Axially Symmetric Radial Flow of Rigid/Linear-Hardening Materials

1979 ◽  
Vol 46 (2) ◽  
pp. 322-328 ◽  
Author(s):  
D. Durban
Keyword(s):  
Radial Flow ◽  
Closed Form Solution ◽  
Wire Drawing ◽  
Form Solution ◽  
Flow Rule ◽  
Axially Symmetric ◽  
Linear Hardening ◽  
Stress Components ◽  
Von Mises ◽  
Good Agreement

A closed-form solution has been discovered for axially symmetric radial flow of rigid/linear-hardening materials. It is assumed that the materials obey the von Mises flow rule and that the flow field is in steady state. Explicit expressions for the stress components and the radial velocity are given. The applicability of the solution to wire drawing or extrusion is discussed. Some approximate formulas are derived and shown to be in good agreement, within their range of validity, with experimental results for drawing.

Drawing of Tubes

1980 ◽  
Vol 47 (4) ◽  
pp. 736-740 ◽  
Author(s):  
D. Durban
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Radial Flow ◽  
Material Behavior ◽  
Wall Friction ◽  
Flow Rule ◽  
Flow Conditions ◽  
Steady State Flow ◽  
Linear Hardening ◽  
Von Mises

The process of the tube drawing between two rough conical walls is analyzed within the framework of continuum plasticity. Material behavior is modeled as rigid/linear-hardening along with the von-Mises flow rule. Assuming a radial flow pattern and steady state flow conditions it becomes possible to obtain an exact solution for the stresses and velocity. Useful relations are derived for practical cases where the nonuniformity induced by wall friction is small. A few restrictions on the validity of the results are discussed.

Derivation of Position-Probability Density for the Transient Nano-Tunnel Problem in SET

2010 ◽  
Author(s):  
Sheam-Chyun Lin ◽  
Hsien-Chang Shih ◽  
Fu-Sheng Chuang ◽  
Ming-Lun Tsai ◽  
Harki Apri Yanto ◽  
...  
Keyword(s):  
Probability Density ◽  
Error Function ◽  
Closed Form Solution ◽  
Form Solution ◽  
Single Electron ◽  
Mathematical Operation ◽  
Similarity Parameter ◽  
Set Up ◽  
Position Probability ◽  
Good Agreement

This theoretical investigation intends to study the nano-tunnel problem of the single electron transistor (SET), which is one of the most important components in the nano-electronics industry. With a combined effort of quantum mechanics and similarity parameter, the partial differential equation of transient position-probability density is attained and can be applied to predict the electron’s position inside the nano tunnel. Also, an appropriate set of the initial and the boundary conditions is set up in accordance to the actual electron behavior for solving this PDE of probability density function. Thereafter, a simple, closed-form solution for the probability density is obtained and expressed in terms of the error function for a new similarity variable η. Note that this analytic similarity solution is easy to perform the calculation and suitable for any further mathematical operation, such as the optimization applications. In addition, it is shown that these predications are reasonable and in good agreement to the physical meanings, which are evaluated from both microscopic and macroscopic viewpoints. In conclusions, this is an innovative approach by using the Schro¨dinger equation directly to solve the nano-tunnel problem. Moreover, with the aids of this analytic position-probability-density solution, it is illustrated that the free single electron in the SET’s tunnel can only appear at some specified regions, which are defined by a dimensionless parameter η within a range of 0 ≤ η ≤ 2. This result can be served as a valuable design reference for setting the practical manufacture requirement.

Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots

2014 ◽  
Vol 6 (3) ◽  
Author(s):  
Mahdi Agheli ◽  
Stephen S. Nestinger
Keyword(s):  
Closed Form ◽  
Structural Parameters ◽  
Closed Form Solution ◽  
Form Solution ◽  
Axially Symmetric ◽  
Kinematic Chains ◽  
Design And Optimization ◽  
Hexapod Robots ◽  
Iterative Optimization Algorithm ◽  
Orientation Workspace

The workspace of hexapod robots is a key performance parameter which has attracted the attention of numerous researchers during the past decades. The selection of the hexapod parameters for a desired workspace generally employs the use of numerical methods. This paper presents a general methodology for solving the closed-form constant orientation workspace of radially symmetric hexapod robots. The closed-form solution facilitates hexapod robot design and minimizes numerical efforts with on-line determination of stability and workspace utilization. The methodology can be used for robots with nonsymmetric and nonidentical kinematic chains. In this paper, the methodology is used to derive the closed-form equations of the boundary of the constant-orientation workspace of axially symmetric hexapod robots. Several applications are provided to demonstrate the capability of the presented closed-form solution in design and optimization. An approach for workspace-based design optimization is presented using the provided analytical solution by applying an iterative optimization algorithm to the find optimized structural parameters and an optimized workspace.

Using Isochronous Method to Calculate Creep Damage in Pressure Vessel Components: Part 2

2017 ◽  
Author(s):  
Chithranjan Nadarajah ◽  
Benjamin F. Hantz ◽  
Sujay Krishnamurthy
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Pressure Vessel ◽  
Closed Form Solution ◽  
Creep Damage ◽  
Form Solution ◽  
Creep Model ◽  
Stress Strain ◽  
Element Analysis ◽  
Good Agreement

This paper is Part 2 of two papers illustrating how isochronous stress strain curves can be used to calculate creep stresses and damage for pressure vessel components. Part 1 [1], illustrated the use of isochronous stress strain curves to obtain creep stresses and damages on two simple example problems which were solved using closed form solution. In Part 2, the isochronous method is implemented in finite element analysis to determine creep stresses and damages on pressure vessel components. Various different pressure vessel components are studied using this method and the results obtained using this method is compared time explicit Omega creep model. The results obtained from the isochronous method is found to be in good agreement with the time explicit Omega creep model.

