An Interactive Finite Element Analysis Learning Platform
Interactive Learning
Master Finite Element Analysis
Build deep intuition for FEA concepts through interactive visualizations, hands-on experiments, and real-time simulations — from meshing to convergence.
8Modules
20+Interactives
FEAFocus
Available Modules
What is FEA?Fundamentals & Concepts
Discover how FEA breaks complex problems into simple pieces — from continuous domains to discrete solutions.
Animation Glossary Process
MeshingDomain Discretization
Generate meshes interactively, compare structured vs unstructured, and drag nodes to see quality metrics update live.
Generator Metrics Drag
Element TypesThe FEA Catalog
Explore element families from 1D bars to 3D hexahedra. Visualize shape functions as interactive 3D surfaces.
Dimension Filter 3D Plots Comparison
h vs p MethodRefinement Strategies
Compare h-refinement (more elements) vs p-refinement (higher order) side-by-side with live convergence tracking.
Side-by-Side Sliders Convergence
Element ComplexityLinear to Cubic
See how element polynomial order affects accuracy. Compare linear, quadratic, and cubic elements on a cantilever beam.
Order Toggle Visualization Accuracy
ConvergenceApproaching the Truth
Run convergence studies, understand Richardson extrapolation, and learn about common pitfalls like mesh dependence.
Run Study Extrapolation Pitfalls
Abaqus LibraryElement Reference
Decode Abaqus element names, browse element families, and follow an interactive selection flowchart.
Decoder Flowchart Browser
Pros & ConsElement Selection Guide
Compare element performance, learn best practices by domain, avoid common mistakes, and test your knowledge with a quiz.
Matrix Performance Quiz
What is FEA?
Meshing
Element Types
h vs p
Complexity
Convergence
Abaqus
Pros & Cons
What is Finite Element Analysis?
Finite Element Analysis (FEA) is a numerical method that breaks a complex domain into smaller, simpler pieces called elements. By solving simple equations on each element and assembling the results, we can approximate the behavior of structures, heat flow, fluid dynamics, and more.
From Continuous to Discrete
Watch how a continuous domain gets discretized into a mesh, then solved to reveal the stress distribution.
Applications of FEA
Structural
Stress, strain, and deformation analysis of bridges, buildings, and mechanical components.
Thermal
Heat conduction, convection, and radiation in electronic devices, engines, and furnaces.
Fluid
Computational fluid dynamics for aerodynamics, pipe flow, and weather prediction.
FEA Glossary
Click a term to see its visual explanation.
Node
A point where element corners meet
DOF
Degree of freedom at each node
Element
A small sub-region of the domain
Shape Function
Interpolation within an element
Stiffness Matrix
Relates forces to displacements
The FEA Process
Pre-processing
Solving
Post-processing
Pre-processing: Define geometry, create the mesh, assign material properties and boundary conditions. This is where you set up the problem — the quality of your mesh directly affects accuracy.
Meshing: Domain Discretization
A mesh divides your domain into elements. Mesh quality — element shape, size, and distribution — directly affects solution accuracy and convergence speed.
Interactive Mesh Generator
Select a shape and adjust the density to see how the mesh changes.
6
0
Elements
0
Avg Aspect Ratio
0
Avg Skewness
Structured vs Unstructured Meshes
Structured
Regular connectivity pattern
Easy to generate for simple shapes
Higher quality elements
Limited to regular geometries
Unstructured
Irregular connectivity
Can handle complex geometries
Variable element quality
More flexible refinement
Element Shapes
Triangle (Tri3)
3 nodes, 2D
Quad (Q4)
4 nodes, 2D
Tetrahedron
4 nodes, 3D
Hexahedron
8 nodes, 3D
Drag-Node Quality Demo
Drag the interior node to see how element quality metrics change in real-time.
1.00
Aspect Ratio
0.00
Skewness
Element Types Catalog
FEA elements come in many flavors — from simple 1D bars to complex 3D hexahedra. Each has its strengths, trade-offs, and ideal use cases.
