of the 1.5 T‐MRI antenna loaded by an elliptic cylindrical subject is discussed theoretically. It is found that the sensitivity of the antenna fed at the angle of 45 degrees measured from the minor axis of the ellipsoid of the subject is different from that of the antenna fed at the angle of ‐ 45 degrees because the elliptic polarization is produced inside the antenna.

A finite-element analysis of electromagnetic scattering from a moving dielectric cylinder of arbitrary cross section

This paper deals with the electromagnetic scattering of a plane wave obliquely incident on an infinite penetrable cylinder in uniform motion with velocity v along its axis. The analysis is carried out by means of a hybrid technique, which combines the finite-element method and the well-known modal expansion of a field scattered by cylindrical structures. The method presented allows for analysis of moving cylinders of arbitrary cross section and material properties.

A bounded beam solution for the pulse-echo transducer response of an arbitrary on-axis scatterer in a fluid

A model is formulated for the ultrasonic response of a scatterer in a fluid that lies on the axis of a transducer, where the transducer acts as both a sender and receiver of ultrasonic waves (pulse-echo setup). The transducer is modelled as a uniform velocity (piston) source and the scatterer can have arbitrary shape and material properties. Using a superposition of plane waves to form the bounded beam generated by the transducer, the T-matrix formalism to handle the scattering process exactly, and a combination of coordinate transformations and high frequency asymptotics, explicit analytical expressions are derived for the measured ultrasonic response. Experiments made for the response of an on-axis sphere show excellent agreement with the theory even in the near-field of the transducer.

Use of a human‐body simulator for analysis of MRI antennas

AbstractOptimization of an antenna for magnetic resonance imaging (MRI) requires an accurate analysis of antennas loaded by a human body. We have developed a computer code for obtaining the current distribution on the antenna loaded by a human model with an arbitrary geometry and material properties by incorporating the impedance method into the Richmond method. Numerical results for the input impedance are compared with measured impedances confirning the validity of the proposed method. Furthermore, sensitivity. distributions of antennas loaded by a human model are calculated.

Finite element analysis of electromagnetic scattering from periodic cylindrical structures at oblique incidence

A hybrid technique which combines the finite element method (FEM) and an expansion of the field in terms of Floquet modes is presented for the analysis of the scattering from, and the transmission through, penetrable periodic cylindrical structures, at skew incidence. The method is very flexible and allows the analysis of practical cylindrical configurations with arbitrary cross-section and material properties.

Hybrid technique for analysing scattering from periodic structures

A hybrid technique which utilises the finite element method (FEM) and an expansion of the field in terms of the Floquet modes is presented for the analysis of the scattering from and through periodic structures, having arbitrary geometry, material properties and periodicity with respect to the wavelength. This formulation can play an important role in validating approximate methods and in the analysis of the interaction of an electromagnetic wave with complex periodic structures. The periodic boundary conditions which are imposed for applying the FEM procedure are discussed in detail. Numerical results for both TEZ and TMZ scattering are presented.

Joined dissimilar thin elastic tubes containing steady perfect flow

Two tubes of circular cross-section and of the same radius initially, but composed of different elastic materials, are joined together to form a single straight tube with discontinuous properties. Stretching in the axial direction causes radial displacement that varies along the length of the tube. In a perfect inviscid incompressible flow through the tube of variable cross-section the internal pressure varies as described by Bernoulli's equation, and the variable pressure also causes variation of the radial displacement. The equations of coupled finite deformation and fluid pressure problem can be integrated explicitly (using membrane theory for the tube) for arbitrary material properties, but determination of the integration constants is not trivial. The results are interpreted numerically for Mooney materials. Also considered in this context is the similar problem where two semi-infinite cylindrical membranes of the same material are separated by a cuff of different material. Numerical illustrations are obtained for various upstream velocities. The results obtained here thus solve the problem of steady internal pressure loading of this type in extended dissimilar thin isotropic tubes. The tube will become unstable if the fluid velocity is too large. Applications to engineering structures are possible.

On Interface Crack Growth in Composite Plates

Analysis of fracture growth, and in particular at interfaces, is pertinent not only to load-carrying members in composite structures but also as regards, e.g., adhesive joints, thin films, and coatings. Ordinarily linear fracture mechanics then constitutes the common tool to solve two-dimensional problems occasionally based on beam theory. In the present more general effort, an analysis is first carried out for determination of the energy release rate at general loading of multilayered plates with local crack advance either at interfaces or parallel to such. The procedure is accomplished for arbitrary hyperelastic material properties within von Karman plate theory and the results are expressed by aid of an Eshelby energy momentum tensor. By a feasible superposition it is then shown that the original nonlinear plate problem may be reduced to that of an equivalent beam in case of linear material properties. As a consequence of the so-established principle, the magnitude of mode-dependent singular stress amplitude factors is then directly determinable from earlier two-dimensional linear beam solutions for isotropic and anisotropic bimaterials and relevant at determination of cohesive and adhesive fracture. The procedure is illustrated by an analysis of combined buckling and crack growth of a delaminated plate having a nontrivial crack contour.

