06.4 / Worked examples

Open an example. See what changes when you change it.

Start with a baseline that has recorded checks, or work through a recent coupled study. Each example uses the same inputs, model choices, tasks and limits as its exercise.

About difficulty levels and time estimates

Instructional ratings describe setup and interpretation effort, not solver accuracy or license access. Existing catalog stages remain separate. Estimates include setup, comparisons and interpretation; they are not solver runtimes and will vary with experience.

  1. Foundation — a single basic material or micromechanics relationship.
  2. Developing — orientation, short-fiber comparisons or an introductory laminate setup.
  3. Intermediate — a structural response, transport history or process study.
  4. Advanced — coupled fields, nonlinear response or optimization with more interpretation.
  5. Integrated — a multi-field study combining thermal, moisture and mechanical effects.

The numbered ring fills as difficulty increases. The clock fill indicates walkthrough duration on a two-hour scale; the adjacent number gives the estimate in minutes. These initial ratings are assigned from the model scope and curriculum stage and can be refined by instructors.

32 matching examples and stored-data studies

Baselines with recorded passing checks

Open the checks below an example to see which quantities were compared, the inputs used and the tolerances. The 2026-10-31 report compares specific quantities with analytical references. Passing those checks is not experimental validation and does not certify an edited study or the current solver.

Laminates

02.08 · Laminate orientation and tensile response →

Level 2
Developing
Est. 25 min
View fixed-layout exercise workflow
Enlarge workflow ↗
02.08 · Laminate orientation and tensile response · Fixed layout with all supplied blocks · not solved results
About this workflow view

All blocks keep the CREATE / DISCOVER / SIMULATE positions, with Equipment below Geometry; unused records remain disconnected. This changes the view only, not the exercise records. The diagram shows the setup, not solved results.

Open the copied laminate and record the initial stacking sequence and total thickness.

Classical laminate theory · Linear static · ASTM D3039-17(2025)-based

ASTM-based teaching geometry, not certification. Grips, tabs, alignment and physical test validity are not simulated.

Recorded checks · 2026-10-31

Reference validation · 2026-10-31

Benchmark validated — analytical scope

Listed reference-elastic extensional constants only; free curvature, ply stresses, strength and every user variation are outside this badge.

Recorded baseline only—not a certification of the current database, edited inputs, or every output. Analytical agreement is not experimental material or failure validation.

Source validation, comparisons and tested inputs

Execution: Completed (not validation)

Acceptance: absolute error ≤ absolute tolerance + relative tolerance × |reference|.
QuantityCDSReferenceError %Tolerance (relative + absolute)Result
Ex (GPa)51.9214751.92147-0.0000074555590.01% + 0.00002 GPaPass
Ey (GPa)51.9214751.92147-0.0000074555590.01% + 0.00002 GPaPass
Gxy (GPa)19.8140719.814070.000019597580.01% + 0.00002 GPaPass
νxy (—)0.310220.31021750.00079347340.01% + 0.00002 —Pass
  • MIT / David Roylance — Laminated Composite Plates ↗Transformed plane-stress constitutive law and laminate extensional stiffness, equations 10–11 and 20–25. Independent strain/stress transformation and thickness integration; prescribed input elasticity is not validated.
Tested inputs
Reference ply list (GPa, mm, degrees)
[{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":0,"t":0.25},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":45,"t":0.25},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":-45,"t":0.25},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":90,"t":0.25},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":90,"t":0.25},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":-45,"t":0.25},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":45,"t":0.25},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":0,"t":0.25}]

Input SHA-256: bcd87ea7ad5c3bc06958f1b2d1fadd0146279a7b20a56c59eb14e9ef46701135
Solver source SHA-256: cde316d69ee40b2714f26fd4d6d822f774242b37323c9419f2b6142aff317ca9

  • ASTM-based teaching geometry, not certification. Grips, tabs, alignment and physical test validity are not simulated.

Download source-validation results (JSON) · Full 184-exercise study

Workbench workflow

02.09 · ±45° coupon: in-plane shear →

Level 2
Developing
Est. 25 min
View fixed-layout exercise workflow
Enlarge workflow ↗
02.09 · ±45° coupon: in-plane shear · Fixed layout with all supplied blocks · not solved results
About this workflow view

All blocks keep the CREATE / DISCOVER / SIMULATE positions, with Equipment below Geometry; unused records remain disconnected. This changes the view only, not the exercise records. The diagram shows the setup, not solved results.

Inspect the balanced ±45° laminate and its axial tensile load.

