Why and when do we prefer finite element analysis (FEA)?

In today's fast-paced world. There is more and more demand for better and high-performing devices/machines. This demands the design cycle to be shorter and faster and asks for more number of iterations for improvements. Doing real experiments in such a fast-paced world is time-consuming and costly. Hence analysis softwares are used to reduce the "design cycles".

The partial differential equations are used to describe the laws of physics for space-time-dependent problems. These PDEs give exact solutions to simple and basic problems. But it becomes almost impossible to solve PDEs analytically for geometries that are too complex. Hence to solve these phenomena, numerical methods are used iteratively until the required accuracy is achieved.

What are the applications of FEA?

The finite element method is used in the following cases:

Static Analysis

Fluid flows, Heat Transfer

Buckling

Maximum Stress in components

Electromagnetic phenomenon

Which parameter is fundamentally most important in the FEA solution?

Usually, when FEA is applied to structural problems, the most important fundamental parameter to calculate is displacement. Other derived quantities such as stress and strain can be calculated once displacement at each node is known.

What is discretization/meshing in FEA?

Everything in nature is continuous. It is very difficult to model continuous functions with the current computing power at hand. Hence, discretization methods are used. The discretization or meshing is nothing but a 'to divide and conquer' strategy applied to the geometries. The complex geometry is divided into smaller triangular, quad and hex elements and these elements are connected to each other at their nodes. Each quad element/cell has 4 nodes and each triangular element has 3 nodes.

Triangular and Quadrilateral Elements (2D elements)

On the other hand, in the case of 3D structures hex elements have 8 nodes and tetrahedron element has 4 nodes, pyramid element has 4 nodes and triangular prism element has 6 nodes.

3D Mesh Elements

Note: The above-mentioned elements are all first-order elements. In second-order elements, additional nodes are present on the edges in between end nodes.

The process of dividing the complex(continuous) geometry into small discrete elements is called discretization or meshing.

Below is an example of a simple T-shaped structure with and without mesh.

Why and when do we prefer finite element analysis (FEA)?In today's fast-paced world. There is more and more demand for better and high-performing devices/machines. This demands the design cycle to be shorter and faster and asks for more number of iterations for improvements. Doing real experiments in such a fast-paced world is time-consuming and costly. Hence analysis softwares are used to reduce the "design cycles".

The partial differential equations are used to describe the laws of physics for space-time-dependent problems. These PDEs give exact solutions to simple and basic problems. But it becomes almost impossible to solve PDEs analytically for geometries that are too complex. Hence to solve these phenomena, numerical methods are used iteratively until the required accuracy is achieved.

What are the applications of FEA?The finite element method is used in the following cases:

Static Analysis

Fluid flows, Heat Transfer

Buckling

Maximum Stress in components

Electromagnetic phenomenon

Which parameter is fundamentally most important in the FEA solution?Usually, when FEA is applied to structural problems, the most important fundamental parameter to calculate is

displacement. Other derived quantities such as stress and strain can be calculated once displacement at each node is known.What is discretization/meshing in FEA?Everything in nature is continuous. It is very difficult to model continuous functions with the current computing power at hand. Hence, discretization methods are used. The discretization or meshing is nothing but a 'to divide and conquer' strategy applied to the geometries. The complex geometry is divided into smaller triangular, quad and hex elements and these elements are connected to each other at their nodes. Each quad element/cell has 4 nodes and each triangular element has 3 nodes.

On the other hand, in the case of 3D structures hex elements have 8 nodes and tetrahedron element has 4 nodes, pyramid element has 4 nodes and triangular prism element has 6 nodes.

Note: The above-mentioned elements are all first-order elements. In second-order elements, additional nodes are present on the edges in between end nodes.

The process of dividing the complex(continuous) geometry into small discrete elements is called discretization or meshing.

Below is an example of a simple T-shaped structure with and without mesh.