Intro to FEA

Notes taken from the following course: https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?id=20959&printable=1 and https://www.engr.uvic.ca/~mech410/lectures/FEA_Theory.pdf

What is FEA?

Finite element analysis is an extremely potent engineering design utility. It is a numerical method for solving problems of engineering and mathematical physics.

. What can it do?

FEA can simulate the following cases among others:

• Stress

• Strain

• Fluid Pressure

• Heat Transfer

• Temperature

• Vibration

• Sound Propagation

• Electromagnetic Fields

• Any of the above put together

To be more specific, it can handle any problems that have any/all of the following:

• Any mathematical or physical problem described by the equations of calculus.

• Boundary value problems and initial value problems.

• The domain of the problem may be any geometric shape, in any number of dimensions. Complicated geometries are as straightforward to handle as simple geometries, with the only difference being that the former may require a bit more time and expense. For example, a quite simple geometry would be the shape of a circular cylindrical waveguide for acoustic or electromagnetic waves (fiber optics). A more complicated geometry would be the shape of an automobile chassis, which is perhaps being analyzed for the dynamic stresses induced by a rough road surface.

• Physical properties may also vary throughout the system.

• The external influences, generally referred to as loads or loading conditions, may be in any physically meaningful form. The loads are typically applied to the boundary of the system (boundary conditions), to the interior of the system (interior loads) or at the beginning of time (initial conditions).

• Problems may be linear or non-linear.

So yeah…FEA can pretty much do anything, the website mentioned at the beginning has many, many. many more examples of how you can use FEA, if you would like to know the extremely specific, technical things it can do, refer to sections 1.1-1.4 from the above course.

Types of Finite Elements

Open

Examples:

Open

Basic Principles

Consider a body or engineering component where the distribution of a field variable is required, for example, displacement or stress. Some other examples could be a component under load, temperature subject to heat input, etc. The body is modelled as being hypothetically subdivided into small parts which we will call elements, i.e. finite elements. These elements are then assumed to be connected to each other but, only by way of interconnected joints which are known as nodes. Elements put together with nodes make what’s called a mesh (illustrated below).

The field variable is described throughout the body by a set of partial differential equations that are impossible to solve mathematically. Instead, what is done is that we assume the variable will act through/over each element in a predefined manner. This assumption could be, for example, constant, linear, quadratic, or a higher-order function distribution.

Process:

The following is a pictorial representation of the process of FEA:

Hints

• Don’t just rely on one run, refine the mesh and repeat two or three times.

• A good finite element model is about a 95% accurate solution of the field equations.

The following is the reality of the finite element model:

Summary:

The following is a condensed summary of the whole FEA procedure: