MDC Codex predicts shell buckling from first principles — imperfection-sensitive, regime-aware, validated against real collapse tests. Nine design standards on one canvas, compared the way engineers actually need to compare them.
Peer-reviewed methodology Proc. Royal Society A, 2025No login. Cylinder axial & bending, right in your browser.
Most structural teams face the same tradeoff: accept conservative empirical factors and carry unnecessary mass, or run expensive nonlinear FE campaigns for every design iteration. Neither approach gives you full visibility into the margin you're working with.
NASA SP-8007 prescribes a single knockdown factor regardless of geometry, imperfection amplitude, or fabrication quality. Every cylinder gets the same penalty. The result is systematic overdesign — kilograms that cost thousands to launch or millions to fabricate.
Running GNIA/GMNIA analyses for every candidate geometry is thorough but slow. Weeks per iteration, high FE expertise required, limited parameter exploration. The design space stays narrow because exploration is costly.
When different standards give different allowables for the same shell, which one is correct? Without a transparent, physics-based reference, teams default to the most conservative answer. The margin exists, but it's invisible.
MDC Codex computes knockdown factors as a function of geometry (Batdorf Z) and imperfection amplitude (w/t). The result is a transparent, traceable design basis that works across standards — and recovers the structural margin that empirical methods leave behind.
Empirical knockdown factors compress the physics into a single number. MDC keeps the four effects that actually govern shell stability visible, measurable, and traceable.
Small geometric deviations (weld distortion, out-of-roundness, dent) drive shells far below their classical buckling limit. MDC sweeps w/t continuously.
Compare amplitudes from Q=A workshop to Q=C field fabrication — see the recoverable margin at each level.
Elastic, transition, plastic — every shell sits in one regime. MDC detects which one governs and surfaces the transition points.
No more accidentally applying an elastic formula to a plastic collapse. The governing regime is stated in every report.
Yielding changes the buckling response — and the interaction with the imperfection hook. MDC applies the physics-based correction, not an empirical knockdown.
Patte-d’elephant correction for combined axial + bending + internal pressure. Calibrated on 400+ collapse tests.
Orthogrid, stringer-frame, ring-only — stiffening shifts both the global and local buckling modes. MDC verifies every mode, not just the first.
Web buckling, flange crippling, torsional buckling checked at every optimisation candidate. No infeasible optima.
MDC Codex handles the structural stability problems that actually appear in real hardware — from rocket tanks to wind turbine towers.
MDC is not a black box. Every knockdown factor can be traced back to mechanistic models and compared against experimental collapse data. The methodology is published, the data is auditable, and the statistical basis is explicit.
Buckling test data from 60+ years of published research. Blachut, Seaman, Kaplan-Fung, Wiggins, DNV-GL, and more. Filter by geometry, load case, author, and failure mode. Every MDC curve is overlaid against real collapse measurements.
The MDC framework is published in the Proceedings of the Royal Society A (2025). Full derivation, full author attribution. The scientific foundation is transparent and independently verifiable — not proprietary curve fitting.
Results are available on A-Basis (p01: 99% survival, 95% confidence), B-Basis (p10: 90% survival), and Mean. Choose the basis that matches your certification requirement and regulatory context.
MDC Codex is the engineering surface of more than a decade of research on shell stability. The methodology is peer-reviewed, the underlying data is traceable, and the scope is documented.
Structural engineer with 14+ years of shell-buckling research. Doctorate awarded by TU Braunschweig (2018). Lead author of the MDC methodology paper published in Proceedings of the Royal Society A (2025). Based in Braunschweig, Germany.
Every feature exists because an engineer needed it to close a design trade or produce a certifiable result. Nothing is decorative.
NASA SP-8007, SP-8019, SP-8032, Eurocode 2007 & 2025, DNV RP-C202, ECSS, PD 5500, GOST 34233, and MDC — computed simultaneously on the same geometry and load case. Results side by side. No re-entry, no separate models.
Define a target load. Get the minimum compliant wall thickness across all applicable standards. Integrated with standard sheet thickness catalogues. Answers the question “how thin can I go?” in seconds.
Automated mass minimization for stiffened shells. Orthogrid, stringer-frame, frame-only. Discrete design space search with local stability verification — web buckling, flange crippling, torsional buckling checked at every candidate.
Sweep w/t from 0 to 20 and see exactly how your design responds to manufacturing variability. Identify the threshold where safety margin erodes — before it becomes a test failure or a redesign.
Classical Laminate Theory with full ABD matrix computation. Carbon, aramid, glass presets. Arbitrary stacking sequences. Smeared-thickness conversion for shell buckling. Anisotropy robustness assessment included.
Automatic regime detection across elastic, transition, and plastic domains. Patte d'elephant correction for combined stress states. 20+ load cases including axial, bending, torsion, external and internal pressure, and all relevant combinations.
1,000+ experimental records. Every prediction can be compared against physical test data from published literature. Filter by campaign, geometry, material, failure mode. Discrepancies are visible, not hidden.
PDF, HTML, CSV, and JSON export. Full traceability: inputs, intermediate values, charts, applicable standard, statistical basis, and design verdict. Structured for inclusion in design review packages and certification documentation.
