Traditionally, engineering problems were solved using massive calculations made by hand by a usually large team of engineers. Some problems, however, were so complex that they simply could not be solved by hand, leading to the development of a numerical method-based approach called Finite Element Analysis (FEA). **Autodesk FEA**, while greatly reducing human effort and error, introduced a new type of error –approximation. **Engineers using finite element analysis now had to decide** what level of solution accuracy would be acceptable, and whether that degree of accuracy would justify the increased computational time.

## How to quantify the balance through finite element mesh

The most common way to quantify this balance is **through the finite element mesh**, specifically the number of elements and the mesh convergence rate. In general, **a higher element count leads to greater solution accuracy**. This is because more nodes are available to more accurately represent the geometry and for calculating the results. In most problems, refining the mesh beyond a certain point leads to very small, if any, changes in the solution, while significantly increasing solve time. The mesh is said to have converged at this stage and the solution is called a mesh-independent solution.

*Solve time and Vertical Deflection vs Number of Elements. Solve time exponentially increases after a certain number of elements with no significant effect on the solution. This is a mesh-independent solution. [1]*

The **reduction of computation time** can be quite challenging, especially with complex designs, interacting parts and advanced materials. Some commonly used techniques include:

- Altering mesh size
- Rigid body constraints
- Symmetry

### Altering mesh size

The most common way to reduce the computational time is to **modify the mesh parameters**. A fine mesh (high mesh density) automatically means increased computational time, while a mesh that is too coarse (low mesh density) may not accurately capture the behavior of the design. A good approach to achieving this mesh balance is to refine the mesh in the most critical areas of the design, and to use a coarser mesh in areas that are not critical in determining design performance.

**Having different mesh densities at different regions** of the model can significantly impact the computational time, and potentially improve the accuracy of the overall result as well.

This approach is illustrated in the images below. Here, we have a tire rolling on a pavement, where the only regions of interest are the ones in the path of motion of the tire. Accordingly, the mesh has been locally refined in those regions and the rest of the pavement has relatively coarse elements.

The expected path of the tire on the pavement has finer elements than the surrounding regions.

### Rigid Body Constraints

A good way to reduce the simulation time without affecting the results need out of the simulation is by **defining rigid bodies constraints in the model**. These rigid body defined sections of the model require relatively less simulation time since the deformations of these sections are not calculated. For example, consider the same tire example, **where the focus is understanding the interaction between the tire and pavement**. The tire is assembled over a rim, but the deformation of the rim is not relevant to the problem objectives. So, the rim may be defined as a rigid body to reduce the time taken to solve the finite element problem.

### Symmetry

One of the easiest and most effective ways to reduce the computational time is to **simulate symmetric sections of the design**. Most structures and their loads are symmetric, usually about a plane, line or axis. A big advantage of identifying symmetric geometry is the simplification of the associated FEA problem, thus reducing the problem run time.

The most important considerations for using symmetry are the nature of the load and the material orientation. For example, in the beam structural problem below, symmetry can be used to model half the beam only because the following constraints are known:

- The rotation at the center of span is zero
- The vertical displacement on both sides of the cut are identical
- The lateral displacement on both sides of the cut is zero

*Symmetric beam structural response [2]*

**Conclusion**

The use of **simplification tools for FEA began** as a workaround to the **limited computing power available on old computers**. That limitation has entirely been reversed now, with **dual and multi-core processing almost becoming the norm**. The use of these simplification techniques can now cut run-times in the design cycle from days to hours, which opens the door to more design exploration, and design iterations can be simulated and compared side by side. Design simplification and exploration, when done efficiently, can truly be leveraged as a competitive advantage to make better products.

Learn more about Autodesk Simulation with FEA here.