A Model for Studying the Stress-Field around Simple Fractures in Human Patella

1983 ◽  
Vol 34 (4) ◽  
pp. 303-313
Author(s):  
J.C. Misra ◽  
V.V.T.N. Murti
Keyword(s):  
Mechanical Properties ◽  
Mathematical Model ◽  
Integral Equation ◽  
Stress Field ◽  
Boundary Value Problem ◽  
Quadrature Formula ◽  
Fredholm Integral Equation ◽  
Engineering Structures ◽  
Mellin Transforms ◽  
Chebyshev Quadrature

SummaryA mathematical model for estimating the stress-field in the vicinity of cracks in human patella has been studied. In conformity with experimental observations with regard to the mechanical properties of osseous tissues, elasticity and anisotropy of the patella have been paid due consideration. The present study being analytical, the problem is first formulated mathematically, and posed as a boundary value problem. Using Mellin transforms technique, the problem is reduced to solving a Fredholm integral equation which is treated numerically by employing Chebyshev quadrature formula. Numerical results are presented. It is suggested that the techniques used may also find application to engineering structures.

A METHOD FOR MODELING THE RESISTIVITY AND IP RESPONSE OF TWO‐DIMENSIONAL BODIES

Geophysics ◽  
1976 ◽  
Vol 41 (5) ◽  
pp. 997-1015 ◽  
Author(s):  
Donald D. Snyder
Keyword(s):  
Integral Equation ◽  
Fourier Transform ◽  
Boundary Value Problem ◽  
Method Of Moments ◽  
Fredholm Integral Equation ◽  
Electric Potential ◽  
Inverse Fourier Transform ◽  
Two Dimensional ◽  
Numerical Techniques ◽  
Point Of Interest

A method has been developed for the solution of the resistivity and IP modeling problem for one or more two‐dimensional inhomogeneities buried in a space for which the Dirichlet Green’s function is known. The boundary‐value problem reduces to a Fredholm integral equation of the second kind which is parametrically a function of a spatial wavenumber. Using the method of moments, the integral equation is solved for a number of values of the wavenumber. An inverse Fourier transform is then performed in order to obtain the electric potential at any point of interest. The method agrees well with both experimental results and other numerical techniques.

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

The effect of pressure on the compressibility of aluminum alloys

2020 ◽  
pp. 102-107
Keyword(s):  
Mechanical Properties ◽  
Mathematical Model ◽  
Liquid Metal ◽  
Control Systems ◽  
Physical And Mechanical Properties ◽  
Reliable Data ◽  
Output Process ◽  
Automated Control ◽  
Input And Output ◽  
Crystallization Under Pressure

To obtain reliable data on the properties of liquid metal and create automated control systems, the technological process of molding with crystallization under pressure is studied. A mathematical model of the input and output process parameters is developed. It is established that the compressibility of the melt can represent the main controlled parameter influencing on the physical-mechanical properties of the final products. The obtained castings using this technology are not inferior in their physical and mechanical properties to those produced by forging or stamping.

Ultrasonic Torsion Welding of Aging Resistant Al/CFRP Joints - Concepts, Mechanical and Microstructural Properties

2017 ◽  
Vol 742 ◽  
pp. 395-400 ◽  
Author(s):  
Florian Staab ◽  
Frank Balle ◽  
Johannes Born
Keyword(s):  
Mechanical Properties ◽  
Process Parameters ◽  
Materials Science ◽  
Dissimilar Materials ◽  
Material Design ◽  
Ultrasonic Welding ◽  
Fatigue Properties ◽  
Aviation Industry ◽  
Efficient Design ◽  
Engineering Structures

Multi-material-design offers high potential for weight saving and optimization of engineering structures but inherits challenges as well, especially robust joining methods and long-term properties of hybrid structures. The application of joining techniques like ultrasonic welding allows a very efficient design of multi-material-components to enable further use of material specific advantages and are superior concerning mechanical properties.The Institute of Materials Science and Engineering of the University of Kaiserslautern (WKK) has a long-time experience on ultrasonic welding of dissimilar materials, for example different kinds of CFRP, light metals, steels or even glasses and ceramics. The mechanical properties are mostly optimized by using ideal process parameters, determined through statistical test planning methods.This gained knowledge is now to be transferred to application in aviation industry in cooperation with CTC GmbH and Airbus Operations GmbH. Therefore aircraft-related materials are joined by ultrasonic welding. The applied process parameters are recorded and analyzed in detail to be interlinked with the resulting mechanical properties of the hybrid joints. Aircraft derived multi-material demonstrators will be designed, manufactured and characterized with respect to their monotonic and fatigue properties as well as their resistance to aging.

Mathematical Model of the Sintering Process of Iron-Copper Bearings

2007 ◽  
Vol 23 ◽  
pp. 119-122
Author(s):  
Cristina Teișanu ◽  
Stefan Gheorghe ◽  
Ion Ciupitu
Keyword(s):  
Experimental Data ◽  
Mechanical Properties ◽  
Mathematical Model ◽  
Regression Analysis ◽  
Function Optimization ◽  
Chemical Compositions ◽  
Sintering Process ◽  
Molybdenum Disulphide ◽  
Iron Copper ◽  
Antifriction Properties

The most important features of the self-lubricating bearings are the antifriction properties such as friction coefficient and wear resistence and some mechanical properties such as hardness, tensile strength and radial crushing strength. In order to improve these properties new antifriction materials based on iron-copper powders with several additional components (tin, lead and molybdenum disulphide) have been developed by PM techniques. To find the optimal relationship between chemical compositions, antifriction and mechanical properties, in this paper a mathematical model of the sintering process is developed, which highlighted the accordance of the model with data by regression analysis. For the statistical processing of the experimental data the VH5 hardness values of the studied materials were considered. The development of mathematical model includes the enunciation of the model, the establishment of the performance function (optimization) and the establishment of the model equations and verifying. The accordance of the model with experimental data has been highlighted by regression analysis

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