random vibrations, impacts, or shocks. Fatigue analysisis used to determine the life
of a material or structure. It shows the effects of occasional (periodic) or cyclic loading
on a structure or object, pointing out where cracks or fractures are most likely to
occur. Engineers measure heat transferto determine a material or structure’s con-
ductivity or thermal fluid dynamics. In this way, researchers understand how a mater-
ial will respond to various hot and cold conditions—or even how it diffuses heat and
cold—over time.What is dimensional analysis?
Simply put, dimensional analysis is a way of manipulating unit measures using alge-
bra to determine the proper units for a quantity that is being computed. For example,
the units of length over time represent velocity in feet per second; acceleration is
velocity over time. Thus, acceleration will then have units of feet per second per sec-
ond, or feet per second squared.What is the least squares method?
This mathematical procedure, called either the least squares method or the method of
least squares, finds the best-fitting curve for a given set of points by minimizing the
326 sum of the squares of all deviations from the curve. It is often used in engineering for
Why is finite element analysis important to many industries?
F
inite element analysis (FEA) is important to various industries—especially
those that need to predict failure of a structure, object, or material when
under unknown stresses—because it allows designers to understand all of the
theoretical stresses within the structure. This cuts manufacturing costs that
would occur if a sample of the structure was actually built and tested.FEA uses a complex system of points (nodes), making up a grid called a
mesh. The mesh is programmed to contain all the material, properties, and
other factors that constitute the structure and determine how it will react to
certain load conditions, such as thermal, gravitational, pressure, or point loads.
The nodes are then assigned a density throughout the material, all depending on
the stress levels anticipated in a certain area. In general, points with more stress
(such as corners of a building or contact points on a car frame) will usually have
a higher node density than those with little or no stress. As researchers examine
the results of the FEA, they learn how the structure responds to the various
stresses. In this way, a prototype of the structure won’t have to be built until the
majority of the theoretical “kinks” are worked out of the system.