Research Beginings on the Finite Element Method

Specifically, the Finite Element Method or Finite Element Analysis is a system to take a complex problem and separate it into parts. From these smaller parts you can derive approximate solutions of each element and then combine the solutions and begin to a form an overall solution for the problem. The overall accuracy of FEA depends on the number of elements the problem was divided into, the assumptions made about the individual elements to derive a mathematical solution, and how the isolated elements were amalgamated into a coherent result.

Depending on the complexity of the problem there are steps for the finite method to follow so as to achieve the desired result, the more complex the problem, the more steps in the method. It is important to remember that much of finite element method can be defined in simple one-dimensional or two dimensional mechanical physics if the elements are divided properly1.

The first step is Idealization, or taking the problem and reducing the entire system into a simplified, physics model. In other words, taking the question and relating it to an already developed system of physics and mathematics.

The second step is Finite Element Discretization, decomposing the question into the required amount of elements to gain an accurate solution. Essentially this part is taking the mathematical or physics model that is used to represent the question and partitioning it into separate, more manageble parts.

Local Approximation or the Discrete Solution is the the third step. This is the mathematical portion of solving the individual parts by the sum of their forces (in mechanical physics models).

The final step is the Amalgamtion. This is taking all of the individual solutions and forming them into a single cohesive, overall solution. In other words, this is the assembly of all of the parts to answer the question.

It is important to note that there is a give and take relationship between step one and two as well as step two and three. If the mathematical model assumed to represent a part of the question is incorrect than the entire solution will also be incorrect, therefore it is important to be extremely precise in the suppositions made from step one to step two. On the other hand it is not always possible to know the specific amount of parts you need and the FE discretization step might need to be returned to on multiple occasions to gather the correct information needed. There is a certain amount of “guess and check” involved with the finite element method to gain a faithful solution.



FEM opens wide range of possibilities for architects and designers to analyze their projects before realization. Using softwares based on FEM one can predict how particular form will work and behave considering loads impact. One of the softwares based on the FEM is Abaqus.
Abaqus suite consist of Abaqus/Standard, Abaqus/Explicit, Abaqus/CAE. Abaqus Standard is applied to static, low-speed dynamic, or steady-state transport analisis; while Abaqus/Explicit may be applied to those portions of the analysis where high-speed, nonlinear, transient response dominates the solution. Using Abaqus CAE one can create geometry, import CAD models for meshing or integrate geometry – based meshes that don’t have associated CAD geometry.

The software is used by engeneers working in fields of aerospace & defense, automotive & transportation, industrial design such as furniture and packaging (including both the design and the production process), high-tech, industrial equipment, services industry, shipbuilding, power process & petroleum industry, life sciences, and of course in the field of architecture and construction.

The process of analysis using the Abaqus software is divided in three parts:
Phase 1 preprocessor, phase 2 processor, phase 3 postprocessor. All phases are described below.


Phase 1 preprocessor
The object of the preprocessor is to define the discrete model.
First the geometry which one wants to analyze, prepared in 3d (imported from other software as .stl or .igs file, or created in Abaqus) is simplified to the physical model. To get the discrete model one has to defined all the data such as mesh definition, material data, loads for the physical model. Those decisions influent on the precision and time taken for calculations of the part 2.
Finally one gets the input file (.inp) - text file - which contains the numerical description of the model.

The model is defined by:
ß geometry: defined by mesh based on the finite elements
Library of Abaqus let the user choose from 200-300 kinds of elements which will create the mesh from the analyzed surface. It is possible to change the size and amount of elements, it means the density of the mesh.

ß element section properties: complement information about geometry

ß material data

ß loads and boundary conditions

Two typical loads are: the concentrated load ( force [N] ) which defines the force impact on particular point of the mesh and the distribution load (pressure [Pa] ) which defines the pressure on the area of the mesh.

Boudary conditions define degrees of freedom for the geometry. Each point of the geometry has six degrees of freedom – three transitions and three rotations, considering x, y ,z axis.

ß kind of analysis : static (in Abaqus/Standard )or dynamic (in Abaqus/Explicit)


Phase 2 processor
It is the phase of calculations based on the input file. Adequate procedures are activated and the task is accomplished.
The program informs user of any problem or mistake of the input file. Some typical mistakes are “comma” instead of “dot” or “o” instead of “zero”.
Considering the complexity of the analysis the processor phase can take from few seconds up to several hours.
Outcome of the processor is described as text file or binary file.

Phase 3 postprocessor
That is the final part. It transforms the result of calculations into visual file such as pictures or animation. Abaqus/CAE also offers comprehensive visualization options which enable users to interpret and communicate the results of any Abaqus analysis.
The postprocessor part is really important considering communication between engineer and architect or designer, and communication between them and the client.