Science Elasticity
Science Elasticity
TERM PAPER
SCIENCE IV
_Mr. Michael Edar_
_Reynaldo B. Castro Jr._
Teacher Student
Fourth Year Section Seven
Elasticity
Modeling Elasticity
Linear Elasticity
Young’s Modulus of Elasticity
Approximation
Elasticity Tenser
Transition to Inelasticity
Stress-Strain Curves
Non-Newtonian Fluids
Viscoelastic Fluids
Viscosity
Fluids Physics
Newtonian Fluid
Velocity Gradient
The Centinuum Hypothesis
Molecules
Statistical Mechanics
Knudsen Number
Mean Free
Unity
Navier Stokes Equation
Momentum
Acceleration
Friction
Computational Fluid Dynamics
Newtonian vs. Non-Newtonian Fluids
Newtonian Fluids
Perpendicular
Velocity Gradient
Non-Newtonian Fluid
Fluid Appears Thinners
I. Modeling Elasticity
a. Linear Elasticity
There are three basic definitions for integral linearity in common use: independent linearity, zero-based linearity, and terminal, or end-point, linearity. In each case, linearity defines how well the devices actual performance across a specified operating range approximates a straight line. Linearity is usually measured in terms of a deviation, or non-linearity, from an ideal straight line and it is typically expressed in terms of percent of full scale, or in ppm (parts per million) of full scale. Typically, the straight line is obtained by performing a least-squares fit of the data. The three definitions vary in the manner in which the straight line is positioned relative to the actual devices performance. Also, all three of these definitions ignore any gain, or offset errors that may be present in the actual devices performance characteristics.
Many times a devices specifications will simply refer to linearity, with no other explanation as to which type of linearity is intended. In cases where a specification is expressed simply as linearity, it is assumed to imply independent linearity.
Independent linearity is probably the most commonly-used linearity definition and is often found in the specifications for DMMs and ADCs, as well as devices like potentiometers. Independent linearity is defined as the maximum deviation of actual performance relative to a straight line, located such that it minimizes the maximum deviation. In that case there are no constraints placed upon the positioning of the straight line and it may be wherever necessary to minimize the deviations between it and the devices actual performance characteristic.
Zero-based linearity forces the lower range value of the straight line to be equal to the actual lower range value of the devices characteristic, but it does allow the line to be rotated to minimize the maximum deviation. In this case, since the positioning of the straight line is constrained by the requirement that the lower range values of the line and the devices characteristic be coincident, the non-linearity based on this definition will generally be larger than for independent