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.

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.

DIVISIBLE LOAD DISTRIBUTION IN A NETWORK OF PROCESSORS

2008 ◽  
Vol 09 (01n02) ◽  
pp. 31-51 ◽  
Author(s):  
SAMEER BATAINEH
Keyword(s):  
Closed Form ◽  
Load Distribution ◽  
Closed Form Solution ◽  
Form Solution ◽  
The Other ◽  
Optimum Number ◽  
Sequencing Problem ◽  
Divisible Load ◽  
Finish Time ◽  
Optimum Sequence

The paper presents a closed form solution for an optimum scheduling of a divisible job on an optimum number of processor arranged in an optimum sequence in a multilevel tree networks. The solution has been derived for a single divisible job where there is no dependency among subtasks and the root processor can either perform communication and computation at the same time. The solution is carried out through three basic theorems. One of the theorems selects the optimum number of available processors that must participate in executing a divisible job. The other solves the sequencing problem in load distribution by which we are able to find the optimum sequence for load distribution in a generalized form. Having the optimum number of processors and their sequencing for load distribution, we have developed a closed form solution that determines the optimum share of each processor in the sequence such that the finish time is minimized. Any alteration of the number of processors, their sequences, or their shares that are determined by the three theorems will increase the finish time.

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.

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 A Parametrical Analysis for the Rotational Ductility of Reinforced Concrete Beams

2013 ◽  
Vol 7 (1) ◽  
pp. 242-253
Author(s):  
Domenico Raffaele ◽  
Giuseppina Uva ◽  
Francesco Porco ◽  
Andrea Fiore
Keyword(s):  
Reinforced Concrete ◽  
Cross Section ◽  
Concrete Beams ◽  
Closed Form Solution ◽  
Form Solution ◽  
Reinforced Concrete Beams ◽  
Shear Cracks ◽  
Technical Standards ◽  
Mechanical Reinforcement ◽  
Plastic Rotation

The assessment of the plastic rotation of reinforced concrete beams is an essential aspect to avoid structural brittle collapses. The value actually available can be generally determined as sum of two different components. The first, due to bending, the second for inclined shear cracks. This paper presents a simplified model which provides the flexural plastic rotation of the rectangular beams with a ``closed-form solution''. The approach is substantially dimensionless and includes main influencing factors the cross -section, as mechanical material properties, ductility, geometrical and mechanical reinforcement ratio, confinement effects. In closing, in order to appreciate the reliability of the procedure, a comparison with models proposed by international technical standards is made.

Torsional Creep Buckling of Thin-Walled Open Tubes With a Cross Section Having an Axis of Symmetry

1962 ◽  
Vol 29 (1) ◽  
pp. 99-107
Author(s):  
George Lianis
Keyword(s):  
Cross Section ◽  
Closed Form Solution ◽  
Critical Time ◽  
Small Deformation ◽  
Form Solution ◽  
Creep Buckling ◽  
Thin Walled Tube ◽  
Axis Of Symmetry ◽  
Thin Walled ◽  
Stress Patterns

The variational theorem by Sanders, McComb, and Schlechte [1] is applied to find the critical collapse time of an open thin-walled tube with a cross section having an axis of symmetry subjected to torsional creep buckling. Large deformation strains are considered. It is shown that small deformation strains yield inaccurate results in predicting the critical time. A simplified stress distribution is introduced which gives a closed-form solution. More accurate stress patterns present considerable difficulties and a tedious numerical integration is needed. In examining most cases, however, the simplified stress configuration predicts the critical time very accurately.

Plastic Limit Pressure Solutions for Elbows With Slant Through-Wall Cracks

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Minkyu Kim ◽  
Jaehee Kim ◽  
Moon Ki Kim ◽  
Jae-Boong Choi ◽  
Nam-Su Huh ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Closed Form Solution ◽  
Limit Load ◽  
Form Solution ◽  
Fe Model ◽  
Plastic Limit ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Limit Pressure ◽  
Plastic Limit Pressure

Abstract For leak-before-break (LBB) assessment, an idealized through-wall crack (TWC) is typically postulated to determine the critical crack length of cracked piping. However, such an idealization in terms of crack shape can lead to underestimations of plastic limit pressure. Although many studies have been performed to obtain accurate limit load solutions for cracked straight pipes by considering realistic crack geometries, there is still a lack of information regarding slant TWC at elbow. Therefore, three-dimensional finite element (FE) models of an elbow considering the effects of slant TWC on plastic limit pressure are developed. The proposed FE model and analysis procedure were verified through comparisons to the existing solutions for idealized TWCs in elbow. On this basis, the effect of slant TWC on the plastic limit pressure is analyzed, and a closed-form solution of the plastic limit pressure is proposed, for an elbow containing a longitudinal or a circumferential through-wall crack.

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.

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