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# What is simulation by finite element calculation? Why should my company invest in a simulation?

**Simulating consists of virtually modelling the behaviour that a system would present under certain conditions.** This system can be a prototype of an industrial design and the fluids that circulate through it, several solids in contact, different fluids mixing in a container and, ultimately, any group of present elements in an engineering problem.

**When we talk about behaviour in this area, we usually refer to the magnitude of certain variables, **either in a steady or a variable dependent state. These variables can be the body position over time, its speed, pressure, energy, temperature or more commonly in the field of structural engineering, the deformation or total stress suffered by a certain element under loads, among many others.

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## Introduction to finite element calculus.

Any modelling of a physical behaviour in a virtual environment is based on solving a mathematical problem of greater or lesser complexity. There are many techniques and software to solve specific problems, finite element method is only one of them.

Unlike analytical methods, which make it possible to reach an exact solution to a problem such as the resolution of the mass and energy balance equations of a chemical plant, **this method consists of reaching an approximate solution with a certain degree of precision.** The great advantage offered by finite element calculus is that it allows solving problems whose analytical solution is not possible to know, as is the case with solutions based on empirical techniques, only that the latter, in order to be achieved, require the construction of a real prototype.

## The finite element method.

**The method based on finite elements consists of decomposing an unsolvable continuous problem, associated with a known geometry, into a multitude of discontinuous but solvable problems,** applying the relevant equations and a subsequent assembly of all of them to reach the final solution. The degree of precision of a finite element simulation will depend to a great extent on the number of divisions into which the problem has been decomposed, their morphology, the amount of available starting data, the amount and plausibility of simplifications that have been made and finally the time and computing power available for its resolution. The more resources are used in solving this type of problem, the bigger and better divisions can be made, and the greater number of iterations can be solved before reaching the definitive solution.

**Each of these divisions receives the name of element and the set of all of them the mesh.** To create them, control algorithms are usually applied that, starting from a geometry normally obtained through assisted design, allow the creation of a suitable mesh to achieve a precise solution depending on the nature of the problem. Generally, the mesh will be adequate when the final solution to the problem does not vary significantly by reducing the size of the elements that make it up, its elements do not present singularities and the elements meet a series of determined morphological quality characteristics, among other aspects.

**Once a mesh is available, the corresponding equations to each of the elements are applied.** For this task, it must be defined the resolution method, boundary conditions, data relating to the materials present in the system, forms of contact between those elements that belong to different geometries and other particularities that will depend on each specific case. Finally, an algorithm is configured to reach an adequate solution and, at the same time, that the process is convergent and efficient.

**After reaching the resolutions of the equations in each of the elements of the mesh, a post-processing is carried out so that the analysis of the final solution of the complete system is possible,** which again requires the configuration of specific algorithms to it.

By means of this technique, so many different problems can be solved that there is neither a specific mesh size considered as generally valid nor a specific resolution time, so that sometimes these simulations can take minutes, hours or even days to be completed.

## The benefit of simulating by finite element computation.

Although a priori the cost of carrying out a simulation using finite elements may seem high, since in certain cases it is associated with the use of expensive specific software licenses and the investment in time of the entire process, the truth is that on many occasions it is not it is against the benefit of carrying them out.

A great advantage of the finite element method is that, starting from an initial simulation properly carried out, it is possible to modify the design of the initial prototype without greatly affecting the configuration of the algorithms used to reach the initial solution. **This allows you to analyse how each design modification affects quickly, safely and at a much lower cost than conducting experimental tests.**

For this reason**, the simulation using finite elements is complementary to the experimental tests, since it is highly recommended to carry out in a virtual environment all the tests that are considered appropriate until an optimized prototype is reached** and finally to test this prototype in the workshop for its subsequent certification or commercialization.

On other occasions, a finite element simulation can be carried out using free software or in a few hours if you have the appropriate knowledge and data, so **it can serve as support for the design calculations for each specific project at low cost.**

Therefore, whatever the size of your company or the size of the project to be carried out, simulations using finite elements can contribute to save money in design costs, improvement of designs or the verification of engineering calculations.