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Engineering Analysis explained:

Problems that are linear in nature and relatively simple in geometry can be dealt with adequately using classical analysis methods, Hand calculations based on established formulae can be documented as a sufficient record when developing new designs. ABMech Design and Analysis Ltd will provide clients with such calculations when appropriate. When the problem is more complex and the factors of safety need to be less conservative it becomes necessary to employ computer-aided engineering (CAE), in the form of finite element analysis (FEA).

FEA works by subdividing the component or structure to be analysed into finite elements with assumed displacement behaviour and solving the resulting set of simultaneous equations by enforcing conditions of equilibrium and compatibility between each element. A finite element can represent a single entity, such as a structural beam, truss or column but commonly this is not the case. Commonly an element merely represents a small section of a complete component or continuous volume. Typically, finite elements can be long and thin (i.e. beams), flat or curved (i.e. plates) or solids, all three of which can be seen in the model of a folk guitar shown below.

As well as stress, structural, thermal and field problems finite element analysis can also be used to determine the natural (resonant) frequencies of structures and components together with their associated mode shapes, as illustrated in the pictures below; which show two of the characteristic resonances of the guitar body.