Finite Element Analysis (FEA) is a powerful tool that enables engineers to gain a deep understanding of how any given structure responds to external loads, combined with an appreciation of how these loads flow through a structure. This understanding helps them to then identify areas of local, high stress.
Despite this value, outside structural engineering circles, it is also one of the least
understood areas of engineering analysis. This misunderstanding is two fold:
• how does FEA do what it does?; and
• how can it add value to a project?
Addressing the first question, FEA works by building a representative numerical model of a structure. In every case, this model is an approximation of the real thing, often thought of in terms of how it is portrayed on screen.
It is important to realise that this is just a visualisation of the underlying numerical model made up, in the simplest sense, of four main sections, namely:
- Element list
- Nodal co-ordinates list
- Connectivity section
- Load cases section
The element list consists of a library of standard elements (nodes, beams, plates, 3D brick elements etc). These standard elements are typically referred to repeatedly and are stored in a “lookup table” of one form or another. This lookup table, in its simplest form, assigns each element a unique number, alongside various properties such as thickness, section properties, material assignment etc.
The nodal co-ordinates list details all the points in space that represent a position where one element connects to another or to a point that represents the model boundary (foundation, anchor point on a ship, interface with a large structure etc).
The connectivity section assigns how nodes are connected to each other and which element is to be assigned to that connection, for example node 1 is connected to node 3 via a beam 2 from the element list. It also allows the restraints on nodes to be specified, for example node 2 is rigidly connected to a foundation and so cannot translate in x, y or z directions and is also not free to rotate about any of these same 3 axis.
The final section, load cases, specifies how the loads are to be applied and where. So, for example, load case 1 has a force of 10kN applied in y direction to node 4 and load case 2 has a force of 10kN applied in the z direction to node 5 etc.
The number of elements used to describe any one given structure is driven by the mesh size which drives cost of building the model (modelling) and analysing the output (post processing) measured in man hours. Once all this has been specified either in a text file (if you are old enough to remember doing it this way) or via a more modern graphical user interface, the connections and element properties are arranged into a stiffness matrix. The power (or magic) of matrix algebra is then harnessed to solve thousands and thousands of simultaneous equations to ultimately tell us how the structure reacts to the applied load. It is a common misconception that the key output is structural stress. It is in fact structural deflection, and this is then turned into a stress plot and visualised on the screen.
By understanding the key fact that the analysis is centred on stiffness rather than stress, the power of FEA becomes apparent, suggesting, as it does, how it may be practically used in a heavy lift project where timeliness and applicability of any engineering is key.