Filter by Dimension
Shape Function Visualizer
Select an element type to visualize its shape functions as 3D surfaces. Hover over a node to highlight its shape function.
Drag to rotate · Scroll to zoom
Element Comparison
Element
Dim
Nodes
DOFs/Node
Order
Best For
Accuracy
Cost
Bar2
1D
2
1
Linear
Trusses
Medium
Low
Beam2
1D
2
2
Cubic
Frames
High
Low
CST (Tri3)
2D
3
2
Linear
Simple shapes
Low
Low
LST (Tri6)
2D
6
2
Quadratic
Curved boundaries
High
Medium
Q4
2D
4
2
Linear
Planar problems
Medium
Low
Q8
2D
8
2
Quadratic
Stress concentration
High
Medium
Tet4
3D
4
3
Linear
Complex 3D shapes
Low
Low
Tet10
3D
10
3
Quadratic
General 3D
High
Medium
Hex8
3D
8
3
Linear
Regular 3D regions
Medium
Medium
Hex20
3D
20
3
Quadratic
High-accuracy 3D
High
High
h-Refinement vs p-Refinement
There are two fundamental ways to improve FEA accuracy: h-refinement (using more, smaller elements) and p-refinement (using higher-order polynomial shape functions). Each has distinct convergence properties.
h-Refinement
Subdivide elements into smaller ones. The polynomial order stays the same, but you get more elements to capture variation. Like using more pixels in an image.
4
p-Refinement
Increase the polynomial order of shape functions within existing elements. Like increasing color depth — same pixels, more information per pixel.
1
Convergence Comparison
Error vs DOFs for both refinement strategies on a cantilever beam.
Element Complexity: Linear to Cubic
The polynomial order of an element determines how many nodes it has and how accurately it can represent curved displacement fields. Higher order = more accurate per element, but costlier to compute.
Polynomial Order Visualization
2
Nodes/Element
—
Total DOFs
—
Relative Error
Cantilever Beam: Accuracy vs Element Count
4
Convergence Rate Comparison
See how linear, quadratic, and cubic elements converge at different rates as you increase the number of elements.
Convergence Studies
A convergence study verifies that your FEA solution is independent of the mesh. As you refine the mesh, the solution should approach the exact value. If it doesn't converge, something is wrong.
Mesh Refinement Sequence
Watch the FEA solution approach the exact value as the mesh is refined.
h-Convergence Study
Click "Run Study" to progressively refine the mesh and watch the error decrease.
Results shown on log-log scale
p-Convergence Study
Increase polynomial order on a fixed mesh and observe exponential convergence.
Results shown on log-log scale
Richardson Extrapolation
Estimate the exact solution from two mesh levels. Enter your FEA results at two refinement levels:
Common Pitfalls
Mesh Dependence
If your results change significantly with each mesh refinement and never stabilize, your model may have issues. Check for stress singularities at sharp corners, incorrect boundary conditions, or material model problems. A proper convergence study should show diminishing changes between refinement levels.
Stress Singularities
At re-entrant corners or point loads, stresses theoretically go to infinity. Refining the mesh near these points will cause stress values to keep increasing without bound. Use Saint-Venant's principle: read results away from the singularity, or introduce fillets to remove the sharp corner.
Volumetric / Shear Locking
Low-order fully-integrated elements can artificially stiffen in bending or near-incompressible situations. The cure: use reduced integration (e.g., C3D8R instead of C3D8), or switch to higher-order elements. Reduced integration requires hourglass control to prevent zero-energy modes.
Abaqus Element Library
Abaqus uses a systematic naming convention for its elements. Understanding the code lets you quickly identify what any element does.
Element Name Decoder
Type an Abaqus element name to decode it in real-time.
Element Family Browser
Continuum (Solid) Elements
C3D8 — 8-node linear brick, full integration C3D8R — 8-node linear brick, reduced integration C3D20 — 20-node quadratic brick, full integration C3D20R — 20-node quadratic brick, reduced integration C3D4 — 4-node linear tetrahedron C3D10 — 10-node quadratic tetrahedron CPE4 — 4-node plane strain quad CPS4 — 4-node plane stress quad