On Some Problems in Transversely Isotropic Elastic Materials

1966 ◽  
Vol 33 (2) ◽  
pp. 347-355 ◽  
Author(s):  
W. T. Chen
Keyword(s):  
Circular Cylinder ◽  
Potential Function ◽  
Closed Form Solution ◽  
Transversely Isotropic ◽  
Static Solution ◽  
Infinite Medium ◽  
Form Solution ◽  
Concentrated Force ◽  
Applied Forces ◽  
Discontinuous Pressure

This paper treats some problems in a homogeneous transversely isotropic elastic material, occupying an infinite space, or an infinitely long circular cylinder. The analysis is based upon the potential function method by Elliott, with the addition of another potential function. The static solution is extended to include quasi-static, or steady-state problems. Closed-form solution is found for the problem of an arbitrarily oriented concentrated force in an infinite medium. The case of discontinuous pressure over an infinitely long circular cylinder is also studied with the aid of a numerical method of integration. The applied forces are assumed to be moving with uniform velocity along the anisotropic direction.

The Axially Loaded Circular Cylinder

1962 ◽  
Vol 29 (2) ◽  
pp. 318-320
Author(s):  
H. D. Conway
Keyword(s):  
Exact Solution ◽  
Fourier Transform ◽  
Circular Cylinder ◽  
Closed Form ◽  
Cross Sections ◽  
Closed Form Solution ◽  
Form Solution ◽  
Concentrated Force ◽  
Transform Method ◽  
Fourier Transform Method

Commencing with Kelvin’s closed-form solution to the problem of a concentrated force acting at a given point in an indefinitely extended solid, a Fourier transform method is used to obtain an exact solution for the case when the force acts along the axis of a circular cylinder. Numerical values are obtained for the maximum direct stress on cross sections at various distances from the force. These are then compared with the corresponding stresses from the solution for an infinitely long strip, and in both cases it is observed that the stresses are practically uniform on cross sections greater than a diameter or width from the point of application of the load.

Potential Flow Solution for Crossflow Impingement of a Slot Jet on a Circular Cylinder

1976 ◽  
Vol 98 (2) ◽  
pp. 249-255 ◽  
Author(s):  
H. Miyazaki ◽  
E. M. Sparrow
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Circular Cylinder ◽  
Potential Flow ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stream Velocity ◽  
Cylinder Surface ◽  
Stagnation Region ◽  
Flow Solution

A closed-form solution has been obtained for the potential flow about a circular cylinder situated in an impinging slot jet. Among other results, the potential flow solution yields the free stream velocity for the boundary layer adjacent to the cylinder surface. A basic feature of the solution is the division of the flow field into subdomains, thereby making it possible to employ harmonic functions that are appropriate to each such subdomain. The boundary conditions on the free streamline and the conditions of continuity between the subdomains are satisfied by a combination of least squares and point matching constraints. Numerical evaluation of the solution was carried out for cylinder diameters greater or equal to the nozzle width and for a range of dimensionless separation distances between the nozzle and the impingement surface. Results are presented for the velocity and pressure distributions on the cylinder surface, for the position of the free streamline, and for the velocity gradients at the stagnation point. The latter serve as input information to the Nusselt number and skin friction expressions that are given by boundary layer theory. Comparisons were made with available experimental results for the pressure distribution, velocity gradient, and Nusselt number, and good agreement was found to prevail in the stagnation region.

scholarly journals Analytical Solution of the Hyperbolic Heat Conduction Equation for Moving Semi-Infinite Medium under the Effect of Time-Dependent Laser Heat Source

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
R. T. Al-Khairy ◽  
Z. M. AL-Ofey
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Heat Conduction Equation ◽  
Closed Form Solution ◽  
Infinite Medium ◽  
Form Solution ◽  
Time Dependent ◽  
Hyperbolic Heat Conduction ◽  
Laser Heat Source

This paper presents an analytical solution of the hyperbolic heat conduction equation for moving semi-infinite medium under the effect of time dependent laser heat source. Laser heating is modeled as an internal heat source, whose capacity is given by while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discussion of solutions for different time characteristics of heat sources capacity (constant, instantaneous, and exponential) is presented. The effect of absorption coefficients on the temperature profiles is examined in detail. It is found that the closed form solution derived from the present study reduces to the previously obtained analytical solution when the medium velocity is set to zero in the closed form solution.

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.

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.

Dynamic Response of Kirchhoff Plate on a Viscoelastic Foundation to Harmonic Circular Loads

2003 ◽  
Vol 70 (4) ◽  
pp. 595-600 ◽  
Author(s):  
L. Sun
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Closed Form Solution ◽  
Static Solution ◽  
Form Solution ◽  
Kirchhoff Plate ◽  
Viscoelastic Foundation ◽  
Hankel Functions ◽  
Circular Load

In this paper Fourier transform is used to derive the analytical solution of a Kirchhoff plate on a viscoelastic foundation subjected to harmonic circular loads. The solution is first given as a convolution of the Green’s function of the plate. Poles of the integrand in the integral representation of the solution are identified for different cases of the foundation damping and the load frequency. The theorem of residue is then utilized to evaluate the generalized integral of the frequency response function. A closed-form solution is obtained in terms of the Bessel and Hankel functions corresponding to the frequency response function of the plate under a harmonic circular load. The result is partially verified by comparing the static solution of a point source obtained in this paper to a well-known result. This analytical representation permits one to construct fast algorithms for parameter identification in pavement nondestructive test.

Hydrodynamic coefficients of a vertical circular cylinder

1990 ◽  
Vol 17 (3) ◽  
pp. 302-310 ◽  
Author(s):  
Michael Isaacson ◽  
Thomas Mathai ◽  
Carol Mihelcic
Keyword(s):  
Circular Cylinder ◽  
High Frequency ◽  
Closed Form Solution ◽  
Added Mass ◽  
Offshore Structures ◽  
Form Solution ◽  
Ocean Engineering ◽  
Radiation Problem ◽  
The Vertical Distribution ◽  
Linear Radiation

The added mass and the damping coefficient of a large surface-piercing circular cylinder extending to the seabed and undergoing horizontal oscillations are described. A closed-form solution to the corresponding linear radiation problem is obtained by the use of eigenfunction expansions. Attention is given to the vertical distribution of these coefficients and to their high-frequency asymptotic behaviour. Comparisons are made with experimental measurements. The application to typical offshore structures is discussed. Key words: added mass, cylinders, damping, hydrodynamics, ocean engineering.

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.

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