Ingeniero

Job Alberto Alonso González

1090712 IMT

The production of new materials, which increases its principal
properties.

The invention of the personal computer and electronic calculator,
which gives the engineer the capability to use the main processor to solve
mathematical problems. *
Advances in experimental techniques, some of them are realized with a
simulation program which allowsthe engineers to predict the behavior of a
single tool piece or a whole construction under certain circumstances.

It’s the problem that occurs when a program is giving wrong results
because we are not providing the correct inputs, is a common cause of
error in the data output and we have to be capable of identifying it.

The use of the FEM in computational programs to build 3D models orenvironments.
The use of the FEM in calculus of electromagnetic equations to predict
the effects of some forces.
The use of the FEM in model analysis for some nanostructures
involving nanoforces at molecular level. (Providing help to analyze data
obtain with an AFM).
The use of the FEM in weather prediction.*

It is required to have mathematical knowledge about differential equations
andsome numerical methods like numerical integration, lineal algebra and
interpolation. *

Rounding error: In this case error appears because of the use of finite
numerical representations. It can be solved using more decimals, but this
takes us to use more memory (resources).1
Discretization error: Is error resulting from the fact that a function of a
continuous variable is represented in thecomputer by a finite number of
evaluations. It can usually be reduced by using a more finely spaced lattice,
with an increased computational cost.2

2

Its development can be traced back to the work by Alexander Hrennikoff
(1941) and Richard Courant (1942).3

In the FEM, the structural system is modeled by a set of appropriate finite
elements interconnected at points called nodes.Elements may have physical
properties such as thickness, coefficient of thermal expansion, density,
Young's modulus, shear modulus and Poisson's ratio. The elements are
interconnected only at the exterior nodes, and altogether they should cover
the entire domain as accurately as possible. Nodes will have nodal (vector)
displacements or degrees of freedom which may include translations,
rotations,and for special applications, higher order derivatives of
displacements. When the nodes displace, they will drag the elements along
in a certain manner dictated by the element formulation. In other words,
displacements of any points in the element will be interpolated from the
nodal displacements, and this is the main reason for the approximate nature
of the solution. 4

Geometrydescription.
Preparation of analysis data.
Computer analysis.
Visualization of results.*

Data preprocessing describes any type of processing performed on raw data
to prepare it for another processing procedure. Commonly used as a
preliminary data mining practice, data preprocessing transforms the data
into a format that will be more easily and effectively processed for the
purpose of the user.There are a number of different tools and methods used
for preprocessing, including: sampling, which selects a representative subset
from a large population of data; transformation, which manipulates raw data
to produce a single input; denoising, which removes noise from data;
normalization, which organizes data for more efficient access; and feature
extraction, which pulls out specified datathat is significant in some
particular context. 5

3

Solvers, or optimizers, are software tools that help users find the best way to
allocate scarce resources. The resources may be raw materials, machine
time or people time, money, or anything else in limited supply. The "best"
or optimal solution may mean maximizing profits, minimizing costs, or
achieving the best possible quality. An...