scholarly journals Added Mass and Damping of a Vibrating Rod in Confined Viscous Fluids

1976 ◽  
Vol 43 (2) ◽  
pp. 325-329 ◽  
Author(s):  
S. S. Chen ◽  
M. W. Wambsganss ◽  
J. A. Jendrzejczyk
Keyword(s):  
Experimental Data ◽  
Experimental Study ◽  
Cylindrical Shell ◽  
Closed Form Solution ◽  
Added Mass ◽  
Form Solution ◽  
Viscous Fluids ◽  
Series Of Experiments ◽  
Theoretical Results ◽  
Good Agreement

This paper presents an analytical and experimental study of a cylindrical rod vibrating in a viscous fluid enclosed by a rigid, concentric cylindrical shell. A closed-form solution for the added mass and damping coefficient is obtained and a series of experiments with cantilevered rods vibrating in various viscous fluids is performed. Experimental data and theoretical results are in good agreement.

scholarly journals Stress Tensor and Gradient of Hydrostatic Pressure in the Contact Plane of Axisymmetric Bodies Under Normal and Tangential Loading

2020 ◽  
Author(s):  
Emanuel Willert ◽  
Fabian Forsbach ◽  
Valentin L. Popov
Keyword(s):  
Hydrostatic Pressure ◽  
Stress Tensor ◽  
Normal Component ◽  
Hertzian Contact ◽  
Von Mises Stress ◽  
Axially Symmetric ◽  
Principal Stresses ◽  
Contact Plane ◽  
Stress Components ◽  
Von Mises

The Hertzian contact theory, as well as most of the other classical theories of normal and tangential contact, provides displacements and the distribution of normal and tangential stress components directly in the contact surface. However, other components of the full stress tensor in the material may essentially influence the material behaviour in contact. Of particular interest are principal stresses and the equivalent von Mises stress, as well as the gradient of the hydrostatic pressure. For many engineering and biomechanical problems, it would be important to find these stress characteristics at least in the contact plane. In the present paper, we show that the complete stress state in the contact plane can be easily found for axially symmetric contacts under very general assumptions. We provide simple explicit equations for all stress components and the normal component of the gradient of hydrostatic pressure in the form of one-dimensional integrals.

scholarly journals Developed Mathematical Model for Indeterminate Elements with Variable Inertia and Curved Elements with Constant Cross-Section

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Mohamed A. El Zareef ◽  
Mohamed E. El Madawy ◽  
Mohamed Ghannam
Keyword(s):  
Mathematical Models ◽  
Numerical Integration ◽  
Cross Section ◽  
Closed Form Solution ◽  
Form Solution ◽  
Optimum Number ◽  
Fe Model ◽  
Constant Cross Section ◽  
Structural Elements ◽  
Good Agreement

Issues such as analysis of indeterminate structural elements that have variable inertia as well as a curved shape still have no closed form solution and are considered one of the major problems faced by design engineers. One method to cope with these issues is by using suitable the finite element (FE) software for analyzing these types of elements. Although it saves time, utilization of FE programs still needs professional users and not all engineers are familiar with it. This paper has two main objectives; first, to develop simple mathematical models for analyzing indeterminate structural elements with variable inertia and that have a curved shape with constant cross section, this model is much easier to be used by engineers compared to the FE model. For simplicity and saving time, a MATLAB program is developed based on investigated mathematical models. The force method combined with numerical integration technique is used to develop these models. The developed mathematical models are verified using the suitable FE software; good agreement was observed between the mathematical and the FE model. The second objective is to introduce a mathematical formula to determine the accurate number of divisions that would be used in the mathematical models. The study proves that the accuracy of analysis depends on the number of divisions used in the numerical integration. The optimum number of divisions is obtained by comparing the output results for both FE and developed mathematical models. The developed mathematical models show a good agreement with FE results with faster processing time and easier usage.

On the Analytical Solution of Externally Pressurized Porous Gas Journal Bearings

1978 ◽  
Vol 100 (3) ◽  
pp. 442-444 ◽  
Author(s):  
B. C. Majumdar
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Journal Bearings ◽  
Form Solution ◽  
Performance Characteristics ◽  
Gas Bearing ◽  
Good Agreement

A closed form solution of pressure distribution which leads to the determination of bearing performance characteristics of an externally pressurized porous gas bearing without journal rotation is obtained. A good agreement with a similar available solution confirms the validity of the method.

Analysis on a Counter-Current Flow Hemodialyzer

2009 ◽  
Vol 4 (5) ◽  
Author(s):  
Norman W Loney
Keyword(s):  
Experimental Data ◽  
Mass Transfer ◽  
Closed Form Solution ◽  
Maximum Error ◽  
Form Solution ◽  
Transfer Coefficients ◽  
Confluent Hypergeometric Functions ◽  
Proposed Model ◽  
Counter Current ◽  
Good Agreement

The closed form solution to the conjugated boundary value problem posed by a counter current hemodialyzer facilitates the estimation of the overall mass transfer coefficient. Comparison of the proposed model results with published experimental data shows good agreement for Urea and Creatinine clearances over a published range of blood and dialyzate flow rates. This model predicts clearances with a maximum error of less than 4% for both Urea and Creatinine when blood flow is 75% of the dialyzate flow. However, when both blood and dialyzate flows are identical the model over predicts the experimental data by 1.47% in the case of Urea and 4.75 for Creatinine flows of 300 ml/min. Although the concentration profile is an infinite series involving confluent hypergeometric functions, 2 terms of the series were sufficient (Mathematica notebook program) to produce these results. Overall mass transfer coefficients can now be deduced from the Sherwood numbers and provide possible improvement over currently used area coefficients.

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