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Finite Element Analysis: (Mesh)Free At Last!

Over the last fifty years, Finite Element Analysis (FEA) has become the predominant tool in engineering analysis, offered by virtually all Computer Aided Engineering (CAE) vendors and used in a majority of analysis and simulation applications. Yet, the acceptance and adoption of CAE tools has been slow, largely because they are still difficult to apply to realistic geometric models. By all accounts, the main culprit is not the FEA method itself, but the process of preparing geometric data in a form acceptable for FEA. Specifically, until now, all commercial FEA codes require that the geometric model be converted into a conforming mesh of elements via an expensive and heuristic procedure known as “meshing.” The resulting mesh is not intrinsic to the original geometric model, introduces additional errors, is expensive to compute, and affects the quality (or lack of it) in the FEA solutions. By definition, meshes must conform to the smallest geometric detail in geometric model, leading to excessively large meshes, and making accurate meshing impractical for any geometric model with small features or geometric errors.

The adopted industry-wide solution is to simplify the geometric model (for example, by smoothing or by removing blends and fillets), to defeature it (for example, by eliminating small holes and protrusions), and to heal and repair it (for example, gaps, self-intersection errors, tiny edges and surfaces, etc.). Unfortunately, these additional heuristic steps are only partially automated, and break the integration between geometric design and engineering analysis that now operate on two distinct loosely related geometric models. Many man-years and millions of dollars have been and continue to be invested into improving finite element meshing technologies. But it is important to recognize that the above limitations are intrinsic to all mesh-based approaches, and cannot be resolved by incremental improvements in meshing technologies. These very same limitations prevent wider adoption of finite element analysis in many scientific, engineering and consumer applications, ranging from engineering to art, architecture, and medicine – not because finite element analysis is difficult, but because the tedious and error prone process of data preparation and meshing make it impractical.

Scan&Solve™ was developed specifically to liberate FEA from the tyranny of meshing, while preserving most of the advantages of this classical and widely accepted method of engineering analysis. The basic idea is simple: create separate geometric and physical representations of the model in question and combine them only when necessary, without requiring expensive and error-prone data conversions and always using the most authentic representation available. The concept is illustrated below.


The analysis model is constructed on a (typically, but not necessarily) uniform orthogonal grid of space that initially knows nothing about the model being analyzed. It can be thought of as a 3D “graph paper”. The usual variety of basis functions may be associated with the vertices of this mesh. The geometric model exists in the same space, in its native unaltered form, and is not aware of the mesh surrounding it. The usual FEA procedure is then modified at run time to account for the existence of the geometric boundaries, restraints, and loads via the Scan&Solve™ process that eliminates or modifies the relevant finite elements. From the user perspective, the whole process is totally transparent and mesh-free, or more accurately “meshing-free”. See a short video demonstrating Scan&Solve™ application to a complex model with small features.

Now, you have a choice. (Mesh)Free at last!

Here is the comparison of the classical mesh-based FEA and Scan&Solve™ technology. If you want to know more technical details about the Scan&Solve™ technology, you can find them in this white paper.





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