Axisymmetric Stresses in an Elastic Radially Inhomogeneous Cylinder Under Length-Varying Loadings

2016 ◽  
Vol 83 (11) ◽  
Author(s):  
Yuriy Tokovyy ◽  
Chien-Ching Ma
Keyword(s):  
Integration Method ◽  
Analytical Form ◽  
Radial Coordinate ◽  
Solid Cylinder ◽  
Total Stress ◽  
Resolvent Kernel ◽  
Axial Coordinate ◽  
Direct Integration Method ◽  
Axisymmetric Elasticity ◽  
Radially Inhomogeneous

In this paper, we present an analytical solution to the axisymmetric elasticity problem for an inhomogeneous solid cylinder subjected to external force loadings, which vary within the axial coordinate. The material properties of the cylinder are assumed to be arbitrary functions of the radial coordinate. By making use of the direct integration method, the problem is reduced to coupled integral equations for the shearing stress and the total stress (given by the superposition of the normal ones). By making use of the resolvent-kernel solution, the latter equations were uncoupled and then solved in a closed analytical form. On this basis, the effect of variable material moduli in the stress distribution has been examined with special attention given to the negative Poisson's ratio.

scholarly journals Elastic and Thermoelastic Responses of Orthotropic Half-Planes

Materials ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 297
Author(s):  
Yuriy V. Tokovyy ◽  
Anatoliy V. Yasinskyy ◽  
Sebastian Lubowicki ◽  
Dariusz M. Perkowski
Keyword(s):  
Governing Equation ◽  
Elastic Moduli ◽  
Integration Method ◽  
Plane Elasticity ◽  
Orthotropic Materials ◽  
Explicit Solutions ◽  
Unified Approach ◽  
Resolvent Kernel ◽  
Explicit Analytical Solution ◽  
Direct Integration Method

A unified approach is presented for constructing explicit solutions to the plane elasticity and thermoelasticity problems for orthotropic half-planes. The solutions are constructed in forms which decrease the distance from the loaded segments of the boundary for any feasible relationship between the elastic moduli of orthotropic materials. For the construction, the direct integration method was employed to reduce the formulated problems to a governing equation for a key function. In turn, the governing equation was reduced to an integral equation of the second kind, whose explicit analytical solution was constructed by using the resolvent-kernel algorithm.

Bright and dark optical solitons for the generalized variable coefficients nonlinear Schrödinger equation

2020 ◽  
Vol 21 (7-8) ◽  
pp. 675-681
Author(s):  
Rehab M. El-Shiekh ◽  
Mahmoud Gaballah
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Integration Method ◽  
Variable Coefficients ◽  
Nonlinear Schrodinger Equation ◽  
Equation Method ◽  
Direct Integration ◽  
Wave Solutions ◽  
Direct Integration Method

AbstractIn this paper, the generalized nonlinear Schrödinger equation with variable coefficients (gvcNLSE) arising in optical fiber is solved by using two different techniques the trail equation method and direct integration method. Many different new types of wave solutions like Jacobi, periodic and soliton wave solutions are obtained. From this study we have concluded that the direct integration method is more easy and straightforward than the trail equation method. As an application in optic fibers the propagation of the frequency modulated optical soliton is discussed and we have deduced that it's propagation shape is affected with the different values of both the amplification increment and the group velocity (GVD).

scholarly journals Precise Integration Method for Solving Noncooperative LQ Differential Game

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Hai-Jun Peng ◽  
Sheng Zhang ◽  
Zhi-Gang Wu ◽  
Biao-Song Chen
Keyword(s):  
Differential Equation ◽  
Differential Game ◽  
Integration Method ◽  
Transformation Method ◽  
Linear Quadratic ◽  
Riccati Differential Equation ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Direct Integration Method ◽  
Two Parameters

The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”.

Nonlinear structures: soliton, shocklike and explosive waves in quantum semiconductor plasma

2021 ◽  
Author(s):  
Haifa Al-Yousef
Keyword(s):  
Analytical Procedure ◽  
Integration Method ◽  
Fluid Model ◽  
Three Dimensional ◽  
Semiconductor Plasma ◽  
Direct Integration Method ◽  
Solution Methods ◽  
Gradient Forces ◽  
Quantum Semiconductor ◽  
Nonlinear Solutions

Abstract The properties and conditions for the appearance of some nonlinear waves in a three-dimensional semiconductor plasma are discussed, by studying the described plasma fluid system with quantum gradient forces and degraded pressures. Our analytical procedure is built on the reductive perturbation theory to obtain the Kadomtsev-Petvashvili equation for the fluid model and solving it using the direct integration method and the Bäcklund transform. Through different solution methods we got different nonlinear solutions describing different pulse profiles such as soliton, kink and explosive pulses. This model can be used to identify the potential disturbances in a semiconductor plasma.

