Magnetoelastic stresses in a three-phase composite cylinder subject to a uniform magnetic induction

A solution of magnetoelastic stresses on a three-phase composite cylinder subjected to a remote uniform magnetic induction is derived in this study. Based upon the complex variable theory and the method of analytical continuation together with alternating technique, the general expressions of both the magnetic and the magnetoelastic field quantities can be obtained. The variations of the magnetoelastic stress on various parameters are displayed in graphic form. Comparisons between the results of this work and the existing solutions in literature under special cases reveal that the present solution is correct and general.     

An exact analytical solution of the inverse problem for a plasma cylinder expanding in a compressible medium

A strict analytical solution of the wave equation with cylindrical symmetry in a region with mobile boundaries was obtained by the method of inverse problems with allowance for the interaction of nonlinear arguments. The proposed method is universal and applicable to solving both inverse and direct problems for arbitrary values of the initial radius and displacements. The solution describes the near wave field of an expanding plasma piston, including the field formed in the initial moments of a pulsed expansion process. The solution gives exact values of a given pressure and velocity wave profile at a fixed point of the wave zone in the initial moment, as well as particular finite values of the pressure and velocity at a mobile boundary of the expanding plasma piston at the moments of time approaching zero. The solution is obtained with allowance for additional nonlinear conditions.     

An exact solution for an anisotropic plate with an elliptic hole under arbitrary remote uniform moments

The problem of an anisotropic plate containing an elliptic hole subjected to remote bending or twisting moments is considered. In contrast with the previous works on the problem, the requirement that the deflection be a single-valued function is satisfied by introducing a correction constant. An exact solution for general anisotropic materials under arbitrary uniform loading conditions is derived. Explicit expressions for the deflection and moments on the edge of an elliptic hole in an orthotropic plate subjected to bending or twisting moments are obtained. The moment intensity factors as the elliptic hole degenerates into a crack are given.     

A piezoelectric screw dislocation in a three-phase composite cylinder model with an imperfect interface

The electroelastic coupling interaction between a piezoelectric screw dislocation and the embedded circular cross-section inclusions with imperfect interfaces in piezoelectric solids is investigated by using a three-phase composite cylinder model. By means of a complex variable technique, the explicit solutions of electroelastic fields are obtained. With the aid of the Peach-Koehler formula, the explicit expression for the image force exerted on the piezoelectric screw dislocation is derived. The image force on the dislocation and its equilibrium positions near one of the inclusions are discussed for variable parameters (interface imperfection and material electroelastic dissimilarity) and the influence of nearby inclusions is also considered. The results show that when compared with the previous solution (the perfect interface), more equilibrium positions of the screw dislocation in the matrix may be available due to the effect of the interface imperfection when the dislocation is close to the electroelastic stiff inclusion. It is also found that the magnitude of the image force exerted on the piezoelectric screw dislocation produced by multiply inclusions is always smaller than that produced by a single inclusion and the impact of nearby inclusions on the mobility of the screw dislocation is very important.     

Application of the exact solution for scattering by an infinite cylinder to the estimation of scattering by a finite cylinder

A new algorithm for cylindrical Bessel functions that is similar to the one for spherical Bessel functions allows us to compute scattering functions for infinitely long cylinders covering sizes ka = 2πa/λ up to 8000 through the use of only an eight-digit single-precision machine computation. The scattering function and complex extinction coefficient of a finite cylinder that is seen near perpendicular incidence are derived from those of an infinitely long cylinder by the use of Huygens's principle. The result, which contains no arbitrary normalization factor, agrees quite well with analog microwave measurements of both extinction and scattering for such cylinders, even for an aspect ratio p = l/(2a) as low as 2. Rainbows produced by cylinders are similar to those for spherical drops but are brighter and have a lower contrast.     

An analytical solution for the analysis of symmetric composite adhesively bonded joints

Analytical solutions for adhesively bonded balanced composite and metallic joints are presented in this paper. The classical laminate plate theory and adhesive interface constitutive model are employed for this deduction. Both theoretical and numerical (finite element analysis) studies of the balanced joints are conducted to reveal the adhesive peel and shear stresses. The methodology can be extended to the application of various joint configurations, such as single-lap and single-strap joints to name a few. The methodology was used to evaluate stresses in several balanced adhesively bonded metallic and composite joints subjected to the tensile, moment and transverse shear loadings. The results showed good agreements with those obtained through FEM.     

An exact solution for the stress intensity factor for a double cantilever beam

An exact solution for the stress intensity factor for a double cantilever beam (DCB) specimen loaded by opposing point loads has been obtained by the Wiener-Hopf technique. A simple approximate formula is given for the stress intensity factor that is accurate to within 1.1 percent for all crack lengths with a large uncracked ligament.

---

Résumé En utilisant la technique de Wiener-Hopf, on a obtenu une solution exacte pour le facteur d'intensité d'entaille correspondant à une éprouvette en forme de poutre double Cantilever sollicitée par des charges ponctuelles opposées. On a déterminé le facteur d'intensité de contraintes sous forme d'une formulation approchée simple dont la précision est inférieure à 1,1%, pour toute longueur de fissures compatible avec une zone ligament non fissurée d'assez grande dimension.

     

An exact solution for tube and slit flow of a FENE-P fluid

Summary A fully analytical solution is derived for rectilinear flow of a nonlinear viscoelastic fluid obeying the constitituve FENE-P model, under fully developed conditions. Both the plane case (slit flow) and the axisymmetric case (tube flow) are considered. Physical interpretation of the results is provided. The normal stress profile is found to vary in a non-monotone way with the dimensionless parameter characterizing viscoelasticity, the Deborah number (De). For Deborah numbers below a critical value (dependent on the extensibility parameter of the modelL ²) the normal stress raises with elasticity, but this trend is reversed for values above the critical one. This effect is due to the competing influence of elasticity and shear thinning. Also, as a consequence of shear thinning the velocity profile becomes flatter asDe increases andL ² decreases, leading to higher flow rates for the same pressure drop.     

