Fundamentals of finite element method CAE analysis and application to strength design

Introduction to Finite Element Method (FEM) in CAE Analysis

The finite element method (FEM) is a powerful computational technique used in computer-aided engineering (CAE) analysis.
It is designed to solve complex structural, thermal, and electromagnetic problems by subdividing a large system into smaller, simpler parts called finite elements.
These finite elements are interconnected at points known as nodes.

By breaking down a complex problem into manageable elements, engineers can simulate real-world conditions with great accuracy.
FEM is widely employed in various industries, including aerospace, automotive, civil engineering, and consumer electronics.

Understanding the Fundamentals of FEM

To effectively use the finite element method, it is imperative to comprehend its basic principles and components.
This understanding enables engineers to apply FEM analysis to design processes efficiently, enhancing product quality and performance.

Discretization of the Domain

One of the primary steps in FEM is the discretization of the domain.
This process involves dividing a complex geometry into smaller elements, which can be of various shapes such as triangles, quadrilaterals, tetrahedrons, or hexahedrons.
The choice of element shape and size significantly impacts the accuracy and computational cost of the analysis.

Different types of elements are used depending on the nature of the problem.
For instance, 1D elements are used for line-like structures, 2D elements for surface structures, and 3D elements for volumetric structures.

Formulation of Element Equations

Once the domain is discretized, the next step is formulating the element equations.
This involves creating mathematical models that capture the behavior of each element based on governing equations, such as the equations of motion, heat conduction, or electromagnetic field equations.
Each element is governed by these localized equations, derived using principles from physics.

Assembly of Global System Equations

The locally defined element equations are then assembled into a global system of equations.
The global equations take into account the interconnectivity of the elements through the shared nodes.
The objective is to represent the entire structure or system in terms of these assembled equations.
In solving the global system, boundary conditions and initial conditions are also incorporated to ensure the results are applicable to the real-world scenario.

Solution of the Global System

Solving the global system of equations is a critical step in FEM analysis.
Typically, numerical methods, such as the Gaussian elimination or iterative solvers, are used to find approximate solutions to these equations.
The accuracy of the FEM solution depends on the numerical method employed and the quality of the discretization.

Application of FEM in Strength Design

The finite element method is extensively applied in the strength design of components.
By simulating the performance and behavior of a product under various loads and conditions, engineers can optimize designs to ensure durability, safety, and compliance with standards.

Structural Analysis

Structural analysis is one of the most common applications of FEM in strength design.
By analyzing the stresses and deformations of structures under different loads (such as forces, pressures, or moments), engineers can identify potential failure points and redesign the structure to enhance its strength and stability.

Thermal Analysis

In thermal analysis, FEM is used to study how heat transfer affects a structure or component.
It helps in predicting temperature distributions, identifying thermal hotspots, and optimizing thermal management strategies.
This is particularly important for components subjected to high temperatures or significant thermal cycles.

Vibration Analysis

Vibration analysis is essential in ensuring that components remain stable under dynamic conditions.
By using FEM, engineers can evaluate the natural frequencies and mode shapes of a component, preventing resonance phenomena which can lead to catastrophic failures.
This application is particularly crucial in the design of mechanical systems, automotive parts, and aerospace components.

Fatigue and Fracture Analysis

FEM is also valuable in predicting the lifespan of components subjected to cyclic loading, known as fatigue analysis.
Engineers can simulate the propagation of cracks and potential fracture points, allowing for proactive design improvements.
This type of analysis is critical in industries where component failure can have severe safety or financial repercussions.

Conclusion

The finite element method is an indispensable tool in computer-aided engineering analysis and strength design.
Its ability to provide accurate simulations of real-world behavior makes it invaluable in various industries, enhancing product performance, safety, and reliability.
By mastering the fundamentals of FEM, engineers can effectively apply this method to tackle complex design challenges and innovate in their respective fields.