Portfolio/03 — FEA / ABAQUS

FEA / ABAQUS · SOLID MECHANICS

Does the hook mesh change the answer?

I modelled a loaded hook in Abaqus and compared element types and mesh densities. The focus was convergence: whether stress and displacement settle as the mesh is refined.

Abaqus2D plane stressMesh refinementConvergence study
Abaqus von Mises stress contour and finite element mesh across the hook
VON MISES STRESS / GLOBAL MESH SIZE 6

01 / MODEL

Geometry, support & load

The hook was represented as a 2D plane-stress model. I fixed the upper support hole and applied pressure along the lower inner curve, then assigned low-carbon steel properties.

Dimensioned hook profile used to define the finite element geometry
HOOK PROFILE / DIMENSIONS IN MM
Hook model showing the fixed upper hole and pressure load along the lower inner curve
BOUNDARY CONDITIONS / PRESSURE LOADING
MaterialLow-carbon steel
Young’s modulus200,000 MPa
Poisson’s ratio0.28
Section thickness20 mm

02 / METHOD

Refine where the result changes fastest

I partitioned the model to concentrate finer elements around the inner curve, where stress and displacement gradients were highest. The rest of the hook used a coarser mesh to keep the analysis manageable.

01 / PartitionDivide the geometry to target the inner curve and its changing stress field.
02 / RefineUse a finer local mesh in critical regions and a coarser mesh elsewhere.
03 / CompareTrack peak stress and displacement across element order and mesh families.

Mesh families: linear and quadratic elements were assessed with both tri-dominated and quad-dominated meshes. The convergence plots below track element count against peak von Mises stress and displacement.

03 / CONVERGENCE

Do the values stabilise?

Across the four mesh families, stress settled in the same general range and displacement approached 1.9 mm. Quadratic elements reached stable values with fewer elements in the comparisons reported.

Stress convergence chart comparing linear and quadratic tri-dominated meshes
01 / STRESS · TRI-DOMINATED MESHES
Stress convergence chart comparing linear and quadratic quad-dominated meshes
02 / STRESS · QUAD-DOMINATED MESHES
Displacement convergence chart comparing linear and quadratic tri-dominated meshes
03 / DISPLACEMENT · TRI-DOMINATED MESHES
Displacement convergence chart comparing linear and quadratic quad-dominated meshes
04 / DISPLACEMENT · QUAD-DOMINATED MESHES

04 / TAKEAWAY

Convergence builds confidence

The comparison shows why a single contour plot is not enough: element formulation and mesh density affect the result, so convergence is part of interpreting the analysis.

≈1.18–1.21 GPaReported converged peak stress range across the mesh comparisons
≈1.90 mmDisplacement approached by both linear and quadratic element curves

Quadratic elements gave a more efficient route to stable results in this study. The stress concentration appeared along the hook’s inner curve, consistent with bending through the curved section.

Model limits: the analysis assumes linear elasticity and 2D plane stress. The reported peak stress is a numerical result under those assumptions, not a validated safe working load; nonlinear material behaviour, 3D effects and further refinement would be needed for a design assessment. Global refinement was also limited by the academic software license.