scholarly journals On 3D Anticrack Problem of Thermoelectroelasticity

2018 ◽  
Vol 12 (2) ◽  
pp. 109-114 ◽  
Author(s):  
Andrzej Kaczyński
Keyword(s):  
Arbitrary Shape ◽  
Closed Form Solution ◽  
Transversely Isotropic ◽  
Static Problem ◽  
Form Solution ◽  
Boundary Integral ◽  
The Body ◽  
Circular Rigid Inclusion ◽  
Stress Discontinuity ◽  
Suitable Potential

Abstract A solution is presented for the static problem of thermoelectroelasticity involving a transversely isotropic space with a heat-insulated rigid sheet-like inclusion (anticrack) located in the isotropy plane. It is assumed that far from this defect the body is in a uniform heat flow perpendicular to the inclusion plane. Besides, considered is the case where the electric potential on the anticrack faces is equal to zero. Accurate results are obtained by constructing suitable potential solutions and reducing the thermoelectromechanical problem to its thermomechanical counterpart. The governing boundary integral equation for a planar anticrack of arbitrary shape is obtained in terms of a normal stress discontinuity. As an illustration, a closed-form solution is given and discussed for a circular rigid inclusion.

On the solution near the critical frequency for an oscillating and translating body in or near a free surface

1993 ◽  
Vol 254 ◽  
pp. 251-266 ◽  
Author(s):  
Yuming Liu ◽  
Dick K. P. Yue
Keyword(s):  
Free Surface ◽  
Closed Form Solution ◽  
Geometric Interpretation ◽  
Form Solution ◽  
The Body ◽  
Geometric Condition ◽  
Sufficient Condition ◽  
Gravitational Acceleration ◽  
Submerged Body ◽  
Necessary And Sufficient

We consider a floating or submerged body in deep water translating parallel to the undisturbed free surface with a steady velocity U while undergoing small oscillations at frequency ω. It is known that for a single source, the solution becomes singular at the resonant frequency given by τ ≡ Uω/g=¼, where g is the gravitational acceleration. In this paper, we show that for a general body, a finite solution exists as τ → ¼ if and only if a certain geometric condition (which depends only on the frequency ω but not on U) is satisfied. For a submerged body, a necessary and sufficient condition is that the body must have non-zero volume. For a surface-piercing body, a sufficient condition is derived which has a geometric interpretation similar to that of John (1950). As an illustration, we provide an analytic (closed-form) solution for the case of a submerged circular cylinder oscillating near τ = ¼. Finally, we identify the underlying difficulties of existing approximate theories and numerical computations near τ = ¼, and offer a simple remedy for the latter.

Calculation of the slowness vector from the ray vector in anisotropic media

2006 ◽  
Vol 462 (2067) ◽  
pp. 883-896 ◽  
Author(s):  
Václav Vavryčuk
Keyword(s):  
Symmetry Plane ◽  
Closed Form Solution ◽  
Transversely Isotropic ◽  
Form Solution ◽  
Polynomial Equations ◽  
Wave Surface ◽  
Wave Fields ◽  
Slowness Vector ◽  
Arbitrary Strength ◽  
Anisotropic Elastic

The wave quantities needed in constructing wave fields propagating in anisotropic elastic media are usually calculated as a function of the slowness vector, or of its direction called the wave normal. In some applications, however, it is desirable to calculate the wave quantities as a function of the ray direction. In this paper, a method of calculating the slowness vector for a specified ray direction is proposed. The method is applicable to general anisotropy of arbitrary strength with arbitrary complex wave surface. The slowness vector is determined by numerically solving a system of multivariate polynomial equations of the sixth order. By solving the equations, we obtain a complete set of slowness vectors corresponding to all wave types and to all branches of the wave surface including the slowness vectors along the acoustic axes. The wave surface can be folded to any degree. The system of equations is further specified for rays shot in the symmetry plane of an orthorhombic medium and for a transversely isotropic medium. The system is decoupled into two polynomial equations of the fourth order for the P –SV waves, and into equations for the SH wave, which yield an explicit closed-form solution. The presented approach is particularly advantageous in constructing ray fields, ray-theoretical Green functions, wavefronts and wave fields in strong anisotropy.

A novel method for defining the Greyhound talocrural joint axis of rotation for hinged transarticular external skeletal fixation

2013 ◽  
Vol 26 (04) ◽  
pp. 298-303 ◽  
Author(s):  
N. R. Hadley ◽  
A. M. Wallace ◽  
G. R. Colborne
Keyword(s):  
Articular Surface ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
The Body ◽  
Transverse Axis ◽  
Talocrural Joint ◽  
Distal Articular Surface ◽  
Intertarsal Joint ◽  
Centre Of Rotation

SummaryIn order to apply hinged transarticular external skeletal fixation for stabilization of the injured canine tarsal joint, knowledge of the three-dimensional (3D) location and orientation of the transverse axis is necessary. This method of immobilization may be used as a primary or adjunctive method of stabilisation for a large number of traumatic conditions. Using pin-mounted markers in the cadaveric Greyhound crus and talus, a closed-form solution of absolute orientation was used to identify, on radiographs, the lateral and medial locations of the transverse axis by tracking the 3D excursions of the markers during flexion and extension. A line was drawn across the dorsal aspect of the calcaneus from the most dorsal point on the distal articular surface (proximal intertarsal joint: PIJ) to the most dorsal point on its proximal articulation with the body of the talus, and the location of the centre of rotation was expressed in terms of the length of that line. In seven Greyhound tarsal joints, the medial end of the axis was located 73 ± 10% proximal to the PIJ and 11 ± 7% dorsal to the line. The lateral end was 73 ± 9% proximal to the PIJ and -2 ± 3% plantar to the line.

