The method of elements up to (MEH) is a numerical technique used to find the immediate solution of the partial differential equation. In engineering context, MEH is often used to analyze physical structure behavior such as buildings, bridges, machines, and electronic components.

How does it work?

1. Discretization: Complex structures are divided into smaller elements. This element could be a triangle, a rectangle, or any other shape, depending on structure geometry.
2. Function aproxification: In every element, the variable that we want to analyze (for example, displacement, voltage) is assumed to have a specific shape, like a polynomial.
3. Element equation: The differential equation that regulates structure behavior is converted into an algebra equation system for each element.
4. Assembling: The algebra equation of all elements combined into one big system of equations representing the entire structure.
5. Completion: This huge system of equations was then solved numerically using the computer to get variable values at any node point.

Exclusive Methods Element Up

• Geometric Flexibility: MEH can be used to analyze structures with a very complex form of geometry.
• High accuracy: By dividing the structure into smaller elements, the analysis's accuracy can be improved.
• Non-Linear Analysis: MEH can be used to analyze nonlinear behavior of materials and structures.
• Visualize: Analytic results can be graphically visualized, making them easy to interpret.

Element Methods Applications Up

• Civil Engineering: Analysis of structure, bridges, dams, etc.
• Engineering: Analysis engine components, plane skeletons, etc.
• Biomedical: Scrambled bones, organs, and implants.
• Geoteknik: Ground analysis and foundation.

Applied Example

For example, to analyze the voltage on a loaded beam, the beam structure will be divided into multiple elements of the trunk. Each bar element is assumed to be linear deformation. By using MEH, we can calculate the voltage at any point in the beam and plot the distribution of the voltage.

MEH Software

There's a lot of commercial and open@@

• ANSYS: One of the most popular MEH software, used widely in various industries.
• ABAQUS: Known for its ability to analyze nonlinear and complex problems.
• NASTRAN: A lot of software used in the aerospace industry.
• OpenFOAM: The open-source software is very flexible and strong.

Conclusion

The method of elements up to is a very powerful tool in numerical simulations. With his ability to analyze complex structures, MEH has become an irreplaceable tool in various fields of engineering.

Source: Bathe, K. J. (2006). Finite Element Procedures. Prospective Hall.