Analytical Estimation for Static Deformation of Wire Ropes With Fibrous Core

1990 ◽  
Vol 57 (4) ◽  
pp. 1000-1003 ◽  
Author(s):  
K. Kumar ◽  
J. E. Cochran
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Close Agreement ◽  
Helix Angle ◽  
Closed Form Solutions ◽  
Wire Ropes ◽  
Axial Forces ◽  
End Conditions ◽  
Analytical Estimation ◽  
Rigidity Modulus

This papers develops closed-form solutions for the extension of twisted wire ropes with fibrous cores which are subjected to axial forces as well as axial moments. The analytical results are compared with the corresponding numerical results obtained by Costello and Phillips. A close agreement between the two establishes validity of the analytical solutions. Finally, an expression for the effective rigidity modulus of wire ropes with fibrous core is obtained in terms of the helix angle and the number of helical wires in the rope for each of the two end conditions.

Assessment of Aided-INS Performance

2011 ◽  
Vol 65 (1) ◽  
pp. 169-185 ◽  
Author(s):  
Itzik Klein ◽  
Sagi Filin ◽  
Tomer Toledo ◽  
Ilan Rusnak
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Navigation Systems ◽  
Inertial Navigation Systems ◽  
Closed Form Solutions ◽  
Land Vehicles ◽  
Error Covariance ◽  
Model Dependency ◽  
Error State ◽  
Insight Into

Aided Inertial Navigation Systems (INS) systems are commonly implemented in land vehicles for a variety of applications. Several methods have been reported in the literature for evaluating aided INS performance. Yet, the INS error-state-model dependency on time and trajectory implies that no closed-form solutions exist for such evaluation. In this paper, we derive analytical solutions to evaluate the fusion performance. We show that the derived analytical solutions manage to predict the error covariance behavior of the full aided INS error model. These solutions bring insight into the effect of the various parameters involved in the fusion of the INS and an aiding sensor.

Analysis of transient amplification for a torsional system passing through resonance

2014 ◽  
Vol 229 (13) ◽  
pp. 2341-2354 ◽  
Author(s):  
Laihang Li ◽  
Rajendra Singh
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Classical Problem ◽  
Peak Frequency ◽  
Empirical Formulas ◽  
Closed Form Solutions ◽  
Analytical Approximations ◽  
Numerical Predictions ◽  
Prior Literature ◽  
Run Up

The classical problem of vibration amplification of a linear torsional oscillator excited by an instantaneous sinusoidal torque is re-examined with focus on the development of new analytical solutions of the transient envelopes. First, a new analytical method in the instantaneous frequency (or speed) domain is proposed to directly find the closed-form solutions of transient displacement, velocity, and acceleration envelopes for passage through resonance during the run-up or run-down process. The proposed closed-form solutions are then successfully verified by comparing them with numerical predictions and limited analytical solutions as available in prior literature. Second, improved analytical approximations of maximum amplification and corresponding peak frequency are found, which are also verified by comparing them with prior analytical or empirical formulas. In addition, applicability of the proposed analytical solution is clarified, and their error bounds are identified. Finally, the utility of analytical solutions and approximations is demonstrated by application to the start-up process of a multi-degree-of-freedom vehicle driveline system.

scholarly journals Analytical Solutions for Flow of a Dusty Fluid Between Two Porous Flat Plates

1994 ◽  
Vol 116 (2) ◽  
pp. 354-356 ◽  
Author(s):  
Ali J. Chamkha
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Skin Friction ◽  
Analytical Solutions ◽  
Velocity Profiles ◽  
Flat Plates ◽  
Friction Coefficients ◽  
Dusty Fluid ◽  
Closed Form Solutions

Equations governing flow of a dusty fluid between two porous flat plates with suction and injection are developed and closed-form solutions for the velocity profiles, displacement thicknesses, and skin friction coefficients for both phases are obtained. Graphical results of the exact solutions are presented and discussed.

scholarly journals Analytical and Semi-Analytical Solutions for the Self and Mutual Inductances of Concentric Coplanar Ordinary and Bitter Disk Coils

2021 ◽  
Author(s):  
Slobodan Babic
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Simple Form ◽  
Elliptic Integral ◽  
Mutual Inductance ◽  
The Self ◽  
Computational Time ◽  
Closed Form Solutions

In this paper, closed and semi-closed form solutions are presented for the self - and mutual inductance of ordinary and Better disk coils which lie concentrically in a plane. The solutions are given as the combination of the elliptic integral of the first kind and a simple integral or only as the second elliptic integral of the second kind. All formulas or obtained in remarkably simple form and give extremely accurate results with significantly neglectable computational time. All cases either regular or singular (disks in contact or overlap) are covered. The formulas for the mutual inductances can be directly used to calculating the self-inductance of the ordinary disk coil or the Bitter disk coil, respectively. Many presented examples show the excellent numerical agreement with previous publish methods.

The Lure of the Mean Axes

2006 ◽  
Vol 74 (3) ◽  
pp. 497-504 ◽  
Author(s):  
Leonard Meirovitch ◽  
Ilhan Tuzcu
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Space Structures ◽  
Aerodynamic Forces ◽  
State Equations ◽  
Flexible Bodies ◽  
Closed Form Solutions ◽  
The Mean

A variety of aerospace structures, such as missiles, spacecraft, aircraft, and helicopters, can be modeled as unrestrained flexible bodies. The state equations of motion of such systems tend to be quite involved. Because some of these formulations were carried out decades ago when computers were inadequate, the emphasis was on analytical solutions. This, in turn, prompted some investigators to simplify the formulations beyond all reasons, a practice continuing to this date. In particular, the concept of mean axes has often been used without regard to the negative implications. The allure of the mean axes lies in the fact that in some cases they can help decouple the system inertially. Whereas in the case of some space structures this may mean complete decoupling, in the case of missiles, aircraft, and helicopters the systems remain coupled through the aerodynamic forces. In fact, in the latter case the use of mean axes only complicates matters. With the development of powerful computers and software capable of producing numerical solutions to very complex problems, such as MATLAB and MATHEMATICA, there is no compelling reason to insist on closed-form solutions, particularly when undue simplifications can lead to erroneous results.

