What is Finite Element Analysis? FEA Explained

Summary

In this introductory session on Finite Element Analysis (FEA), John from Pro Dake Labs explains the fundamentals of FEA, including its meaning, applications, and how it works. FEA is a numerical method widely used in various fields like structural analysis, solid mechanics, dynamics, thermal analysis, and electrical studies. The session covers key concepts such as boundary conditions, solid objects, and FEA assumptions related to geometry, material properties, boundary conditions, and fasteners. John also discusses the general procedure of FEA, from defining the problem to post-processing the results, providing a comprehensive understanding for beginners.

Takeaways

• 😀 FEA (Finite Element Analysis) is a numerical method used to solve complex engineering problems, including multi-physics challenges.
• 😀 FEA can be applied in various fields, such as structural analysis, solid mechanics, dynamics, thermal analysis, CFD, and electrical analysis.
• 😀 FEA originally focused on solving solid mechanics problems, but it now extends to other areas like fluid dynamics and electrical signal propagation.
• 😀 The basic FEA process involves breaking down the problem into smaller elements, solving for unknowns, and assembling the results.
• 😀 Solving FEA problems requires a numerical approach since finding an exact solution for partial differential equations is nearly impossible.
• 😀 FEA approximates solutions by dividing the model into smaller sections and using simple functions to estimate the results.
• 😀 The accuracy of FEA results improves as the mesh size becomes finer, reducing the error percentage.
• 😀 The general procedure of FEA includes: defining the problem, pre-processing (material properties, meshing, boundary conditions), solving (using approximate functions and solving equations), and post-processing (visualizing and explaining results).
• 😀 Assumptions in FEA include simplified geometry, linear material behavior, and negligible effects of environmental factors like humidity or corrosion.
• 😀 Key assumptions also cover boundary conditions, such as assuming small displacements, neglecting friction, and considering interfacing components as rigid.

Q & A

What does FEA stand for, and what is its main purpose?

FEA stands for Finite Element Analysis. It is a numerical method used to solve complex engineering problems, especially in solid mechanics, fluid dynamics, thermal analysis, and multi-physics simulations. It helps in approximating the behavior of physical systems under different conditions.

What are some areas where FEA can be applied?

FEA can be applied in various fields, including structural analysis (e.g., bridges, oil platforms), solid mechanics (e.g., gears, automotive powertrains), dynamics (e.g., vibrating structures, bullet impact), thermal analysis (e.g., PCB boards, heat radiation), and CFD (computational fluid dynamics) for fluid flow analysis.

How is the problem solved in FEA?

In FEA, mathematical equations are used to find approximate solutions to problems. These equations often consist of partial differential equations, and an exact solution is difficult to obtain. Instead, FEA provides an approximation to the exact solution through numerical methods.

What is the process of applying FEA to a problem?

The process includes defining the problem (converting a real-world engineering issue into an FEA problem), pre-processing (defining material properties, meshing, and applying boundary conditions), solving the equations (using FEA theory), and post-processing (visualizing and explaining the results).

What is the importance of mesh size in FEA?

The mesh size is crucial in FEA. A finer mesh (with more sections) leads to a more accurate solution as it reduces the error in the approximation. As the number of divisions increases, the percentage of error decreases, resulting in more precise results.

What are the key assumptions related to geometry in FEA?

Key assumptions include that displacements will be small for linear solutions, stress behavior outside the area of interest is not significant, and only internal features in the area of interest are included. External features that don't affect stiffness or performance are omitted.

How does FEA handle material properties?

FEA assumes that material properties remain within the linear region, and the non-linear behavior is not accounted for. Additionally, the material properties are considered unaffected by load rate, surface imperfections, and environmental factors like temperature and humidity.

What assumptions are made regarding boundary conditions in FEA?

FEA assumes that displacements are small, meaning the magnitude, orientation, and distribution of loads remain constant during deformation. Frictional losses are considered negligible, and all interfacing components are assumed rigid.

What assumptions are made regarding fasteners in FEA?

FEA assumes that residual stresses due to fabrication, pre-loading of bolts, welding, or other processes are neglected. All welds between components are considered ideal and continuous, and failure of fasteners is not considered.

How does FEA approximate the solution to an integral equation?

FEA approximates the solution by dividing the interval of integration into sections, using a constant function at the midpoint of each section, and summing the products of the function and the section lengths. This gives an approximate solution to the integral, with finer divisions improving accuracy.