FEA – Finite Element Analysis

FEA is a numerical method used for design analysis of complex engineering problems. This design analysis is done by first modeling the body and dividing it into equivalent finite (known) elements interconnected at nodes and/or boundary lines and/or surfaces, this process is also known as discretization. Further to which solutions are obtained by for each individual elements and then combined to get the results for the whole body.

In a more technical way, most engineering problems can be represented by as mathematical models which express the problems in terms of differential or integral equations. We face a problem of solving these equations because of complexity in geometry, boundary conditions and other real world problems. FEA is the procedure which we utilize to get us approximate solutions our engineering problems.

Engineering problems can be categorized as any case of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential.

Briefly, the solution for structural problems typically refers to determining the displacements at each node and the stresses within each element making up the structure that is subjected to applied loads. In nonstructural problems, the nodal unknowns may be in case of thermal analysis the temperature field or heat flux or in case of fluid flow the stream function or the velocity potential function.

The results are approximate because numerical methods make assumptions to defining the governing equations and getting their solutions. This is also a reason to not accept any FEA result blindly.

FEA is synonymously known as FEM (Finite Element Method).

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(Image: Idrasimulation)

For now we would be focusing on the application of FEA to the problems of structural analysis with background of solid mechanics.

FEA is generally used from a software package, which is installed on a computer. The FEA software has a user graphics interface where the required shape of the body can be modeled and properties can be assigned further to which the body is meshed i.e discretized or we can say that the geometry is defined. Further to which the loads acting on the body are applied and constrains are placed. This step can also be defined as preprocessing.

Now, that the geometry is defined and loads are applied the FEA application uses its solver component to define solutions for the discretized geometry and solve them for each individual element.

Finally the chosen results are displayed by the application by the post processing component of the FEA application. These results are interpreted by utilizing engineering judgment and iterations to the above problem.

Therefore FEA can be summed up as Defining Geometry – Applying Loads and Boundary Conditions – Solving – Interpreting Results.