Wave interaction with rubble toe protection

A model is formulated to predict wave-induced flows and pressures in rubble toes fronting a seawall or caisson. The model is based on the linearized Forchheimer equation of fluid motion in the coarse, granular medium. The toe may be a multilayered rubble mound with arbitrary material properties and cross-section. The waves are taken to be simple periodic and normally incident to the structure. The boundary value problem is solved using a hybrid solution technique which employs the boundary element method within the rubble toe and near field matched with an analytical far field solution. Results indicate that the reflection coefficient is inversely related to the size and dissipation of the rubble toe and that long waves are more highly reflected. The presence of the rubble toe may result in wave pressures on the seawall greater than if no toe was present. This yields a corresponding increase in the wave-induced forces and mud line moments. The force may be increased by as much as 20%. The theory was verified by large-scale experiments. The comparison between theoretical and experimental results of the reflection coefficient and the dynamic pressure inside the rubble toe are in reasonable agreement.

Adhesive processing by electromagnetic irradiation

AbstractA mathematical model is presented which describes the degree of cure in a thermosetting adhesive used to bond sheet molding compound (SMC) components. The model allows computer aided optimization of the thermosetting process for any type of electromagnetic heating of the various layers of the structure (e.g. dielectric, microwave or induction), arbitrary material properties and arbitrary layer thickness. Computer simulated results are given for the particular case when the cure of the thermosetting material is initiated by its exposure to a high‐power radio‐frequency electric field (dielectric heating). These results indicate a strong sensitivity of the process to the thickness of the adhesive layer and the degree of coupling with the electromagnetic field. The analysis demonstrates that substantial heat losses from the relatively thin adhesive layer to the structural members of the joint by diffusive heat flow can be counterbalanced by additional electric power dissipated either in the adhesive or the structural members of the joint. Although derived for dielectric heating, those results are general, being independent of the type of electromagnetic heating employed.

Tubesheet Analysis—A Proposed ASME Design Procedure

A simplified design procedure is presented to determine tubesheet thickness in U-tube, floating-head, and fixed-tubesheet shell-and-tube exchangers. The procedure is based on classical plate-and-shell theory and permits a design code-oriented manual solution procedure. The configuration analyzed includes an unperforated rim, three different tubesheet head-shell-joint configurations, and arbitrary material properties for each component. Thermal loading due to differential radial expansion and the effect of local pressures acting on the head and shell walls are included.

Quantification of Saint-Venant's principle for a general prismatic member

A method to quantify Saint-Venant's principle for general prismatic members is described. Finite elements are used to model the member cross-section to allow the analysis of arbitrary geometries, material properties, and nonhomogeneities. The variation in the structural response along the member's length, away from the loaded end, is modelled with an exponential decay which has been established in the literature to be the correct form. Many analytic results exist in the literature for special cases. Because of its ability to handle arbitrary cross sectional geometries, this semi-analytic finite element method can provide a firm footing for the utilization of Saint-Venant's principle for whole new classes of problems. Results for several typical problems are given.

Analysis and design of multiple-beam appliances

A new approach for the analysis of multiple-beam structures, such as headgear bows, is developed for beams which contain arbitrary curvatures, twists, and material properties. The generalized transfer matrix of a single-beam analysis is converted to a stiffness matrix and inserted into a global matrix which describes the entire system. The effect of inner bow wire size (0.044 inch and 0.051 inch) on the force system is demonstrated. The inner bow with the larger cross section shows only a slight (not clinically significant) reduction in rotational moment and buccal force applied because of its greater ability to resist deformation during the loading process. Small amounts of tooth and/or tube rotations ("play") result in a significant reduction of the crown rotational moment. With increasing rotation of the tube to the inner bow, the high lateral forces and large moments found about the long axis of the teeth are found to reduce. Symmetrical headgears are chosen to illustrate the analysis and to indicate the manner in which this approach may be used to study and design similar orthodontic appliances.

Inelastic Tangential Stiffness for 2‐D Frames

A general instantaneous or tangential stiffness matrix for a plane frame member is presented. Expressions in the form of integral equations are developed for members having axial forces and arbitrary material properties, distributed loads and moment-axial force-curvature relations. The expressions are used for w sections of elasto-plastic material and several examples of plane frames are loaded to failure. Experimental results reported in the literature for plane frames tested to inelastic failure are closely matched by the analytical technique.

