The finite element method is a numerical method that can be used for the accurate solution of complex engineering problems. The method was first developed in the mid-1950s for the aircraft industry. During this time it was primarily being used for the structural analysis of aircraft components. In a few years following, the scientific and engineering communities started to realize the full implications of FEA modeling.

Some stress related problems involving various forces and material property elements are very difficult to solve depending on complexity of the geometry. For problems such as this it is not possible to solve for an analytical solution. These analytical solutions generally require the solution of complex differential equations, which are non-obtainable, except in theory.

The finite element formulation of the problem results in a system of simultaneous algebraic equations for solution, rather than requiring the solution of differential equations. In the FEA method, instead of solving the problem for the entire body in one calculation, equations are developed for each finite element and then they are combined as a system where they can be iteratively solved by a computer.

With the advancement of computer technology and processing power, FEA has become the tool of choice for many types of analysis. FEA is used to save cost and analyze stress in bodies with complicated geometries and loadings. Special problems such as modeling the stress on elliptical vessel heads lends itself well to FEA modeling. Refer to the FEA vessel model to the right as an example.

• Structural Analysis/Optimization

• Thermal Analysis

• Fatigue Crack Propagation

• Mechanical Simulation

• Dynamic Analysis

• Vessel Optimization Analysis

• Pipeline Stress Analysis

• Vibration Analysis

ASME Stress Analysis