Papers by Keyword: Analytical Solution

Abstract: An analytical three-dimensional elastic-plastic over-rolling solution is used to evaluate the plastic strains and residual stresses. Central to this plastic contact formulation is the incremental approach to deal with non-linear material behavior. The Prandtl-Reuss constitutive equations in conjunction with Huber-Mises-Hencky yield criterion and Ramberg-Osgood strain-hardening relationships are applied to describe the plastic behavior of common hardened bearing steel. The model was extended to include the tangential force in the rolling direction, assumed to be proportional to the hertzian contact pressure. Comparisons of three-dimensional pure rolling and rolling/sliding contact results were provided to elucidate the differences in residual stresses and residual profiles in case of kinematic and work-hardening materials.

Abstract: Composite mast with rigging system is an example of a complex composite-steel system. The implementation of modern constructional materials such as composite materials in order to construct the composite masts has some consequences. Composites have different properties than materials such as wood (in the past), steel or aluminium which are usually used in construction of the masts.

Abstract: The paper shows a conclusion and a solution of principal resolving equations of the motion of linear and geometrically non-linear theories of thin depressed shells with median surface breaks. A formula has been obtained for determining the shell’s free bending harmonic oscillation frequency in case of a hinge support on rigid diaphragms. Charts are supplied showing the dependence of free oscillation frequency on the change of different factors. A conclusion has been drawn concerning the analytical method efficiency.

Abstract: Diffusion research is important for understanding of many processes based on mass transfer. In many respects, diffusion, determines physical and mechanical characteristics for new materials with fine-dispersed matter and a large number of grain boundaries and phases. Models of diffusion along grain boundaries and their modifications are widely known in literature, but they are not always applicable to nanomaterials due to indistinct determination of some notions. At the present paper the model of diffusion is presented, which considers boundaries and area near boundaries as a phase with special properties. Mass transfer between the volume of a grain and a boundary phase is taken into account. The approximate analytical solution of the problem is formulated. In the general case the problem is solved numerically. Non monotonic distributions of concentrations in volume are obtained.

Abstract: The problem has been analyzed on alloying elements redistribution between the coating (containing Cr and N) and the substrate (Si) in condition of surface heating. The model takes into account the effect of thermal diffusion on the redistribution of elements. The analytical solution of the particular linearized problem about redistribution of elements in the substrate coating is presented. It is shown that the thermal diffusion significantly affects the impurity distribution, resulting in the appearance of supersaturated or depleted regions.

Abstract: The simple isothermal problem is formulated to describe the composition of surface layer change during particle beam action. The finiteness of relaxation time for mass flux is taken into account. The analytical solutions for some limiting cases are presented. Numerical solution of total problem is carried out. It is shown that concentration distributions for reactants and for reaction product depend on relation between various physical scales.

Abstract: The distinctive paper is devoted to correct multilevel discrete-continual finite element method (DCFEM) of structural analysis based on precise analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients. Corresponding semianalytical (discrete-continual) formulations are contemporary mathematical models which currently becoming available for computer realization. Major peculiarities of DCFEM include universality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resulting systems and partial Jordan decompositions of matrices of coefficients, eliminating necessity of calculation of root vectors.

Abstract: In this research, both un-deformed or Lagrangian state and deformed or Eulerian state are used to derive for stability analysis and large deformation. By choosing the deformed radius of curvature and deformed angle of tangent slope as parameters, the governing equations of laminated curved beam under static loading are transformed into a set of equations in terms of angle of tangent slope. All the quantities of axial force, shear force, radial and tangential displacements of circular thin curved beam are expressed as functions of angle of tangent slope by using laminate theory. The buckling load and large deformation analytical solutions of circular thin curved beam under a pair of forces are presented as well.

Abstract: Lateral distributions of depth-averaged velocity in open compound channels with submerged vegetated floodplains are analyzed, based on an analytical solution to the depth-integrated Reynolds-Averaged Navier-Stokes equation with a term included to account for the effects of vegetation. The cases of open channels are: rectangular channel with submerged vegetated corner, and compound channel with submerged vegetated floodplain. The present paper proposes a method for predicting lateral distribution of the depth-averaged velocity with submerged vegetated floodplains. The method is based on a two-layer approach where flow above and through the vegetation layer is described separately. An experiment in compound channel with submerged vegetated floodplain is carried out for the present research. The analytical solutions of the three cases are compared with experimental data. The corresponding analytical depth-averaged velocity distributions show good agreement with the experimental data.

Abstract: The two-dimensional differential transform method is applied to solve the one-dimensional phase change problem for a solid sphere with time-dependent boundary temperature. The problem assumes that the phase change occurs over a range of temperatures and the initial temperature of the sphere is an arbitrary constant. An approximate analytical (series) solution is derived for the temperature profile in the melting or solidifying sphere. The solution is based on the apparent specific heat method. Numerical results illustrate the effects of the Stefan number, which is the ratio of sensible heat to latent heat, on the transient temperature profile in the sphere.