Elements in Finite Element Method and elements shapes

The Finite Element Method (FEM) is a numerical technique used in engineering to solve complex problems by dividing the physical domain into smaller, simpler elements. Each element is then analyzed separately, and the results are combined to provide an overall solution to the problem. In this blog, we will discuss the different types of elements used in the FEM, and how their shape affects the accuracy of the solution.

Types of Elements:

There are several types of elements used in the FEM, including triangular, quadrilateral, tetrahedral, and hexahedral elements. Triangular elements are used in 2D problems, while quadrilateral elements are used in both 2D and 3D problems. Tetrahedral elements are used in 3D problems, while hexahedral elements are used in both 2D and 3D problems. Each element type has its own advantages and disadvantages, and the choice of element depends on the problem being solved.

Element Shape:

The shape of an element is an important factor in the accuracy of the solution. In general, elements with a regular shape, such as triangles and squares, provide more accurate results than irregularly shaped elements, such as polygons. This is because irregularly shaped elements can cause numerical instabilities and introduce errors into the solution.

To reduce the error caused by irregularly shaped elements, a technique called mesh refinement can be used. Mesh refinement involves dividing the elements into smaller sub-elements, which reduces the size of the irregular regions and improves the accuracy of the solution. However, this technique also increases the computational cost of the analysis, as more elements are required to achieve the desired accuracy.

In addition to mesh refinement, other techniques such as adaptive meshing and element distortion correction can also be used to improve the accuracy of the solution when irregularly shaped elements are present.

Conclusion:

In conclusion, the choice of element shape is an important factor in the accuracy of the solution in the Finite Element Method. Regularly shaped elements provide more accurate results than irregularly shaped elements, but irregularly shaped elements can be used with techniques such as mesh refinement, adaptive meshing, and element distortion correction to improve the accuracy of the solution. As always, the choice of element type and shape depends on the specific problem being solved and the desired level of accuracy.