scholarly journals Piecewise Polynomial Fitting with Trend Item Removal and Its Application in a Cab Vibration Test

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Wu Ren ◽  
Qiongqiong Ren ◽  
Lin Han ◽  
Ying Liu ◽  
Bo Peng
Keyword(s):  
Integration Method ◽  
Vibration Signal ◽  
Vibration Test ◽  
Measured Signal ◽  
Direct Integration ◽  
Piecewise Polynomial ◽  
Modal Parameter ◽  
Polynomial Fitting ◽  
Special Equipment ◽  
Direct Integration Method

The trend item of a long-term vibration signal is difficult to remove. This paper proposes a piecewise integration method to remove trend items. Examples of direct integration without trend item removal, global integration after piecewise polynomial fitting with trend item removal, and direct integration after piecewise polynomial fitting with trend item removal were simulated. The results showed that direct integration of the fitted piecewise polynomial provided greater acceleration and displacement precision than the other two integration methods. A vibration test was then performed on a special equipment cab. The results indicated that direct integration by piecewise polynomial fitting with trend item removal was highly consistent with the measured signal data. However, the direct integration method without trend item removal resulted in signal distortion. The proposed method can help with frequency domain analysis of vibration signals and modal parameter identification for such equipment.

Cosserat Spectrum of an Axisymmetric Elasticity Problem for a Finite-Length Solid Cylinder

2018 ◽  
Vol 35 (3) ◽  
pp. 343-349
Author(s):  
Yu. V. Tokovyy
Keyword(s):  
Asymptotic Behavior ◽  
Finite Length ◽  
Solution Method ◽  
Superposition Method ◽  
Algebraic Equations ◽  
Solid Cylinder ◽  
Cosserat Spectrum ◽  
Linear Algebraic Equations ◽  
Key Features ◽  
Axisymmetric Elasticity

ABSTRACTAn algorithm for the computation and analysis of the Cosserat spectrum for an axisymmetric elasticity boundary-value problem in a finite-length solid cylinder with boundary conditions in terms of stresses is proposed. By making use of the cross-wise superposition method, the spectral problem is reduced to systems of linear algebraic equations. A solution method for the mentioned systems is presented and the asymptotic behavior of the Cosserat eigenvalues is established. On this basis, the key features of the Cosserat spectrum for the mentioned problem are analyzed with special attention given to the effect of the cylinder aspect ratio.

An Improved Transfer Matrix-Direct Integration Method for Rotor Dynamics

1986 ◽  
Vol 108 (2) ◽  
pp. 182-188 ◽  
Author(s):  
Jialiu Gu
Keyword(s):  
Transfer Matrix ◽  
Integration Method ◽  
Equations Of Motion ◽  
Rotor Dynamics ◽  
Direct Integration ◽  
Rotating System ◽  
Direct Integration Method ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Matrix Iteration

A transfer matrix-direct integration combined method is proposed, which employs the transfer matrix method to derive the equations of motion of a “characteristic disk,” and uses the direct integration method to determine the critical speeds, modes and unbalance response of a rotor-bearing system, and to analyze its stability. Despite the complexity of the system, the number of governing equations is not greater than eight. For a single-spool rotating system, the number of equations is only four. A transfer matrix for a uniform shaft is derived to consider its distributed mass, moment of inertia and the effect of shearing force. An impedance matrix iteration method is proposed to consider the effect of a complicated bearing-supporting system on the rotor dynamics. Two examples are given, and the results agree satisfactorily with the experiments.

Analysis of Infinitely Short and Infinitely Long Hydrodynamic Journal Bearings Under Micro-Polar Fluid by Direct Integration Method

2017 ◽  
Author(s):  
Bikash Routh
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Integration Method ◽  
Pressure Profile ◽  
Journal Bearings ◽  
Direct Integration ◽  
Polar Fluid ◽  
Direct Integration Method

In the present paper Reynolds equation of lubrication under micro-polar fluid for journal bearing is solved by direct-integration method under infinitely long and infinitely short journal bearing assumptions [1]. Infinitely long-bearing and infinitely short bearing solutions are the two available approximate closed form solutions for journal bearings. In the present investigation, solution of Reynolds equation i.e. pressure profile is compared with pressure profile obtained by previously used approximate method like finite difference method (FDM). Mentionable here that any approximation method needs lots of calculation and computer programing to get the result. In the present work it has been found that direct-integration method leads the almost same result as the conventionally used complex finite difference method. CFD analysis is also presented in the present work to justify the profile obtained by direct numerical method. It has seen here that theoretical and simulation results are in good agreement to each other’s.

Sign in / Sign up

Export Citation Format

Share Document