Classical laminate theory · ASTM D3518-18(2025)-based

Small-strain elastic teaching model; fibre rotation and nonlinear termination rules are not represented.

Recorded checks · 2026-10-31

Reference validation · 2026-10-31

Benchmark validated — analytical scope

Listed reference-elastic extensional constants only; free curvature, ply stresses, strength and every user variation are outside this badge.

Recorded baseline only—not a certification of the current database, edited inputs, or every output. Analytical agreement is not experimental material or failure validation.

Source validation, comparisons and tested inputs

Execution: Completed (not validation)

Acceptance: absolute error ≤ absolute tolerance + relative tolerance × |reference|.
QuantityCDSReferenceError %Tolerance (relative + absolute)Result
Ex (GPa)17.0282717.028270.000027757020.01% + 0.00002 GPaPass
Ey (GPa)17.0282717.028270.000027757020.01% + 0.00002 GPaPass
Gxy (GPa)34.8281334.82813-0.0000064139090.01% + 0.00002 GPaPass
νxy (—)0.773780.77377760.00030594680.01% + 0.00002 —Pass
  • MIT / David Roylance — Laminated Composite Plates ↗Transformed plane-stress constitutive law and laminate extensional stiffness, equations 10–11 and 20–25. Independent strain/stress transformation and thickness integration; prescribed input elasticity is not validated.
Tested inputs
Reference ply list (GPa, mm, degrees)
[{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":45,"t":0.25},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":-45,"t":0.25},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":45,"t":0.25},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":-45,"t":0.25},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":-45,"t":0.25},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":45,"t":0.25},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":-45,"t":0.25},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":45,"t":0.25}]

Input SHA-256: 27ead8b0d87202e94194ece226dc0c310644146bb20037a423cd5a1a31012421
Solver source SHA-256: cde316d69ee40b2714f26fd4d6d822f774242b37323c9419f2b6142aff317ca9

  • Small-strain elastic teaching model; fibre rotation and nonlinear termination rules are not represented.

Download source-validation results (JSON) · Full 184-exercise study

Workbench workflow

02.10 · Three-point bending: span and stiffness →

Level 3
Intermediate
Est. 25 min
View fixed-layout exercise workflow
Enlarge workflow ↗
02.10 · Three-point bending: span and stiffness · Fixed layout with all supplied blocks · not solved results
About this workflow view

All blocks keep the CREATE / DISCOVER / SIMULATE positions, with Equipment below Geometry; unused records remain disconnected. This changes the view only, not the exercise records. The diagram shows the setup, not solved results.

Inspect specimen width, laminate thickness, support span and central force.

Euler–Bernoulli beam · ASTM D7264-26-based

Procedure A teaching setup. Transverse shear deformation, roller contact and indentation are excluded.

Recorded checks · 2026-10-31

Reference validation · 2026-10-31

Benchmark validated — analytical scope

Central-load beam deflection and shear, conditional on the reported effective Ex. Material elasticity, ply stress and failure not validated.

Recorded baseline only—not a certification of the current database, edited inputs, or every output. Analytical agreement is not experimental material or failure validation.

Source validation, comparisons and tested inputs

Execution: Completed (not validation)

Acceptance: absolute error ≤ absolute tolerance + relative tolerance × |reference|.
QuantityCDSReferenceError %Tolerance (relative + absolute)Result
Ex (GPa)51.9214751.92147-0.0000074555590.01% + 0.00002 GPaPass
Ey (GPa)51.9214751.92147-0.0000074555590.01% + 0.00002 GPaPass
Gxy (GPa)19.8140719.814070.000019597580.01% + 0.00002 GPaPass
νxy (—)0.310220.31021750.00079347340.01% + 0.00002 —Pass
Maximum deflection (mm)1.2136671.2136670.000007455560.05% + 0.00002 mmPass
Maximum shear (N)505000.01% + 0.00002 NPass
Tested inputs
Reference ply list (GPa, mm, degrees)
[{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":0,"t":0.5},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":45,"t":0.5},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":-45,"t":0.5},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":90,"t":0.5},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":90,"t":0.5},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":-45,"t":0.5},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":45,"t":0.5},{"e1":135,"e2":9,"nu":0.31,"g":4.8,"angle":0,"t":0.5}]
Beam benchmark inputs
{"widthMm":13,"heightMm":4,"spanMm":128,"forceN":100,"conditionalExGPa":51.92147387103631}

Input SHA-256: 91e88e45a71f71ba3943edfdefd2da46b3257da1978ea92d51c412986e39c8b8
Solver source SHA-256: cde316d69ee40b2714f26fd4d6d822f774242b37323c9419f2b6142aff317ca9

  • Procedure A teaching setup. Transverse shear deformation, roller contact and indentation are excluded.

