These studies appear in Workbench → Models → Structural models and in the exercise collection. Each runs separately from coupled process or progressive analyses. Reference-state results are exploratory; analytical software checks do not establish experimentally validated design allowables.
01 · Open-hole strength
Infinite-width, specially orthotropic tension screening. Point and average stress distances must be calibrated independently for this laminate. Not compression, bearing or a joint allowable.
σ(r)/σ∞ = 1 + ½q² + 3/2 q⁴ − ½(Kt − 3)(5q⁶ − 7q⁸), q = a/r.
Constitutive assumptions and calibration
For loading along x, Kt = 1 + √[2(√(Ex/Ey) − νxy) + Ex/Gxy]. The point criterion evaluates stress at a + d₀; the average criterion integrates it from a to a + a₀. Both compare with measured unnotched laminate strength. Their two characteristic lengths need independent calibration. The isotropic limit is Kt = 3.
02 · Creep & stress relaxation
Linear uniaxial response at the calibration temperature. Reference Ex is the instantaneous modulus. Three Maxwell branches; creep is solved from stress equilibrium, not the reciprocal relaxation modulus. No thermal shifting or nonlinear creep.
E(t) = E∞ + Σ Eᵢ exp(−t/τᵢ), E∞ = E₀(1 − Σgᵢ).
Constitutive assumptions and calibration
The laminate reference Ex is E₀. A held-strain experiment gives stress relaxation. For held stress, the solver evolves Maxwell branch stresses and solves equilibrium for strain; creep compliance is not 1/E(t). The calculation compares two time refinements and rejects excessive differences. Three editable branches, one calibration temperature, small uniaxial strain.
03 · Analytical bonded joint
Identical equivalent-elastic adherends, long free arms and a thin elastic adhesive. Compare shear-only Volkersen with eccentric single-lap shear and peel. Not a debonding, plasticity or strength calculation.
Volkersen: τ(x) = (F/b) β cosh(βx) / [2 sinh(βL/2)].
Constitutive assumptions and calibration
β² = 2Ga/(ta Et) for identical adherends. The companion Goland–Reissner solution adds the eccentric-load moment factor and elastic peel distribution. The shared laminate supplies thickness and Ex, with an equivalent-isotropic beam approximation. Adhesive modulus, Poisson ratio, thickness, width and overlap remain explicit study inputs. Peak elastic stress is not a joint-strength prediction.
04 · LaRC04 failure initiation
NASA LaRC04 linear-shear specialization, evaluated at both faces of every ply under membrane and bending loads. Supplied ply strengths are effective/in-situ values; no automatic thin-ply enhancement. Initiation only, not degradation or nonlinear-shear instability.
LaRC04 evaluates matrix tension/compression and fiber tension/kinking in their appropriate fracture and misalignment frames.
Constitutive assumptions and calibration
This release implements the linear-shear specialization of NASA Table 6. CLT recovers stress at both faces of each ply; the kink-frame rotation solves the linear shear equilibrium equation and the fracture-plane search is refined. Supply effective/in-situ strengths explicitly. Identical ply materials share one calibration; mixed-material calibration is rejected. This separate initiation study does not replace or silently extend the progressive-failure solver. Nonlinear-shear instability and delamination are excluded.
05 · Tool-release shape
Free CLT release from prescribed ply-local shrinkage/thermal eigenstrains. Corner spring-in is a separate uniform-strain estimate. Stress-free temperature and effective post-gel shrinkage need calibration. No tool friction, cure kinetics or viscoelastic restraint history.
[ε₀, κ]ᵀ = ABD⁻¹[N*, M*]ᵀ; Δθ = θ(εparallel − εthrough)/(1 + εthrough).
Constitutive assumptions and calibration
The first expression computes free flat-laminate response to prescribed ply-local thermal and post-gel shrinkage strains. The second is a separate uniform-strain corner estimate; positive Δθ means spring-in. The plotted free sections use their center tangent as reference, not a clamp. Enter effective post-gel strains, not total resin volumetric shrinkage. Tool friction, contact and viscoelastic cure history are not resolved.
06 · Fatigue residual properties
Prescribed power-law retention fitted to constant-amplitude tests at a fixed stress ratio, amplitude and temperature. Stiffness and strength have independent coefficients. S–N life alone cannot calibrate either. Does not modify the saved laminate.
E(N)/E₀ = 1 − aE(N/Nf)^bE; X(N)/X₀ = 1 − aX(N/Nf)^bX.
Constitutive assumptions and calibration
This is a prescribed, user-fitted phenomenological retention law. Stiffness and strength use independent loss fractions and exponents. Nf, stress ratio, peak stress and temperature must describe the same constant-amplitude calibration. No extrapolation beyond Nf is allowed. Curves do not automatically modify the saved laminate, and S–N life alone cannot determine degradation coefficients. The reference illustrates why stiffness-degradation data are needed; CDS does not claim to reproduce that NASA fitted model.
07 · Cylinder buckling
Simply supported, thin, specially orthotropic cylinder under uniform axial compression. Discrete Donnell modes; prescribed knockdown factor explores imperfection sensitivity, not a prediction from measured imperfection amplitude. No pressure, torsion, postbuckling or strength pass.
Nx,cr = [D11 k⁴ + 2(D12 + 2D66)k²l² + D22 l⁴ + k⁴/(R²C)] / k².
Constitutive assumptions and calibration
Here k = mπ/L, l = n/R and C = a22k⁴ + (2a12 + a66)k²l² + a11l⁴, with a = A⁻¹. The solver searches discrete axial and circumferential modes for a thin, specially orthotropic simply supported cylinder. A governing mode at the search boundary requires refinement. An explicit knockdown factor scales the ideal result; it is not an automatic prediction from measured imperfections. Pressure, torsion, postbuckling and failure interaction are excluded.
08 · Uncertainty & sensitivity
Seeded independent uniform sampling of shared modulus, ply-thickness and angle offsets. Recomputes laminate ABD for each sample. Bounds are assumptions, not measured distributions. Percentiles and sensitivity are exploratory, not reliability certification.
For each seeded sample: vary bounded inputs → rebuild ABD → solve the axial response.
Constitutive assumptions and calibration
Sampled independent uniform inputs are a common modulus scale, a common thickness scale and a shared ply-angle offset. The output includes strain percentiles and signed Pearson correlations. Repeating the same seed and inputs reproduces the sample set. Zero input ranges recover the deterministic result. Distributions must be justified before drawing reliability conclusions; a small correlation does not rule out nonlinear influence.
Verification before interpretation
Reference checks cover isotropic notch concentration, exact one-branch creep, joint load transfer, pure-load LaRC04 initiation, zero-curvature free expansion, fatigue-retention endpoints, classical isotropic shell buckling and seeded deterministic sampling. Check the scope of each model and repeat sensitivity/convergence studies for your actual inputs. A completed calculation is not an overall design pass.
References
- NASA: notch-strength modelling and characteristic-distance assumptions
- Abaqus: time-domain Prony-series viscoelasticity
- University of Washington: Goland–Reissner calculation equations
- Pinho et al., NASA/TM-2005-213530: original LaRC04 equations
- Analytical modelling of cure-induced laminate deformation
- NASA: measured stiffness degradation for fatigue prognosis
- NASA: shell buckling and imperfection sensitivity
- NASA: uncertainty modelling in composite analysis