Finite element analysis

Finite element analysis (FEA) is the modeling of products and systems in a virtual environment, for the purpose of finding and solving potential (or existing) structural or performance issues. FEA is the practical application of the finite element method (FEM), which is used by engineers and scientist to mathematically model and numerically solve very complex structural, fluid, and multiphysics problems. FEA software can be utilized in a wide range of industries, but is most commonly used in the aeronautical, biomechanical and automotive industries.

A finite element (FE) model comprises a system of points, called “nodes”, which form the shape of the design. Connected to these nodes are the finite elements themselves which form the finite element mesh and contain the material and structural properties of the model, defining how it will react to certain conditions. The density of the finite element mesh may vary throughout the material, depending on the anticipated change in stress levels of a particular area. Regions that experience high changes in stress usually require a higher mesh density than those that experience little or no stress variation. Points of interest may include fracture points of previously tested material, fillets, corners, complex detail, and high-stress areas.

FE models can be created using one-dimensional (1D beam), two-dimensional (2D shell) or three-dimensional (3D solid) elements. By using beams and shells instead of solid elements, a representative model can be created using fewer nodes without compromising accuracy. Each modeling scheme requires a different range of properties to be defined, such as:

  • Section areas
  • Moments of inertia
  • Torsional constant
  • Plate thickness
  • Bending stiffness
  • Transverse shear

To simulate the effects of real-world working environments in FEA, various load types can be applied to the FE model, including:

  • Nodal: forces, moments, displacements, velocities, accelerations, temperature and heat flux
  • Elemental: distributed loading, pressure, temperature and heat flux
  • Acceleration body loads (gravity)

Types of analysis include:

  • Linear statics: linear analysis with applied loads and constraints that are static
  • Nonlinear statics and dynamics: effects due to contact (where one part of the model comes into contact with another), nonlinear material definitions (plasticity, elasticity, etc.) and large displacement (strains that exceed small displacement theory that limits a linear analysis approach)
  • Normal modes:natural frequencies of vibration
  • Dynamic response: loads or motions that vary with time and frequency
  • Buckling: critical loads at which a structure becomes unstable
  • Heat transfer: conduction, radiation and phase change

Typical results calculated by the solver include:

  • Nodal displacements, velocities and accelerations
  • Elemental forces, strains and stresses

Benefits of FEA

FEA can be used in new product design, or to refine an existing product, to ensure that the design will be able to perform to specifications prior to manufacturing. With FEA you can:

  • Predict and improve product performance and reliability
  • Reduce physical prototyping and testing
  • Evaluate different designs and materials
  • Optimize designs and reduce material usage