On the Hyperelastic Pressurized Thick-Walled Spherical Shells and Cylindrical Tubes Using the Analytical Closed-Form Solutions

2015 ◽  
Vol 07 (02) ◽  
pp. 1550027 ◽  
Author(s):  
D. M. Taghizadeh ◽  
A. Bagheri ◽  
H. Darijani
Keyword(s):  
Closed Form ◽  
Strain Energy ◽  
Soft Tissues ◽  
Behavior Modeling ◽  
Type Model ◽  
Mathematical Form ◽  
Spherical Shells ◽  
Closed Form Solutions ◽  
Axial Forces ◽  
Cylindrical Tubes

This paper focuses on thick-walled spherical shells and cylindrical tubes made of the soft tissues and the rubber-like materials. These materials are characterized by high deformability in which their stress–stretch curves are arranged in the range of S-shaped to J-shaped forms. From the continuum viewpoint, a strain energy density function is postulated for modeling the behavior of these materials. In order to fulfill the main aims of this paper, among all existing energy functions including polynomial, power law, logarithmic and exponential functions, or a linear combination of them, we deduced to evaluate the performance of an Ogden-type model with only integer powers for the mechanical behavior modeling of the S-shaped to J-shaped materials. Most of all, this strain energy function because of its mathematical form can play a constructive role in presentation of the analytical closed-form solutions for the boundary value problems in the field of the finite deformation elasticity. This constitutive model due to the high performance in constitutive modeling and the simplicity of its mathematical form is applied to pressurized thick-walled spherical shells and cylindrical tubes in order to find a closed-form analytical solution for their analysis. Using these analytical solutions, a comprehensive study is done on vanishing circumstance of the snap-through instability that occurs in the inflation of internally pressurized spherical shells and cylindrical tubes. It was observed that the parameters such as shell thickness, the elastic material properties specially the materials with J-shaped mechanical behaviors and the absence and presence of axial forces in cylindrical tubes have significant influence on vanishing of the snap-through instability in the thick-walled pressurized spherical shells and cylindrical tubes.

scholarly journals On the Transient Atomic/Heat Diffusion in Cylinders and Spheres with Phase Change: A Method to Derive Closed-Form Solutions

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
I. L. Ferreira ◽  
A. Garcia ◽  
A. L. S. Moreira
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Single Phase ◽  
Moving Boundary ◽  
Error Function ◽  
Solid State Diffusion ◽  
Two Phase ◽  
Closed Form Solutions ◽  
State Diffusion ◽  
Cylinders And Spheres

Analytical solutions for the transient single-phase and two-phase inward solid-state diffusion and solidification applied to the radial cylindrical and spherical geometries are proposed. Both solutions are developed from the differential equation that treats these phenomena in Cartesian coordinates, which are modified by geometric correlations and suitable changes of variables to achieve closed-form solutions. The modified differential equations are solved by using two well-known closed-form solutions based on the error function, and then equations are obtained to analyze the diffusion interface position as a function of time and position in cylinders and spheres. These exact correlations are inserted into the closed-form solutions for the slab and are used to update the roots for each radial position of the moving boundary interface. The predictions provided by the proposed analytical solutions are validated against the results of a numerical approach. Finally, a comparative study of diffusion in slabs, cylinders, and spheres is also presented for single-phase and two-phase solid-state diffusion and solidification, which shows the importance of the effects imposed by the radial cylindrical and spherical curvatures with respect to the Cartesian coordinate system in the process kinetics. The analytical model is proved to be general, as far as, a semi-infinite solution for diffusion problems with phase change exists in the form of the error function, which enables exact closed-form analytical solutions to be derived, by updating the root at each radial position the moving boundary interface.

scholarly journals Closed-form solution for column buckling optimization

2021 ◽  
Author(s):  
Vladimir Kobelev
Keyword(s):  
Closed Form ◽  
Dimensional Analysis ◽  
Optimization Problem ◽  
Closed Form Solution ◽  
Elliptic Functions ◽  
Isoperimetric Inequalities ◽  
Form Solution ◽  
Algebraic Equations ◽  
Closed Form Solutions ◽  
Axial Forces

Abstract An optimization problem for a column, loaded by axial forces, whose direction and value remain constant, is studied in this article. The dimensional analysis introduces the dimensionless mass and rigidity factors, which simplicities the mathematical technique for the optimization problem. With the method of dimensional analysis, the solution of the nonlinear algebraic equations for the Lagrange multiplier is superfluous. The closed-form solutions for Sturm-Liouville and mixed types boundary conditions are derived. The solutions are expressed in terms of the higher transcendental function. The principal results are the closed form solution in terms of the hypergeometric and elliptic functions, the analysis of single- and bimodal regimes, and the exact bounds for the masses of the optimal columns. The proof of isoperimetric inequalities exploits the variational method and the Hölder inequality. The isoperimetric inequalities for Euler’s column are rigorously verified.

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