Exact solutions for the macro-, meso- and micro-scale analysis of composite laminates and sandwich structures

2018 ◽  
Vol 52 (22) ◽  
pp. 3109-3124 ◽  
Author(s):  
Yang Yan ◽  
Alfonso Pagani ◽  
Erasmo Carrera ◽  
Qingwen Ren
Keyword(s):  
Composite Laminates ◽  
Computational Cost ◽  
Three Dimensional ◽  
Sandwich Beam ◽  
Closed Form Solution ◽  
Single Layer ◽  
Transversely Isotropic ◽  
Global Scale ◽  
Form Solution ◽  
Lagrange Polynomials

The present work proposes a closed-form solution based on refined beam theories for the static analysis of fiber-reinforced composite and sandwich beams under simply supported boundary conditions. The higher-order beam models are developed by employing Carrera Unified Formulation, which uses Lagrange-polynomials expansions to approximate the kinematic field over the cross section. The proposed methodology allows to carry out analysis of composite structure analysis through a single formulation in global-local sense, i.e. homogenized laminates at a global scale and fiber-matrix constituents at a local scale, leading to component-wise analysis. Therefore, three-dimensional stress/displacement fields at different scales can be successfully detected by increasing the order of Lagrange polynomials opportunely. The governing equations are derived in a strong-form and solved in a Navier-type sense. Three benchmark numerical assessments are carried out on a single-layer transversely isotropic beam, a cross-ply laminate [Formula: see text] beam and a sandwich beam. The results show that accurate displacement and stress values can be obtained in different parts of the structure with lower computational cost in comparison with traditional, enhanced as well as three-dimensional finite element methods. Besides, this study may serve as benchmarks for future assessments in this field.

scholarly journals Enhancing the electrical and thermal conductivities of polymer composites via curvilinear fibers: An analytical study

2019 ◽  
Vol 24 (10) ◽  
pp. 3231-3253 ◽  
Author(s):  
Marco Salviato ◽  
Sean E Phenisee
Keyword(s):  
Closed Form ◽  
Electric Conductivity ◽  
Electrostatic Potential ◽  
Mechanical Performance ◽  
Transverse Isotropy ◽  
Closed Form Solution ◽  
Transversely Isotropic ◽  
Form Solution ◽  
Closed Form Expression ◽  
Element Analysis

The new generation of manufacturing technologies such as additive manufacturing and automated fiber placement has enabled the development of material systems with desired functional and mechanical properties via particular designs of inhomogeneities and their mesostructural arrangement. Among these systems, particularly interesting are materials exhibiting curvilinear transverse isotropy (CTI), in which the inhomogeneities take the form of continuous fibers following curvilinear paths designed to, for example, optimize the electric and thermal conductivity, and the mechanical performance of the system. In this context, the present work proposes a general framework for the exact, closed-form solution of electrostatic problems in materials featuring CTI. First, the general equations for the fiber paths that optimize the electric conductivity are derived, leveraging a proper conformal coordinate system. Then, the continuity equation for the curvilinear transversely isotropic system is derived in terms of electrostatic potential. A general exact, closed-form expression for the electrostatic potential and electric field is derived and validated by finite element analysis. Finally, potential avenues for the development of materials with superior electric conductivity and damage sensing capabilities are discussed.

Inviscid reacting flow near a stagnation point

1969 ◽  
Vol 35 (4) ◽  
pp. 799-813 ◽  
Author(s):  
Raul Conti ◽  
Milton Van Dyke
Keyword(s):  
Stagnation Point ◽  
Closed Form Solution ◽  
Molecular Transport ◽  
Basic Structure ◽  
Reaction Rates ◽  
Form Solution ◽  
The Body ◽  
Reacting Flow ◽  
Reaction Parameter ◽  
History Of

A reacting flow free of molecular transport exhibits noteworthy behaviour in the neighbourhood of a blunt, symmetrical stagnation point. A local analytical study using the Lighthill-Freeman gas model reveals the basic structure of such a flow. Chemical activity is found to affect some, but not all, of the local characteristics of the flow. Unaffected are the pressure and velocity fields near the stagnation point, where the pressure varies quadratically and the velocity varies linearly as in an inert flow. In addition, the stagnation point is found to be in chemical equilibrium for all non-zero reaction rates. On the other hand the density, temperature, and concentration fields are affected by the non-equilibrium reactions. The extent of this effect can be predicted on the basis of a reaction parameter that measures the rate of reaction in terms of the velocity gradient at the stagnation point. A rapidly reacting flow (with reaction parameter greater than unity) approaches the stagnation point with vanishing gradients of density and temperature, whereas a slowly reacting flow approaches with infinite gradients. The flow field is represented mathematically by functions that are regular along the body but non-analytic in the normal direction. Numerical computations support the validity of the local closed-form solution, and provide information on the local effects of the chemical history of the flow.

Stress Concentration Around a Hyperboloidal Notch Under Tension in a Transversely Isotropic Material

1971 ◽  
Vol 38 (1) ◽  
pp. 185-189 ◽  
Author(s):  
W. T. Chen
Keyword(s):  
Stress Concentration ◽  
Tensile Stress ◽  
Isotropic Material ◽  
Tensile Force ◽  
Closed Form Solution ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Form Solution ◽  
Transversely Isotropic Material ◽  
Numerical Examples

An elastic solid is composed of a transversely isotropic material bounded by a single-sheeted hyperboloid of revolution, which is traction free. This solid is subjected to a finite tensile force at infinity. A closed-form solution based upon the potential functions approach is obtained. Numerical examples of the tensile stress at the narrowest section are presented.

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