Understanding Mesh Methods in Ansys Mechanical: A Comprehensive Guide

The mesh is the backbone of every finite element analysis (FEA) simulation. It divides your geometry into discrete elements, allowing Ansys Mechanical to approximate the behavior of your model under various conditions. A well-constructed mesh ensures accurate, reliable, and computationally efficient results, while a poorly constructed one can lead to errors, convergence issues, or unnecessarily long solve times.

Let’s explore why the mesh matters, its key considerations, and the benefits of using the different mesh methods available in Ansys Mechanical.

Why Is the Mesh Important?

The mesh is critical in finite element analysis (FEA) because it defines how the geometry of your CAD model is divided into smaller, discrete elements, each of which represents a portion of the model's physical domain. These elements have different shapes, sizes, and characteristics that influence how well they approximate the geometry and physical behavior of the model. The accuracy, efficiency, and reliability of your simulation results are heavily influenced by the type and quality of the mesh.

Understanding the different mesh methods in Ansys Mechanical helps you achieve the desired element shapes, sizes, and quality to ensure your simulation meets its objectives. Below is a detailed discussion of how the mesh works, why it is so important and how element characteristics affect your analysis:

1. Breaking the CAD Model into Elements

• Element Shapes:
  • Tetrahedral (Tet): Pyramid-like elements that adapt well to complex geometries.
  • Hexahedral (Hex): Cube-like elements that provide higher accuracy and convergence for structured regions.
  • Wedges and Pyramids: Used in transitional areas between hex and tet regions.
  • Shell and Beam Elements: Specialized for thin or slender structures.
• Element Characteristics:
  • Size: Smaller elements provide greater detail but increase computational cost.
  • Order: Linear elements are computationally efficient but less accurate, while quadratic elements offer higher precision by including mid-side nodes.

2. Pros and Cons of Different Element Shapes

The choice of element shape depends on the geometry, the type of analysis, and the desired balance between accuracy and computational cost.

3. Accurate Representation of Geometry

The mesh determines how closely the discrete elements represent the physical geometry of the model.

• Complex Shapes: A refined mesh is essential for accurately capturing intricate details, curved surfaces, or small features.
• Stress Concentrations: High-quality meshes ensure critical regions like fillets, holes, or sharp edges are resolved accurately, where stress concentrations are likely to occur.
• Contact Interfaces: In simulations involving contact (e.g., bolted joints), the mesh plays a crucial role in ensuring contact pressures and frictional forces are accurately calculated.

4. Numerical Accuracy and Convergence

FEA is based on solving differential equations over discrete elements, and the mesh dictates the granularity of this approximation.

• Element Size and Distribution: Smaller elements in regions of high stress gradients or complex features improve accuracy. Larger elements can be used in less critical areas to save computational resources.
• Convergence Studies: As the mesh becomes finer, the solution approaches the exact result (if the model and physics are correct). Conducting a mesh refinement study ensures that your results are independent of the mesh density.

5. Degrees of Freedom (DOF)

Each node in the mesh introduces degrees of freedom (DOF), which are the variables solved for in the analysis (e.g., displacements, temperatures).

• Linear Elements: Can be any of the shapes listed above, but only have nodes at their respective vertices (ie, the corners). Provide fewer DOF but may oversimplify results, especially in curved or nonlinear scenarios.
• Quadratic Elements: More complex elements which include mid-side nodes, increasing the total number of DOFs, but allowing the model to capture features like deformation and stress gradients more accurately.
• Impact on Solve Time: While a finer mesh increases the number of DOFs and generally improves solution accuracy, it also raises computational demand. An optimal mesh balances these factors.

6. Stress Gradient and Singularities

• Capturing Gradients: A well-refined mesh can resolve stress gradients effectively, critical for identifying failure points, especially in fatigue or fracture analysis.
• Avoiding Singularities: Poor-quality meshes or overly coarse elements can lead to stress singularities, where stresses appear artificially high due to the mesh, not the actual physics.

7. Element Quality Metrics

Mesh quality impacts both numerical stability and result accuracy. Common metrics include:

• Aspect Ratio: Ideal elements are nearly equilateral or isotropic. Highly stretched elements can lead to inaccuracies.
• Skewness: Measures how distorted the element shape is; lower skewness indicates better quality.
• Jacobian Ratio: Ensures elements maintain consistent shape when mapped into the model geometry.

8. Solver Performance and Stability

• Efficient Computation: An optimized mesh reduces the number of elements without compromising accuracy, saving computation time and memory.
• Avoiding Convergence Issues: Poor-quality meshes can lead to solver instability, requiring additional iterations or failing to converge altogether.

9. Physics-Specific Needs

Different analyses require different mesh considerations:

• Structural Simulations: Accurate stress and strain predictions depend on element types (e.g., hex for solids, shells for thin structures).
• Thermal Analysis: Capturing temperature gradients requires fine meshing near heat sources or boundaries.
• Fluid Simulations: CFD demands refined meshes near walls (boundary layers) to capture turbulence and flow behavior accurately.

