The Principle Of Energy Minimisation In Finite Element Analysis

Do you know what PDE is? To begin with, it is the description of the laws of physics for time and space that often faces a number of problems. The problems are expressed with the help of partial differential equation or PDE. There are a vast majority of geometrical problems and thus, PDEs cannot be solved without analytical methods. So based on the discreditisation, an approximate equation can be constructed to figure out the flaws and engineering disadvantages in a mechanical structure.

Now these discreditisation methods are often expressed with numerical model equations that cannot be comprehended by common people. This is the reason why these equations are simplified through the process of FEM or finite element method.

Understanding the principle of energy minimisation

It is the principle of energy minimisation method that forms the ultimate backbone of the Finite Element Analysis. To make it simpler, whenever a particular boundary condition is applied on a given body or material, it leads to a number of configurations that may prove to be disadvantageous for the same. Therefore, to figure out the appropriate configuration for the substance, FEM is utilised with the process of energy minimisation. However, the simulation may appear to be same even after multiple equations. Do you know why?

The reason is the principle of minimisation of energy. According to its rules, when a boundary condition like displacement or force is applied on the material for a number of reasons, the configuration of the body takes the minimum energy and thus, gives the appropriate reading of the geometrical flaws.

The history of the finite element method

Finite element method has been in the use since the 16th century. However, there are reports that the earliest mathematical papers on FEM belong from the works of Schellback in the year of 1851 and Courant in 1943.

Basically this process of analysis was independently developed by various engineers to determine structural mechanical problems that relates to aerospace and civil engineering. The process of FEM has been further developed in the mid 1950s which kept improving with significant difference in the years 1956, 1957, and 1972.

Multiphysics Modeling that is suited for finite element analysis

FEA provides greater degrees of freedom to multiphysics modeling and thus, accuracy is expected to reach to the tip. However, with the advancements of computers and analysis, achieving this goal is not a problem.

If you want a successful FEM process for your mechanical project, it’s best to hire professional engineers who are trained enough in this sector.


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