Random incidence energy transmission of bending waves at junctions

This paper describes analytical expressions and numerical results for the random incidence transmission efficiencies of bending wave at typical types of junctions. Analyzed junctions are formed by semi-infinite flat plates, perpendicularly intersecting with each other, for which arbitrary plate thickness and material property are permitted. To obtain a basic formula of transmission efficiency, the analysis for oblique incidence energy transmission at the cross-type junction is carried out, and the total transmission efficiency is expressed by the sum of partial transmission efficiencies among the incident and each transmitting plates. The above basic formula can utilize for other types of junctions, L and T types, by omitting some arguments in the formula, corresponding to each junction. As numerical examples, the transmission and the reflection losses for oblique incidence at each incident angle are calculated for L-, T-, and X-type junctions as a function of the plate thickness ratio, and the average transmission loss for each type junction is obtained from the results of oblique incidence. These calculated average transmission losses for L, T, and X types completely agree with the Cremer's results for the case when plate thickness ratio is unity, and increases around 2–4 dB more than that in the normal incidence over the same range of thickness ratio.

Vibrations of segmented beams by a fourier series component mode method

The fundamental nature of the component mode method, based on Fourier series, is examined and applied to a wide variety of non-uniform beam vibration problems. It is shown that a single segment guided-guided beam, coupled with a sine series approach is sufficient to derive an exact master frequency determinant for a general multi-segmented beam with arbitrary material and geometric properties in each segment and general boundary conditions at the ends. Similarly, a single segment simply-supported beam, coupled with a cosine series approach is also sufficient to derive an exact master frequency determinant for the general multi-segment beam problem. The method requires special treatment (via Stokes' transformation) at the end points of each component, while continuity between components is enforced with Lagrange multipliers. Results are shown for non-uniform beams including the effects of intermediate masses and springs.

LASAB - Laser Activated Spot Adhesive Bond - Analysis and Experimental Verification

Abstract A new material bonding technique utilizing a C02 laser and thermally-activated adhesives is proposed for the assembly of similar as well as dissimilar materials where time is crucial and global thermomechanical hazard intolerable. Computerized numerical analysis is presented for the pertinent time transient heat transfer problem with arbitrary material properties and boundary conditions. Bond strength results as well as qualitative and quantitative experimental experiences are discussed.

Use of surface-integral equations for the analysis of the TE-induction problem

A surface-integral-equations approach for the analysis of the linear transverse-electric (TE) induction problem at an arbitrary frequency is presented. It parallels an earlier analysis of the TM induction problem, and uses Helmholtz potentials to derive integral equations correlating the surface values of the tangential current density and axial magnetic field. Two Fredholm integral equations with weakly singular kernels reduce to a single equation for a quasistatic magnetic field. The present approach reduces the dimensions of the numerical problem by one, and is valid for arbitrary cross-sectional shapes, arbitrary material properties and arbitrary frequencies. It is free of the limitations of the separation of variables method used in the low-frequency range and perfect-conductor analysis used in the high-frequency range. It is an exact dual of the TM analysis. This approach is used to compute the power loss over the whole frequency range for a rectangular conducting cylinder placed normal to an H-wave. It is shown that, in the low-frequency range, the surface charges have no appreciable effect on the power loss.

Automatic Design of Shell Structures

A computer-oriented method for the design of a large class of shell structures is presented. The numerical approach is modeled after an experimental technique used to determine shapes for shell structures. In the experimental procedure, the shell geometry is obtained by loading a flexible membrane. The numerical method presented replaces the costly and time-consuming experimental approach with an efficient digital computer program. A finite element formulation of the problem of large displacement in membrane shells is used to determine the equilibrium configuration for the flexible membranes. The approach is general and can be applied to the design of shells having arbitrary geometry, material properties, thickness and boundary conditions. The method is applied to the design of roof structures, arch dams, storage tanks and a tubular joint. Evaluation of the stresses in these structures indicates that the use of membrane shapes represents a rational approach to the design of many civil engineering shell structures.

Closure to “Discussion of ‘A General Solution for the Elastoplastic Thermal Stresses in a Strain-Hardening Plate With Arbitrary Material Properties’” (1962, ASME J. Appl. Mech., 29, p. 762)

Closure to “Discussion of ‘A General Solution for the Elastoplastic Thermal Stresses in a Strain-Hardening Plate With Arbitrary Material Properties’” (1962, ASME J. Appl. Mech., 29, p. 762)