10. Impact on Multiphysics Simulations

For multiphysics simulations (e.g., fluid-structure interaction, thermal-stress coupling), the mesh must align with the requirements of all involved physics.

• A poor mesh in one domain (e.g., fluids) can degrade results in the coupled domain (e.g., structural).
• Ensuring compatible meshes across physics domains minimizes interpolation errors and enhances solution fidelity.

Mesh Methods and Their Benefits

Choosing the right mesh method is crucial for achieving a balance between simulation accuracy, computational efficiency, and ease of setup. Each mesh method in Ansys Mechanical is tailored to specific geometry types and analysis requirements, offering unique advantages depending on the shape and complexity of your model. By understanding these methods and their benefits, you can select the most suitable approach to ensure your mesh meets the demands of your simulation. Below, we explore the available mesh methods and the strengths they bring to your analyses.

1. Automatic Mesh

Description:
The automatic mesh method lets Ansys determine the best meshing approach based on your geometry and simulation type. It’s a combination of the tetrahedral method and sweep method. It will automatically identify sweepable bodies and create a swept mesh on those bodies. Alternatively, if a body is not sweepable, it will be meshed using the Patch Conforming tetrahedral mesh method.

Applications:

• Early-stage simulations where accuracy is less critical.
• Models with simple geometry.

Strengths:

• Quick and easy to use.
• Requires minimal user input.

Limitations:

• May not generate optimal meshes for complex geometries.
• Limited control over element distribution and type.

2. Hexahedral (Hex) Dominant Mesh

Description:
This method focuses on generating hex elements, which are cube-like in shape and ideal for structured geometries. Hex elements provide higher accuracy and faster convergence for structural and thermal analyses due to their regular shape.

Applications:

• Blocky geometries like cubes, prisms, or cylinders.
• Simulations requiring high accuracy, such as structural and thermal problems.

Strengths:

• Excellent accuracy with fewer elements compared to tets.
• Reduced computational cost due to regularity.

Limitations:

• Difficult to apply to irregular or complex geometries.
• Requires well-prepared geometry for structured meshing.

3. Tetrahedral (Tet) Mesh

Description:
Tet meshes use pyramid-like elements that adapt to irregular geometries. They are the default choice for most models due to their versatility.

Applications:

• Complex geometries with intricate details.
• General-purpose simulations, including static and thermal analysis.

Strengths:

• Handles irregular shapes effectively.
• Simple to apply with minimal geometry preparation.

Limitations:

• Can require a higher element count to achieve the same accuracy as hex meshes.
• May exhibit stress concentrations at element edges.

4. Sweep Method

Description:
The sweep method creates structured meshes by extruding or revolving a 2D face along a path. It is particularly effective for parts with consistent cross-sections.

Applications:

• Prismatic or revolved geometries like shafts, pipes, and fins.
• Models requiring a structured mesh in a specific region.

Strengths:

• Produces high-quality hex or wedge elements.
• Ideal for regions where a structured mesh improves accuracy.

Limitations:

• Limited to geometries that support extrusion or revolution.
• Requires a clean, well-defined geometry for sweeping.

5. Shell and Beam Meshing

Description:
Shell elements are 2D elements used for thin structures, while beam elements are 1D elements for slender structures. These methods simplify models while maintaining accuracy in specific scenarios.

Applications:

• Thin-walled structures like plates, walls, or tanks.
• Truss-like structures and slender components, such as beams and rods.

Strengths:

• Greatly reduces computational cost for thin or slender components.
• Captures bending, buckling, and membrane effects efficiently.

Limitations:

• Requires appropriate section definitions for accuracy.
• Less applicable to thick or 3D structures.

6. Multizone Method

Description:
The multizone method combines structured (hex) and unstructured (tet) meshes, dividing the geometry into zones for better element quality.

Applications:

• Models with both regular and irregular geometry.
• Complex parts where structured meshing is desirable in certain regions.

Strengths:

• Offers flexibility and a balance between hex and tet mesh benefits.
• Improves element quality in blocky regions while maintaining adaptability in complex areas.

Limitations:

• May require manual adjustments to define zones effectively.
• Slightly higher setup time compared to automatic methods.

7. Cartesian Mesh

Description:
Cartesian meshes align with the global coordinate system, generating cuboid elements. This method is often used for CFD or simplified geometry representation.

Applications:

• Simplified thermal or structural analyses.
• Models with orthogonal geometries.

Strengths:

• Simplifies meshing for blocky geometries.
• Fast to generate and solve.

Limitations:

• Not suitable for highly detailed or curved geometries.
• Limited flexibility for refining specific areas.

Final Thoughts

A robust mesh is the cornerstone of any successful simulation. By understanding the characteristics and applications of different mesh methods, you can optimize your model for accuracy, efficiency, and reliability. Always validate your mesh with quality checks and convergence studies to ensure your results truly represent the physical behavior of your design.