Download source-validation results (JSON) · Full 184-exercise study

Workbench workflow

02.11 · Thin-wall pressure vessel →

Level 3
Intermediate
Est. 30 min
View fixed-layout exercise workflow
Enlarge workflow ↗
02.11 · Thin-wall pressure vessel · Fixed layout with all supplied blocks · not solved results
About this workflow view

All blocks keep the CREATE / DISCOVER / SIMULATE positions, with Equipment below Geometry; unused records remain disconnected. This changes the view only, not the exercise records. The diagram shows the setup, not solved results.

Inspect the tube dimensions in Geometry and pressure/end conditions in CASES.

Thin-wall membrane · Classical laminate theory

Thin-wall membrane theory: no through-wall radial stress profile or local end effects.

Recorded checks · 2026-10-31

Reference validation · 2026-10-31

Benchmark validated — analytical scope

Thin-wall pressure equilibrium and orthotropic biaxial strain comparison; stiffness inputs are conditional where Micro closure has not been verified.

Recorded baseline only—not a certification of the current database, edited inputs, or every output. Analytical agreement is not experimental material or failure validation.

Source validation, comparisons and tested inputs

Execution: Completed (not validation)

Nonzero-void closure has no matched published calibration in this study

Acceptance: absolute error ≤ absolute tolerance + relative tolerance × |reference|.
QuantityCDSReferenceError %Tolerance (relative + absolute)Result
Hoop stress (MPa)56.456.400.01% + 0.00002 MPaPass
Axial stress (MPa)28.228.200.01% + 0.00002 MPaPass
Hoop strain including Poisson coupling (µε)755.3712755.36980.00018240250.05% + 0.01 µεPass
Axial strain including Poisson coupling (µε)246.3161246.31320.0011490210.05% + 0.01 µεPass
  • MIT / David Roylance — Pressure Vessels ↗Equations 2–3, printed page 3; orthotropic strain compliance from laminated plates reference. Thin-wall, closed-end pristine cylinder. No slit, fracture or failure-pressure validation.
  • MIT / David Roylance — Laminated Composite Plates ↗Transformed plane-stress constitutive law and laminate extensional stiffness, equations 10–11 and 20–25. Independent strain/stress transformation and thickness integration; prescribed input elasticity is not validated.
Tested inputs
Pressure reference inputs
{"pressureMPa":2.4,"externalPressureMPa":0,"innerRadiusMm":47,"wallMm":2,"closed":true,"axialNPerM":0}

Input SHA-256: 1de482a6e7dd14f5b66f5582d58c30b5f08af6a2b097f380ed49640e2fc60fc7
Solver source SHA-256: cde316d69ee40b2714f26fd4d6d822f774242b37323c9419f2b6142aff317ca9

  • Thin-wall membrane theory: no through-wall radial stress profile or local end effects.

Download source-validation results (JSON) · Full 184-exercise study

Laminates

02.23 · T700/Epoxy Quasi-Isotropic · stored-data layup →

Level 2
Developing
Est. 20 min
View fixed-layout exercise workflow
Enlarge workflow ↗
02.23 · T700/Epoxy Quasi-Isotropic · stored-data layup · Fixed layout with all supplied blocks · not solved results
About this workflow view

All blocks keep the CREATE / DISCOVER / SIMULATE positions, with Equipment below Geometry; unused records remain disconnected. This changes the view only, not the exercise records. The diagram shows the setup, not solved results.

Trace the stored material-to-laminate path. Inspect original file, record ID, property status and units; Micro is intentionally not used.

Stored lamina elasticity · Classical laminate theory · Maximum stress

Stored original ply properties; original homogenization and failure-model selections are not rerun. Maximum-stress screening uses original teaching strengths, not qualified allowables. Linear CLT resultants only: no grip/edge boundary layers, buckling, delamination, progressive growth or process coupling. Completion is not validation or a physical pass.

Recorded checks · 2026-10-31

Reference validation · 2026-10-31

Benchmark validated — analytical scope

Listed reference-elastic extensional constants only; free curvature, ply stresses, strength and every user variation are outside this badge.

Recorded baseline only—not a certification of the current database, edited inputs, or every output. Analytical agreement is not experimental material or failure validation.

