A two-level method for calculation of microstress on reinforced plates with circular hole in case of extension normal to principal direction

The stress concentration must often be examined at two levels while analyzing the stress condition of composite materials. The macroconcentration depends on the presence of holes, notches and other local areas of a construction. Typical dimensions of macroconcentration distribution areas are of the order of 0,01–0,1 m. Macroconcentration analysis is performed using the models of homogeneous material. Microstress concentration occurs in structurally inhomogeneous composites due to the structural heterogeneity of the composite. The sizes of concentration areas in regular structures are defined by the sizes of periodically recurring areas. In fibrous composites, such areas have the size of approximately 0,0001 m or less. This makes it necessary to use a two-level approach for the analysis of the stress concentration in the construction of composite materials. The aim of the present study was to compute the stress concentration in unidirectional reinforced composite plate with circular hole with respect to the volume ratio of the component materials in composite. The contour of the circular hole and its dependency on the structure of plates was calculated in order to study the behaviors of macro- and microstresses. The boundary conditions at a large distance from the hole are pressure, uniformly distributed on the plate. Also this problem is analyzed with the finite element method by package ANSYS. Macroconcentration is defined based on the solution of the plane problem of elasticity theory of the orthotropic material by the virtue of functions of a complex variable. The finite element method was used to investigate the stress distribution at microlevel. Boundary conditions that model the state of the specified twodimensional representative cell in the composite structure were established. The results demonstrated the macro- and microstresses and behavior of the orthotropic plate with a circular hole calculated for two different structures

A New Numerical Method for Calculation of Micro- Stress on Unidirectionally Reinforced Plates with Circular Hole In Case of Extension to a Principal Direction

The aim of the present study was to compute the stress concentration in reinforced composite plate with circular hole with respect to the volume ratio of the component materials in composite. The contour of the circular hole and its dependency on the structure of plates were calculated in order to study the behaviors of macro and micro-stresses. The boundary conditions at a large distance from the hole are pressure, uniformly distributed on the plate. Also this problem is analyzed with the finite element method by package ANSYS. The results demonstrated the macro and micro stress and behavior of the orthotropic plate with a circular hole calculated for two different structures

A New Numerical Procedure for Determination of Effective Elastic Constants in Unidirectional Composite Plates

In this paper a composite plate with similar unidirectional fibers is considered. Assuming orthotropic structure, theory of elasticity is used for investigating the stress concentration. Also, complex variable functions are utilized for solving the plane stress problems. Then the effective characteristics of this plate are studied numerically by using ANSYS software. In this research a volume element of fibers in square array is considered. In order to investigate the numerical finite element modeling, the modeling of a quarter unit cell is considered. For determining the elasticity coefficients, stress analysis is performed for considered volume with noting to boundary conditions. Effective elasticity and mechanical properties of composite which polymer epoxy is considered as its matrix, are determined theoretically and also by the proposed method in this paper with finite element method. Finally, the variations of mechanical properties with respect to fiber-volume fraction are studied

Competitive 0 and {\pi} states in S/F multilayers: multimode approach

We have investigated the critical temperature behavior in periodic superconductor/ ferromagnet (S/F) multilayers as a function of the ferromagnetic layer thickness $d_f$ and the interface transparency. The critical temperature $T_c(d_f)$ exhibits a damped oscillatory behavior in these systems due to an exchange field in the ferromagnetic material. In this work we have performed $T_c$ calculations using the self-consistent multimode approach, which is considered to be exact solving method. Using this approach we have derived the conditions of 0 or $\pi$ state realization in periodic S/F multilayers. Moreover, we have presented the comparison between the single-mode and multimode approaches and established the limits of applicability of the single-mode approximation, frequently used by experimentalists

Analysis of the stress-strain state of a pipeline with a viscoelastic repair bandage on different operating modes

