Determining static stresses of deformed solitons

An equation for the quasi-static soliton ansatz depending on an arbitrary set of collective variables is covariantly derived on the basis of the variational approach to the method of collective variables. The field configuration and the static stresses of the deformed ⁴ kink that are produced by the excitation of the internal soliton mode are exactly determined. The kink interaction potential at large distances is considered for the example of the nonlinear Klein—Gordon system. A general approach to the problem of exactly determining the intersoliton potential for the entire set of physically admissible two-soliton configurations is discussed. The role of the gauge invariance of the resulting equations is elucidated in relation to the ambiguity in determining the intersoliton distance at the stage where the solitons lose their individuality as they approach each other.     

Calculation of layered structures by the semianalytic method of finite elements

A semianalytic method of finite elements is developed for calculating layered composite structures. The variables are separated on the basis of the Reissner variation principle. A number of plate deformation problems are solved, and a comparison with the known solutions is made. The method can be efficient when dealing with research, as well as engineering, problems.Ukrainian Transport University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 781–785, November–December, 1997.     

Nonlinear contact problems for thin-walled elements of constructions

Some one-dimensional contact problems for plates and shells are considered for one-side contact with a rigid base. Contrary to analogous papers about the zone of contact, we use applied theories of contraction of Winkler type, which are obtained from equations of elasticity theory by asymptotic methods together with bending equations of thin-walled elements. The possibility of deviation of shells needs a definition of a contact zone in the process of solution of the problem from the condition of continuity of bending and its derivatives up to the second order inclusive. Some conclusions are made with respect to the optimal projects of reinforcement of shells taking into account their deviation.Translated from Dinamicheskie Sistemy, No. 8, pp. 40–45, 1989.     

Calculation of the residual stresses in wound glass-reinforced plastics

The effect of the winding and polymerization conditions on the residual stress distribution in wound glass-reinforced plastic cylinders is subjected to a numerical analysis. The calculations are based on the method proposed in [1]. The computer data are examined and the theoretical and experimental results compared.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1026–1030, November–December, 1970.     

On finite and totally finite elements in vector lattices

, X , , , M l- M X , ( M) M .     

Calculation of thermal stresses in an orthotropic cylinder

The present article describes the determination of thermal stresses in an orthotropic cylinder with an axially symmetric temperature field taking into account the change in the elasticity constants over the cylinder radius. A closed solution is given for constant elasticity coefficients.P. I. Baranov Central Institute of Aircraft-Engine Building, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 310–314, March–April, 1972.     

Coupling of mixed finite elements and boundary elements

The symmetric coupling of mixed finite element and boundaryelement methods is analysed for a model interface problem withthe Laplacian. The coupling involves a further continuous ansatzfunction on the interface to link the discontinuous displacementfield to the necessarily continuous boundary ansatz function.Quasi-optimal a priori error estimates and sharp a posteriorierror estimates are established which justify adaptive mesh-refiningalgorithms. Numerical experiments prove the adaptive couplingas an efficient tool for the numerical treatment of transmissionproblems.     

Calculation of contact stresses in axisymmetric underwater explosions

The problem of an underwater electrical explosion in a long layered elastoplastic cylinder is solved. The solution is obtained numerically with use of artificial viscosity. The law for energy produced by the explosion is determined experimentally and residual stresses are determined by the establishment method. Contact stress is presented as a function of explosion energy for various cylinders.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 20, pp. 106–109, 1989.     

Characterizations and constructions of n-to-1 mappings over finite fields

n-to-1 mappings have wide applications in many areas, especially in cryptography, finite geometry, coding theory and combinatorial design. In this paper, many classes of n-to-1 mappings over finite fields are studied. First, we provide a characterization of general n-to-1 mappings over ${\mathbb{F}}_{p^m}$ by means of the Walsh transform. Then, we completely determine 3-to-1 polynomials with degree no more than 4 over ${\mathbb{F}}_{p^m}$. Furthermore, we obtain an AGW-like criterion for characterizing some close relationship between the n-to-1 property of a mapping over finite set A and that of another mapping over a subset of A. Finally, we apply the AGW-like criterion into several forms of polynomials and obtain some explicit n-to-1 mappings. Especially, three explicit constructions of the form $x^{r}h\left(x^s\right)$ from the cyclotomic perspective, and several classes of n-to-1 mappings of the form $g(x^{q^k}-x+\delta )+cx$ are provided.     

Modeling the mean stresses in structural elements made of fiber composites

Conclusions The results of solution of the above-examined problems show that the method proposed here makes it possible to satisfactorily (with an error smaller than 5% for the maximum stresses) recalculate the mean stresses obtained in models made of fiber composites (such as by the photoelastic method) for the corresponding full-scale parts. The method does not require special election of the model materials, which is its main advantage and makes it easy to use.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 495–500, May–June, 1990.     

Temperature stresses in an inhomogeneous cylinder of finite length

An analytic method of determining the temperature stresses in circular cylinders is described. In the solution of the problem, based on a collocation method, together with the finite length of the cylinder its arbitrary inhomogeneity is also taken into account. In a particular case this may be caused by the effect of temperature on the mechanical constants of the material, which is especially typical of polymers at negative temperatures. The results of a calculation of the stresses in a hollow cylinder of finite length with a variable modulus of elasticity are presented as an example.Dzherzhinskii Military Engineering Academy. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 710–715, July–August, 1968.     

A note on least-squares mixed finite elements in relation to standard and mixed finite elements

^** Email: brandts{at}science.uva.nl The least-squares mixed finite-element method for second-orderelliptic problems yields an approximation u_h V_h H₀¹() of thepotential u together with an approximation p_{h h} H(div ; )of the vector field p = – Au. Comparing u_h with the standardfinite-element approximation of u in V_h, and p_h with the mixedfinite-element approximation of p, it turns out that they arehigher-order perturbations of each other. In other words, theyare ‘superclose’. Refined a priori bounds and superconvergenceresults can now be proved. Also, the local mass conservationerror is of higher order than could be concluded from the standarda priori analysis.     

Canonical construction of finite elements

The mixed variational formulation of many elliptic boundary value problems involves vector valued function spaces, like, in three dimensions, and . Thus finite element subspaces of these function spaces are indispensable for effective finite element discretization schemes. Given a simplicial triangulation of the computational domain , among others, Raviart, Thomas and Nédélec have found suitable conforming finite elements for and . At first glance, it is hard to detect a common guiding principle behind these approaches. We take a fresh look at the construction of the finite spaces, viewing them from the angle of differential forms. This is motivated by the well-known relationships between differential forms and differential operators: , and can all be regarded as special incarnations of the exterior derivative of a differential form. Moreover, in the realm of differential forms most concepts are basically dimension-independent. Thus, we arrive at a fairly canonical procedure to construct conforming finite element subspaces of function spaces related to differential forms. In any dimension we can give a simple characterization of the local polynomial spaces and degrees of freedom underlying the definition of the finite element spaces. With unprecedented ease we can recover the familiar - and -conforming finite elements, and establish the unisolvence of degrees of freedom. In addition, the use of differential forms makes it possible to establish crucial algebraic properties of the canonical interpolation operators and representation theorems in a single sweep for all kinds of spaces.