Source validation, comparisons and tested inputs

Execution: Completed (not validation)

Acceptance: absolute error ≤ absolute tolerance + relative tolerance × |reference|.
QuantityCDSReferenceError %Tolerance (relative + absolute)Result
Ex (GPa)51.5259851.525980.0000064942510.01% + 0.00002 GPaPass
Ey (GPa)51.5259851.525980.0000064942510.01% + 0.00002 GPaPass
Gxy (GPa)19.6770419.677040.000019572390.01% + 0.00002 GPaPass
νxy (—)0.309290.3092921-0.00068465390.01% + 0.00002 —Pass
  • MIT / David Roylance — Laminated Composite Plates ↗Transformed plane-stress constitutive law and laminate extensional stiffness, equations 10–11 and 20–25. Independent strain/stress transformation and thickness integration; prescribed input elasticity is not validated.
Tested inputs
Reference ply list (GPa, mm, degrees)
[{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":0,"t":0.125},{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":45,"t":0.125},{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":-45,"t":0.125},{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":90,"t":0.125},{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":90,"t":0.125},{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":-45,"t":0.125},{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":45,"t":0.125},{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":0,"t":0.125}]

Input SHA-256: 031e3c74177fba796323029d1604301cc3fd56a27666f8b54d1c50d9f2f77dd1
Solver source SHA-256: cde316d69ee40b2714f26fd4d6d822f774242b37323c9419f2b6142aff317ca9

  • Stored original ply properties; original homogenization and failure-model selections are not rerun. Maximum-stress screening uses original teaching strengths, not qualified allowables. Linear CLT resultants only: no grip/edge boundary layers, buckling, delamination, progressive growth or process coupling. Completion is not validation or a physical pass.

Download source-validation results (JSON) · Full 184-exercise study

Structural response

02.37 · Quasi-Isotropic Plate in Uniaxial Tension · resultant response →

Level 3
Intermediate
Est. 20 min
View fixed-layout exercise workflow
Enlarge workflow ↗
02.37 · Quasi-Isotropic Plate in Uniaxial Tension · resultant response · Fixed layout with all supplied blocks · not solved results
About this workflow view

All blocks keep the CREATE / DISCOVER / SIMULATE positions, with Equipment below Geometry; unused records remain disconnected. This changes the view only, not the exercise records. The diagram shows the setup, not solved results.

Trace the stored material-to-laminate path. Inspect original file, record ID, property status and units; Micro is intentionally not used.

Stored lamina elasticity · Classical laminate theory · Maximum stress

Stored original ply properties; original homogenization and failure-model selections are not rerun. Maximum-stress screening uses original teaching strengths, not qualified allowables. Linear CLT resultants only: no grip/edge boundary layers, buckling, delamination, progressive growth or process coupling. Completion is not validation or a physical pass.

Recorded checks · 2026-10-31

Reference validation · 2026-10-31

Benchmark validated — analytical scope

Listed reference-elastic extensional constants only; free curvature, ply stresses, strength and every user variation are outside this badge.

Recorded baseline only—not a certification of the current database, edited inputs, or every output. Analytical agreement is not experimental material or failure validation.

Source validation, comparisons and tested inputs

Execution: Completed (not validation)

Acceptance: absolute error ≤ absolute tolerance + relative tolerance × |reference|.
QuantityCDSReferenceError %Tolerance (relative + absolute)Result
Ex (GPa)51.5259851.525980.0000064942510.01% + 0.00002 GPaPass
Ey (GPa)51.5259851.525980.0000064942510.01% + 0.00002 GPaPass
Gxy (GPa)19.6770419.677040.000019572390.01% + 0.00002 GPaPass
νxy (—)0.309290.3092921-0.00068465390.01% + 0.00002 —Pass
  • MIT / David Roylance — Laminated Composite Plates ↗Transformed plane-stress constitutive law and laminate extensional stiffness, equations 10–11 and 20–25. Independent strain/stress transformation and thickness integration; prescribed input elasticity is not validated.
Tested inputs
Reference ply list (GPa, mm, degrees)
[{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":0,"t":0.125},{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":45,"t":0.125},{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":-45,"t":0.125},{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":90,"t":0.125},{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":90,"t":0.125},{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":-45,"t":0.125},{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":45,"t":0.125},{"e1":134,"e2":8.8,"nu":0.31,"g":4.800000000000001,"angle":0,"t":0.125}]

Input SHA-256: 08903bf6c1fe816959ce21a6a6a829c0add1ee68c7770be19e3f4bd91d04895b
Solver source SHA-256: cde316d69ee40b2714f26fd4d6d822f774242b37323c9419f2b6142aff317ca9

  • Stored original ply properties; original homogenization and failure-model selections are not rerun. Maximum-stress screening uses original teaching strengths, not qualified allowables. Linear CLT resultants only: no grip/edge boundary layers, buckling, delamination, progressive growth or process coupling. Completion is not validation or a physical pass.