An exact solution of the first-exit time problem for a class of structural systems

The mean time to escape from a region of desired operations is one the basic reliability measures in stochastic dynamics. In general, a precise solution of the first-exit time problem is unavailable. This paper demonstrates an exact solution of the mean exit time problem for a multidimensional non-dissipative Lagrangian system excited by additive Gaussian white noise. We identify the Fokker–Planck equation whose solution characterizes the mean time needed to reach a critical energy and explicitly construct the solution. For illustration, we apply the developed theory to engineering examples. We calculate the mean time of the standard operation for a flexural nanotube with likely noise-induced buckling and analyze the mean time of the stable functioning for a gyroscope subjected to random and dissipation torques. It is demonstrated that the solution of the first-exit time problem for a non-dissipative system gives a quite good approximation to a numerical solution of a similar problem for a system with small dissipation.     

An exact solution to the problem of creeping flow around circular cylinder rotating in presence of translating plane boundary

Summary The problem of determination of steady, plane creeping flow around circular cylinder rotating with constant angular velocity in presence of plane boundary, translating with constant linear velocity — is investigated and solved in the paper by means of aspectral method. The original domain of solution is mapped conformally onto an auxiliary, annular one, wherein flow velocity, pressure, and other components of stress tensor are represented by twoGoursat's functions, which are sought for in form ofLaurent's series provided with the necessary logarithmic terms. It is shown, that all coefficients of these series-except seven-must vanish, if boundary conditions expressing impermeability and absence of slip have to be satisfiedsimultaneously at the cylinder and at the plane boundary. Finally, closed formulae for these coefficients are presented — as depending on two velocities defining the problem, and on three constants of the mapping function. The paper can be considered as a counterpart to a former one [1], wherein the problem was solvednumberically by means of apseudospectral method.Dedicated to Professor Dr.-Ing., Dr. Techn. E. h. J. Zierep on the occasion of his decoration with the Prandtl Ring.     

Three dimensional exact solution of thermal stresses in rectangular composite laminate

Three-dimensional exact solutions for temperature distribution and thermal stresses in simply supported finite rectangular orthotropic laminate subjected to prescribed boundary conditions under combined thermal and mechanical loading, are presented which will be used to check the accuracy of more generalized numerical tools. The numerical results are presented for across-ply 3-layered 0/90/0. composite laminate. The numerical results help to draw the conclusion that the influence of the thermal field on deformations and stress is very predominant and induces high transverse normal stress at the interfaces which may cause the failure of the weak interlayer adhesive bond.     

An exact analytical solution for the position-time relationship for an inverse-distance-squared force

The theory of complex variables is used to solve analytically the transcendental equation which defines the position, as a function of time, in an inverse-distance-squared force field, and thereby the desired solution is reduced to elementary quadrature.     

An analytical solution for long-wave scattering by a submerged circular truncated shoal

An analytical solution of the long-wave (or shallow-water) equation in closed-form is obtained for simple harmonic waves scattered by a submerged circular truncated shoal. This analytical solution is firstly validated against Longuet-Higgins’s classical analytical solution for a submerged cylinder, and then validated against numerical solutions obtained by using the DRBEM (dual reciprocity boundary-element method) model for a submerged circular truncated cone. Finally, the analytical solution is used to investigate the changing trend of maximum wave amplification, the trace pattern of focal position of wave-energy versus the wave period and the influence of shoal submergence on wave-energy trapping.     

Heat exchange between a horizontal cylinder and three-phase fluidized bed

S. M. Kirov Ural Polytechnic Institute, Ekaterinburg. Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 62, No. 2, pp. 180–187, February, 1992.     

An efficient approach for damage quantification in quasi-isotropic composite laminates under low speed impact

An efficient method to determine the type, size, and location of damage in impacted quasi-isotropic composite laminates is presented. The method uses the peak force during impact obtained from energy balance, a Hertzian contact formulation and energy minimization to determine the complete state of stress in the laminate. Comparisons of the analytical predictions to limiting cases of infinite thickness plates or to detailed finite element models for finite thickness plates shows the predicted stresses to be in excellent agreement with other methods. The stresses are then modified to account for the creation of damage and used in out-of-plane and in-plane failure criteria to predict delamination sizes, matrix failure and fiber failure. The predicted damage states are then compared to published test results for two different materials, eight different stacking sequences, and a range of impact energies from 5 to 50 J. Very good agreement of the predicted damage sizes with the experimentally measured values is observed for a wide range of energy levels but, for two laminates, the discrepancies are significant. Possible improvements of the method are discussed briefly. This method is very promising and can be used in preliminary design allowing extensive trade studies and, eventually, layup optimization. It can also form the beginning of an efficient methodology to predict compression after impact strength of quasi-isotropic laminates.     

An exact solution of the governing equation of a fluid of second-grade for three-dimensional vortex flow

Three-dimensional vortex flow of a fluid of second-grade, for which the velocity field is in the form of υ_r = f(r), υ_θ = g(r), υ_z = zh(r), where r, θ, z are cylindrical polar coordinates, is considered and an exact solution of the governing equation is given. It is an important fact that for this type of flow of a Newtonian fluid, the axial gradient of radial distribution of pressure does not exist and this is unrealistic in many problems of rotational flow. It is found that the axial gradient of radial distribution of pressure exists for this type of flow of a fluid of second grade. It is emphasized that there are exact solutions for the velocity field considered of the governing equation for an Oldroyd type fluid and a Maxwell type one. For some special cases of the velocity field closed form solution of the governing equation are investigated.