Engineering Applications
There are many real-world examples where Newton’s Method is applied.
Finite Element software packages apply Newton’s Method to solve problems
where a hypothetical weight is applied to a structure. The software then
proceeds to tell at what point the structure will break. However, there are
some stipulations for the application of Newton’s Method to be effective. The initial
guess needs to be close to the exact solution and the slope of the load displacement
curve cannot change (Kren, 2001).
To apply Newton’s Method, the total load is divided into small increments.
This approach treats the load as a piecewise function. Iterations are then
performed with each increment of the load. “The structure is permitted to
deform by a single load increment at a time” (Kren, 2001, p. 62). This no
longer works when the load displacement becomes tangent because it must remain
constant or decrease to remain at equilibrium (Kren, 2001).
A specific company that benefits from the application of Newton’s Method
through the use of Finite Element Analysis would be: EJ, a designer and manufacturer of
manhole covers. In the design of a manhole cover, it is critical to ensure the
manhole cover is designed so that it will safely support traffic loading.
Finite Element Analysis allows them to apply simulated loads to a manhole cover
before the manhole cover is actually manufactured.
The first step in this process is to define the materials the manhole cover would be
manufactured from, whether that is ductile iron or cast iron and what are the properties
of that type of iron. Once the material is decided upon a 3-D drawing of the product
they’re designing is produced. Once the drawing model is produced with all of its
specifications then an analysis on the design can be done through the use of the Finite
Element software.
The simulation depicted above shows the result of a load applied to this
manhole cover. The cover above has support ribs designed into it. The
red areas shows where the load weights are the greatest. There is an
accompanying chart with this output that relates a load or stress associated
with each variation of color. Additionally, the person using the software can
apply incremental loads to show when the manhole cover exceeds acceptable deflection.
This information aides engineers in determining whether or not larger or thicker rib
supports should be put in place to reduce the stress on a particular part or area of the product.
Finite Element software provides companies, like EJ, the ability to produce optimal
products. They are able to assure their costumers that their products will meet the
load stress requirements required for a particular product.
Business Applications
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