Download source-validation results (JSON) · Full 184-exercise study

Recent coupled-study exercises

See how reaction heating, moisture-induced curvature and pultrusion enter a connected study. These exercises come from the maintained catalog. Their diagrams show the setup connections, not calculated results. The teaching objectives do not establish validated manufacturing predictions.

Processing

03.58 · Pultrusion: thick-section cure lag and loaded stiffness →

Level 4
Advanced
Est. 40 min
View fixed-layout exercise workflow
Enlarge workflow ↗
03.58 · Pultrusion: thick-section cure lag and loaded stiffness · Fixed layout with all supplied blocks · not solved results
About this workflow view

All blocks keep the CREATE / DISCOVER / SIMULATE positions, with Equipment below Geometry; unused records remain disconnected. This changes the view only, not the exercise records. The diagram shows the setup, not solved results.

Run the 4 mm profile at 0.1 m/min in the multi-zone die.

1D pultrusion thermal cure · Kamal–Sourour cure kinetics · 1D Darcy film impregnation · CHILE cure-dependent modulus · Classical laminate theory · Thermomechanical coupling

Illustrative constant-speed T700/epoxy process. Uniform face-fed, through-thickness Darcy infusion uses prescribed Kz, a continuous resin manifold and local ply-average cure viscosity; pressure or total flow controls the inlet and pump limits are reported. Fixed equivalent-composite thermal properties; no dry-to-wet feedback, resin heat advection, axial flow, leakage, die thermal mass or pulling-force prediction. Not a calibrated production recipe. Sequential outlet-state structural screening under a prescribed resultant; no pulling force, die friction, impregnation or load feedback into the thermal solution.

Illustrative study · not presented as a verified benchmark.

Moisture

03.61 · Moisture plus applied bending: competing curvature contributions →

Level 4
Advanced
Est. 40 min
View fixed-layout exercise workflow
Enlarge workflow ↗
03.61 · Moisture plus applied bending: competing curvature contributions · Fixed layout with all supplied blocks · not solved results
About this workflow view

All blocks keep the CREATE / DISCOVER / SIMULATE positions, with Equipment below Geometry; unused records remain disconnected. This changes the view only, not the exercise records. The diagram shows the setup, not solved results.

Run the unsymmetric conditioned laminate with Nx = 25,000 N/m and Mx = 5 N per unit width.

1D transient moisture diffusion · Classical laminate theory · Hygromechanical coupling · Extension–bending coupling

Teaching inputs, not qualified allowables. Sequential coupling transfers the reported thermal/moisture state to laminate mechanics; it is not simultaneous 3D multiphysics. Inspect the transferred state and reference values before interpreting stress or curvature. No moisture-driven damage, swelling-dependent diffusion or experimentally calibrated strength degradation.

Illustrative study · not presented as a verified benchmark.

Processing

03.62 · Thick laminate: reaction heating, cure gradient and process stress →

Level 4
Advanced
Est. 40 min
View fixed-layout exercise workflow
Enlarge workflow ↗
03.62 · Thick laminate: reaction heating, cure gradient and process stress · Fixed layout with all supplied blocks · not solved results
About this workflow view

All blocks keep the CREATE / DISCOVER / SIMULATE positions, with Equipment below Geometry; unused records remain disconnected. This changes the view only, not the exercise records. The diagram shows the setup, not solved results.

Run the 6 mm laminate through the 120°C dwell with its linked resin reaction heat.

Heat transfer · Classical laminate theory · Extension–bending coupling · Thermomechanical coupling

Teaching inputs, not qualified allowables. Sequential coupling transfers the reported thermal/moisture state to laminate mechanics; it is not simultaneous 3D multiphysics. Inspect the transferred state and reference values before interpreting stress or curvature. Free laminate CLT curvature, not fixture-constrained distortion, a full tool-release simulation or calibrated cure-shrinkage prediction.

Illustrative study · not presented as a verified benchmark.

Original examples, within the curriculum

Continue one of 25 original stored-data studies using its exercise record. Each retains the source filename, tasks and limitations, so you can follow the original example without maintaining a second set of inputs.

Browse the converted studies

Historical reference examples

The older web examples remain available for their sources and calculation context. They are historical demonstrations, not a statement of current Workbench verification.