В роботі наведено аналітичні дослідження напружено-деформованого стану ділянки сталевого трубопроводу з в’язкопружним ремонтним бандажем для різних режимів монтажу бандажа та умов зміни тиску у трубопроводі. Повна система рівнянь теорії в’язкопружності для ортотропного матеріалу зведена до інтегро-диференційного рівняння в переміщеннях, та запропоновано метод його розв’язання. Проведено аналіз у часі контактних напружень між трубопроводом та бандажем із врахуванням зміни внутрішнього тиску та впливу в’язкопружних властивостей склопластику.The following paper shows an analytical study on the stress-strain state of a steel elastic pipeline section with a fiberglass viscoelastic repair bandage. The aim of the study is to develop an approach to adequate mathematical modeling of viscoelasticity, considering conditions of an installation of the bandage on a loaded pipeline and a tension in it. An original method of a formation of an integral-differential equation in terms of displacements, gained from the full system of equations of viscoelasticity theory for the plane axisymmetric orthotropic case in polar coordinates, allows discovering and exploring such phenomena as stress relaxation in the bandage and their growth in the pipeline section. The developed approach also lets solve obtained boundary value problem analytically. The proposed set of boundary and conjugation conditions reflects different repair and operational modes. An analytical model enables to consider and examine an influence of the prestress conditions in the pipe on a stress-strain state kinetics as well as a change of contact stress due to viscoelatic properties of fiberglass and different values of an initial pressure.В работе приведены аналитические исследования напряженно-деформированного состояния участка стального трубопровода с вязкоупругим ремонтным бандажом для разных режимов монтажа бандажа и условий изменения давления в трубопроводе. Полная система уравнений теории вязкоупругости для ортотропного материала сведена к интегро-дифференциальному уравнению в перемещениях, и предложен метод его решения. Проведен анализ во времени контактных напряжений между трубопроводом и бандажом с учетом изменения внутреннего давления и влияния вязкоупругих свойств стеклопластика

Characterizing Triviality of the Exponent Lattice of A Polynomial through Galois and Galois-Like Groups

The problem of computing \emph{the exponent lattice} which consists of all the multiplicative relations between the roots of a univariate polynomial has drawn much attention in the field of computer algebra. As is known, almost all irreducible polynomials with integer coefficients have only trivial exponent lattices. However, the algorithms in the literature have difficulty in proving such triviality for a generic polynomial. In this paper, the relations between the Galois group (respectively, \emph{the Galois-like groups}) and the triviality of the exponent lattice of a polynomial are investigated. The \bbbq\emph{-trivial} pairs, which are at the heart of the relations between the Galois group and the triviality of the exponent lattice of a polynomial, are characterized. An effective algorithm is developed to recognize these pairs. Based on this, a new algorithm is designed to prove the triviality of the exponent lattice of a generic irreducible polynomial, which considerably improves a state-of-the-art algorithm of the same type when the polynomial degree becomes larger. In addition, the concept of the Galois-like groups of a polynomial is introduced. Some properties of the Galois-like groups are proved and, more importantly, a sufficient and necessary condition is given for a polynomial (which is not necessarily irreducible) to have trivial exponent lattice.Comment: 19 pages,2 figure

Oceanic internal-wave field : theory of scale-invariant spectra

Author Posting. © American Meteorological Society, 2010. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 40 (2010): 2605–2623, doi:10.1175/2010JPO4132.1.Steady scale-invariant solutions of a kinetic equation describing the statistics of oceanic internal gravity waves based on wave turbulence theory are investigated. It is shown in the nonrotating scale-invariant limit that the collision integral in the kinetic equation diverges for almost all spectral power-law exponents. These divergences come from resonant interactions with the smallest horizontal wavenumbers and/or the largest horizontal wavenumbers with extreme scale separations. A small domain is identified in which the scale-invariant collision integral converges and numerically find a convergent power-law solution. This numerical solution is close to the Garrett–Munk spectrum. Power-law exponents that potentially permit a balance between the infrared and ultraviolet divergences are investigated. The balanced exponents are generalizations of an exact solution of the scale-invariant kinetic equation, the Pelinovsky–Raevsky spectrum. A small but finite Coriolis parameter representing the effects of rotation is introduced into the kinetic equation to determine solutions over the divergent part of the domain using rigorous asymptotic arguments. This gives rise to the induced diffusion regime. The derivation of the kinetic equation is based on an assumption of weak nonlinearity. Dominance of the nonlocal interactions puts the self-consistency of the kinetic equation at risk. However, these weakly nonlinear stationary states are consistent with much of the observational evidence.This research is supported by NSF CMG Grants 0417724, 0417732 and 0417466. YL is also supported by NSF DMS Grant 0807871 and ONR Award N00014-09-1-0515