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User Manual / Examples / Laminates

Laminates.
Solver-visible results.

Turn ply data and stacking sequences into extensional stiffness, equivalent laminate families, and design-level comparisons. Every case identifies its inputs, calculated readout, provenance, and primary technical sources.

Traceable by design. Published values are transcribed from linked primary sources. CDS plots are calculated or reconstructed from the stated inputs and are clearly labeled.

02

Example class

Laminates

Turn ply data and stacking sequences into extensional stiffness, equivalent laminate families, and design-level comparisons.

L01Published layup families · CDS CLT

Quasi-isotropic laminate family

Compare four symmetric stacking families using the same T300/5208 lamina so differences come from architecture, not changing material cards.

Sources and theory (2)Nettles (1994), NASA RP-1351Sullivan (1977), quasi-isotropic graphite/epoxy
L01 Quasi-isotropic laminate familyIllustrated example · not a live run
  1. Ply properties
  2. Laminates
  3. Response

1 Inputs

01
QI-8
02
cross-ply
03
±45 angle-ply
04
0/±60 tri-axial
05
0.125 mm plies

Keep these conditions unchanged when comparing with the answer.

2 Output visualization

GPaEx 69.68 GPaGxy 26.88 GPaQI-8Ex 95.99 GPaGxy 7.17 GPacross-plyEx 25.05 GPaGxy 46.59 GPaangle-plyEx 69.68 GPaGxy 26.88 GPatri-axialExGxy
3 What the result shows

QI-8 and 0/±60 return the same Ex = Ey = 69.68 GPa and Gxy = 26.88 GPa.

Result basisPublished layup families · CDS CLT. Values and trends reproduce this page’s example; this is not a fresh solver result or an additional validation claim.
Enlarge output visualization
GPaEx 69.68 GPaGxy 26.88 GPaQI-8Ex 95.99 GPaGxy 7.17 GPacross-plyEx 25.05 GPaGxy 46.59 GPaangle-plyEx 69.68 GPaGxy 26.88 GPatri-axialExGxy

QI-8 and 0/±60 return the same Ex = Ey = 69.68 GPa and Gxy = 26.88 GPa.

L02CDS search · Tsai DD construction

Double-Double stiffness match

Search the Double-Double angle field for a compact laminate that preserves the in-plane stiffness of the default eight-ply quasi-isotropic construction.

Sources and theory (1)Tsai (2021), Double–Double laminate family
L02 Double-Double stiffness matchIllustrated example · not a live run
  1. Ply properties
  2. Laminates
  3. Response

1 Inputs

01
Target [0/45/−45/90]s
02
candidate [±22.5/±67.5]₂
03
T300/5208

Keep these conditions unchanged when comparing with the answer.

2 Output visualization

GPa69.68Ex69.68Ey26.88GxyQI [0/±45/90]sDD [±22.5/±67.5]20.000% A-error
3 What the result shows

The 7.5° grid search reproduces Ex, Ey, Gxy, and the full A matrix to numerical precision.

Result basisCDS search · Tsai DD construction. Values and trends reproduce this page’s example; this is not a fresh solver result or an additional validation claim.
Enlarge output visualization
GPa69.68Ex69.68Ey26.88GxyQI [0/±45/90]sDD [±22.5/±67.5]20.000% A-error

The 7.5° grid search reproduces Ex, Ey, Gxy, and the full A matrix to numerical precision.

L03NASA reported plateaus

Thick-laminate toughness plateaus

Compare reported thickness-independent fracture-toughness regions for three T300/5208 laminate families before selecting a layup for damage-tolerant design.

Sources and theory (1)Harris & Morris (1984), NASA CR-3784
L03 Thick-laminate toughness plateausIllustrated example · not a live run
  1. Ply properties
  2. Laminates
  3. Response

1 Inputs

01
8–120 plies
02
(0/90)ns
03
(0/±45/90)ns
04
(0/±45)ns

Keep these conditions unchanged when comparing with the answer.

2 Output visualization

MPa√mm0 / 90: 869 MPa square root millimeter8690 / 900 / ±45 / 90: 1043 MPa square root millimeter10430 / ±45 / 900 / ±45: 1390 MPa square root millimeter13900 / ±45
3 What the result shows

Reported plateaus range from 869 to 1390 MPa√mm; the 0/±45 family is highest.

Result basisNASA reported plateaus. Values and trends reproduce this page’s example; this is not a fresh solver result or an additional validation claim.
Enlarge output visualization
MPa√mm0 / 90: 869 MPa square root millimeter8690 / 900 / ±45 / 90: 1043 MPa square root millimeter10430 / ±45 / 900 / ±45: 1390 MPa square root millimeter13900 / ±45

Reported plateaus range from 869 to 1390 MPa√mm; the 0/±45 family is highest.

L04CDS r15 ABD assembly

Symmetric versus unsymmetric coupling

Assemble ABD matrices for symmetric and unsymmetric stacks and compare the normalized extension–bending coupling magnitude.

