Papers by Keyword: Analytical Solution

Abstract: Vertical rolling is a vital method for width control in rolling, which has its own deformation characteristic. During the processing, plastic deformation does not go further into center of slab, only in edge where the deformation will be occurred. In this paper, an anti-symmetric parabola is creatively used to describe dog-bone shape and innovatively applied to establish a knematically admissible continuous velocity field for vertical rolling. Based on this field, an analytical form of total deformation power is obtained which is a function of reduction geometric parameters, and friction factor m, as well as parameter of A which is to be determined. With minimization of total power results in rolling forces and torque calculated by this new method is obtained. Copper and aluminum experiments conducted by S.-E.Lundberg are used to verified the results calculated by formula in present paper and compared with those by Lundberg and Duckjoongs’ models. The error is no more than 13%, (average error 7%).

Abstract: Radiation effects on two-dimensional MHD Falkner-Skan boundary layer wedge have been studied. Analytical solution of nonlinear boundary-layer equations is obtained by modified homotopy perturbation method. It is observed that the magnetic field tends to decelerate fluid flow whereas radiations and thermal diffusion tend to increase fluid temperature.

Abstract: Analytical solution of the axisymmetric two-dimensional non-Fourier temperature field within a hollow sphere is investigated considering Cattaneo-Vernotte constitutive equation with general time-dependent heat flux. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The method of solution is the standard separation of variables method. Duhamel integral is used for applying the time-dependent boundary conditions. The presented solution is applied to special case of harmonic heat flux on outer surface.

Abstract: In this paper we shall deal with application of analytical and numerical calculation methods in selected geotechnical problem. It is well-known that numerical modeling by Finite Element Method (FEM) is often used for solving complicated engineering problems. FEM is very universal and efficient tool for their solution. In our case a contact task of rigid shallow (circular, rectangular and strip) foundations loaded by centric force, has been solved. The obtained results of vertical normal stresses distributions according to analytical methods and FEM solutions have been analyzed and mutually compared. Results of the calculations have been presented in graphical and tabular form, too.

Abstract: The functional relationship between rock and coal permeability and gas adsorption quantity has been determined, based on earlier experimental results. Then, by method of mathematical physics, the authors derived an analytical solution for a gas seepage equation in which the adsorption effect has been considered. This analytical solution could be used for developing the theory of Seepage Mechanics and Computational Fluid Dynamics, and for checking and correcting various numerical solutions as a standard solution, and for inspiring various calculating techniques such as difference schemes, grid generation, and others as well. The analytical solution derived in this paper has extremely important practical significance in conducting the arrangement of gas extraction operation in coal mine and the CBM (coal bed methane) development planning.

Abstract: Using the method of complex analysis and by constructing conformal mapping, the study investigates the plane elasticity problem of star-shaped cracks and provides an analytical solution for the stress intensity factor (SIF) of crack-tip type I and II. Problems of the classic Griffith crack, the cross-shaped crack, concurrent uniformly distributed three-cracks and symmetrical eight-cracks are also simulated.

Abstract: A mathematical model on orientation distribution function of short fibers suspensions in shear-uniaxial extensional flow is established. Furthermore, the result of differential equation on fiber orientation can be obtained.

Abstract: This paper is concerned with the analytical solution to lateral equivalent flexural rigidity for fiber-reinforced top-hat stiffened composite plate subjected to pure bending. The plate is divided into three parts consist of single-laminate, double-laminate and hat-laminate. After computing equivalent flexural rigidity of the three parts respectively, the overall rigidity is calculated based on the equality of relative rotation angle. An example has been adopted for analytical calculation and then been modeled by finite elements method. A comparison was made to verify the validity of analytical method.

Abstract: Based on the two-dimensional theory of elasticity, Hamiltonian system is introduced to solve the bending of orthotropic beams and the original problems come down to solve the eigensolutions of zero eigenvalue. The symplectic concept makes no hypothesis of deformation along the thickness direction. Thus, the current method can precisely analyze beams with arbitrary depth-to-length ratio, and can deal with arbitrary end conditions. In additional, a new improved boundary conditions for fixed ends beam is presented. Numerical examples showing comparison with other methods are given to illustrate the accuracy of the present approach.

Abstract: The paper presents surveying and processing procedures used at a reconstruction of a circumferential jacket of a 13-storey building, as well as possibilities of numeric and graphic presentation of measurement results. The suitability of specific used procedures depends mainly on the dimensions of the building and its space zoning. Usually, the space polar method is commonly used for surveying of mediating parameters. Analytic processing is considered to be the most suitable method of evaluation of measured point deviations from the vertical plane, or from the plane in general position, mainly because of its smartness, rapidity and universality.