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The finite element method emerged from the aerospace industry after World War II. The need for lightweight, yet strong, structures and accurate stress analysis fueled its development along with technological advances in computing technology. Advancements in digital computers and programming languages fueled the development of FEM. R. W. Clough (1920—2016), a professor of structural engineering at the University of California, Berkeley, coined the term finite element method.

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The finite element method (FEM) is a numerical technique for finding approximate solutions to boundary value problems using a divide-and-conquer technique. A large problem is subdivided into smaller manageable pieces called finite elements that are then assembled into a larger system of discrete equations that represents the larger problem. Once the physical system is modeled by the larger system of equations, techniques from the calculus of variations are used to find an approximate solution over the entire domain by minimizing an error function. Though meanings of the acronyms FEA and FEM have become synonymous, FEM generally refers to the various approaches early innovators developed to transform a continuous domain into subsets of discrete sub-domains via elements; whereas, FEA refers to the application of the various FEM techniques to solving problems found in engineering, mathematics, and physics.

The finite element method is versatile and can be applied to many problems including acoustics, heat transfer, fluid flow, lubrication, electric and magnetic fields, and many others. When an analytical solution cannot be obtained, the FEM is suitable for problems with complicated geometry, loading conditions, or different material properties. The finite elements create a mesh over the solution domain. The mesh can contain mixed element types or material properties. Especially true in structural mechanics, the finite element mesh closely resembles the actual physical structure. The model represented by the discrete elements is not simply an abstraction.

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The FEM falls under the umbrella of computer aided engineering: the use of computer software to aid in engineering analysis. Problems that were previously intractable can now be solved. Companies often turn to FEM to remain competitive. As hardware and software becomes more affordable, general-purpose FEM is becoming more integrated into computer aided design software (CAD). In CAD software, the FEM software is an additional cost. Many analysis programs are now available, public domain or proprietary, general-purpose or narrow, for lease or purchase.

FEM substantially reduces the time required to develop products through the many steps from conception all the way to production. FEM is used for visualizing stiffness and strength response and in minimizing the weight, materials, and costs of products. FEM allows entire products to be constructed virtually, refined, then optimized before a design is prototyped before committing to mass manufacture. Benefits of FEM include increased safety, better design and insight into critical design parameters, virtual prototyping, fewer hardware prototypes, a faster and cheaper design cycle, increased productivity, greater reliability, and increased revenue.

Engineers at REDI are licensed to practice engineering. REDI employs a team of highly qualified and skilled mechanical engineers. For more information about the computer aided engineering (CAE) services we offer or the states in which we’re licensed, contact us today.