Sources and theory (1)CDS laminate framework and ABD theory
L04 Symmetric versus unsymmetric couplingIllustrated example · not a live run
  1. Ply properties
  2. Laminates
  3. Response

1 Inputs

01
[0/45/−45/90]s versus [0/45/90/−45]
02
0.125 mm plies

Keep these conditions unchanged when comparing with the answer.

2 Output visualization

normalized |B|0.00symmetric0.42unsymmetric
3 What the result shows

The symmetric stack returns zero B coupling while the unsymmetric stack retains a normalized coupling magnitude of 0.42.

Result basisCDS r15 ABD assembly. Values and trends reproduce this page’s example; this is not a fresh solver result or an additional validation claim.
Enlarge output visualization
normalized |B|0.00symmetric0.42unsymmetric

The symmetric stack returns zero B coupling while the unsymmetric stack retains a normalized coupling magnitude of 0.42.

L05CDS r15 hygrothermal CLT solve

Thermal-curvature comparison

Apply the same through-thickness temperature change to balanced stacks with different symmetry and recover free laminate curvature.

Sources and theory (1)CDS hygrothermal laminate equations
L05 Thermal-curvature comparisonIllustrated example · not a live run
  1. Ply properties
  2. Laminates
  3. Response

1 Inputs

01
ΔT 80 K
02
symmetric, mildly unsymmetric, and strongly unsymmetric stacks

Keep these conditions unchanged when comparing with the answer.

2 Output visualization

normalized κT0.00symmetric0.18mild0.42strong
3 What the result shows

The symmetric laminate remains flat while increasing unsymmetry raises normalized thermal curvature to 0.42.

Result basisCDS r15 hygrothermal CLT solve. Values and trends reproduce this page’s example; this is not a fresh solver result or an additional validation claim.
Enlarge output visualization
normalized κT0.00symmetric0.18mild0.42strong

The symmetric laminate remains flat while increasing unsymmetry raises normalized thermal curvature to 0.42.

L06CDS r15 through-thickness recovery

Ply stress recovery by orientation

Recover local material-axis stresses through a quasi-isotropic stack under a common axial membrane load.

Sources and theory (1)CDS laminate stress recovery equations
L06 Ply stress recovery by orientationIllustrated example · not a live run
  1. Ply properties
  2. Laminates
  3. Response

1 Inputs

01
[0/45/−45/90]s
02
Nx 300 N/mm
03
T300/5208

Keep these conditions unchanged when comparing with the answer.

2 Output visualization

σ1 · MPa3400°180+45°180−45°3590°
3 What the result shows

The 0° plies carry the largest local longitudinal stress while the 90° ply response remains transverse-dominated.

Result basisCDS r15 through-thickness recovery. Values and trends reproduce this page’s example; this is not a fresh solver result or an additional validation claim.
Enlarge output visualization
σ1 · MPa3400°180+45°180−45°3590°

The 0° plies carry the largest local longitudinal stress while the 90° ply response remains transverse-dominated.

L07CDS r15 progressive same-load loop

Progressive damage load path

Increase membrane load through the same-load progressive solver and track the governing failure index before and after initiation.

Sources and theory (1)CDS progressive update algorithm
L07 Progressive damage load pathIllustrated example · not a live run
  1. Ply properties
  2. Laminates
  3. Response

1 Inputs

01
QI-8
02
normalized load 0.25–1.25
03
Tsai–Wu with stiffness degradation

Keep these conditions unchanged when comparing with the answer.

2 Output visualization

failure index0.220.250.440.500.680.750.941.001.261.25normalized applied load
3 What the result shows

The governing index reaches 0.94 near the reference load and crosses unity at the next increment.

Result basisCDS r15 progressive same-load loop. Values and trends reproduce this page’s example; this is not a fresh solver result or an additional validation claim.
Enlarge output visualization
failure index0.220.250.440.500.680.750.941.001.261.25normalized applied load

The governing index reaches 0.94 near the reference load and crosses unity at the next increment.

L08CDS r15 effective-property assembly

Laminate transport-property assembly

Combine ply-level conductivity and density into reusable laminate properties for process and structural analyses.

Sources and theory (1)CDS effective laminate properties
L08 Laminate transport-property assemblyIllustrated example · not a live run
  1. Ply properties
  2. Laminates
  3. Response

1 Inputs

01
UD, quasi-isotropic, and cross-ply stacks
02
identical constituents and thickness

Keep these conditions unchanged when comparing with the answer.

2 Output visualization

k3 · W/m·K0.65UD0.48QI0.32cross-ply
3 What the result shows

Orientation changes the effective through-thickness transport response while the constituent-derived mass basis remains consistent.

Result basisCDS r15 effective-property assembly. Values and trends reproduce this page’s example; this is not a fresh solver result or an additional validation claim.
Enlarge output visualization
k3 · W/m·K0.65UD0.48QI0.32cross-ply

Orientation changes the effective through-thickness transport response while the constituent-derived mass basis remains consistent.