Finite element analysis (FEA)

Numerical techniques such as the finite element analysis (FEA) method are available when closed form solutions prove inadequate. Numerical methods take a greater amount of time to prepare and solve than closed form solutions, however, they are becoming more accessible to design engineers and several packages are available for PCs. FEA is based on discretising the actual geometry of the structure using a collection of finite elements, thus facilitating solution. FEA is used in many design and analysis situations, especially when one or more of the following factors is present:

• Complex geometry
• Complex boundary conditions
• Complex loading
• Detailed failure analysis is required
• Loading is dynamic
• Non-linear effects are important

Key to successful application of FEA for analysis of composite structures, is the need for accurate materials data. It is possible to model composite structures either on a laminate level or on a ply by ply basis. Linear elastic material models are used in most packages. It is necessary to carry out mechanical tests to determine the properties of the basic lamina when these are not known. Laminate test data can also be used when modelling complete laminates. These data can also be obtained from the lamina properties and the application of laminated plate theory.

The effects and limitations of different elements should be assessed before starting any analysis and the user should be aware that mapped meshing (controlled meshing) techniques are required in many situations. These factors should be assessed before selecting any new FEA package.

Many properties and parameters must be defined when using FEA and therefore the scope for potential errors is large. Potential pitfalls include:

• Incorrect use of co-ordinate systems
• Incorrect definition of boundary conditions
• Incorrect / incomplete definition of material properties

Failure criteria to compare the output of FEA solutions must be selected carefully and the results should be verified against simplified closed form solutions and ideally, against mechanical testing of the modelled component.