Each capability is exposed as an interactive workflow — not a checkbox. Click through the tabs to see what the tool does when you open it.
The Validation Hub answers a question every certification engineer asks: has this shell — or one close to it — been physically tested before, and did it fail as predicted?
For every MDC analysis, the Hub locates your current design point within the 1,000+ published collapse-test database and surfaces the nearest experimental records. A design surrounded by validated, conservative tests is heritage evidence — often sufficient to reduce or defer qualification testing. A design with few neighbours, or with nearby non-conservative tests, is flagged for review.
A single Hub query can replace days of literature search and support your design review package with traceable experimental evidence. Particularly relevant for Level 2 analyses, where measured imperfection data is being assessed against the experimental record.
In early design, scan data for your shell does not yet exist — but Eurocode, ECSS, and DNV all require an imperfection amplitude. The Guide closes this gap: a statistically-backed w/t estimate from 172 measured shells covering lab-scale specimens through full-scale aerospace hardware (1970–2024).
Outputs include 90% B-Basis and 95% envelope, split by specimen class, with traceable citations to the original measurement campaigns. Use it to enter a defensible imperfection amplitude before the prototype is built. Provides the imperfection assumptions used in Level 1 analyses, where measured data is not yet available.
The Explorer shows where your shell sits in the regime map and how it moves as parameters change. R/t, L/R, imperfection amplitude, yield stress, and load combination — each slider updates the regime band and the knockdown curve in real time.
Step 1 — Imperfection sensitivity. A perfect shell (w/t = 0) sits in Regime 3 across nearly all geometries — local buckling and material yielding dominate. As imperfection amplitude grows, Regime 1 (imperfection-dominated) and Regime 2 (transition) emerge in the lower-Z range, while higher-Z geometries remain comparatively stable. The slider sweep tells you whether your design crosses into a sensitive regime as imperfections rise — and at what amplitude the crossing happens. This sets a practical threshold for fabrication tolerance.
Step 2 — Plasticity penalty. Plasticity does not affect all regimes equally. Regime 1 shells lose more capacity to yielding than Regime 3 shells. The Explorer makes this asymmetry visible in the same view, so the trade-off between regime and material strength is one decision, not several disconnected analyses.
Why this matters in design. A shell deep in Regime 3 with bounded imperfection amplitude is a Level 0 case — the analytical MDC Codex result is sufficient. A shell crossing into Regime 1 or 2 is imperfection-driven; either physical measurement (Level 2) or worst-case envelope assumptions (Level 0) are needed. A shell in an unfavourable regime under any reasonable amplitude is a Level 3 candidate.
If your design lands in an unfavourable regime, the Explorer also shows the geometry levers that would shift it: increasing shell length lowers Z, improving fabrication tolerance lowers w/t — both push toward Regime 3. Ring stiffeners go the opposite direction by raising effective Z (shortening the unsupported field), which can be useful for local mode shaping or manufacturing constraints, but trades regime favourability for those gains. The Explorer quantifies the trade-off rather than guessing at it.
Side-by-side allowable stress for NASA SP-8007, Eurocode 1993-1-6 (2007 and 2025), DNV RP-C202, ECSS-HB-32-24, and MDC-B on the identical geometry and load case. Governing case is flagged. The delta between the most-conservative and the physics-based answer is the margin you can recover.
Report exports with full method breakdown, citation, and reproducibility audit trail.
The MDC A-Basis and B-Basis are the statistical design allowables of the Professional tier. We ship only what is validated against our test database. Anything outside the matrix below runs through the public standards (Eurocode, NASA, DNV, ECSS, GOST) — free for every registered user.
| Geometry | Axial Compression | Bending | Combined Bending + Compression | External Pressure |
|---|---|---|---|---|
| Cylinder | ✓ MDC A & Bincl. plasticity & internal pressure | ✓ MDC A & Bincl. plasticity & internal pressure | ✓ MDC A & B | general availability with SC2 release |
| Cone | ✓ MDC A & Bincl. plasticity & internal pressure | ✓ MDC A & Bincl. plasticity & internal pressure | ✓ MDC A & B | general availability with SC2 release |
| Sphere | — | — | — | ✓ MDC A & Bincl. plasticity |
| Torisphere | — | — | — | ✓ MDC A & Bincl. plasticity |
Load cases marked “general availability with SC2 release” remain fully available through the public standards — you will see results from NASA, Eurocode, DNV, ECSS, and GOST side by side. The MDC column is added once the peer-reviewed methodology for each load case is published. Roadmap milestones are published in each release note.
The MDC framework defines a hierarchy of analysis depth. Each level trades effort for tighter design margin. Level 0 is delivered directly by MDC Codex; Levels 1 to 3 are delivered as MDC Consulting for programs requiring numerical analysis under MDC methodology.
Direct MDC computation in the tool. No measurement, no FEM, no project setup. Returns a defensible knockdown factor on B-Basis or A-Basis statistical foundation. The right starting point for sizing trades, RFQ responses, and pre-design exploration.
Numerical analysis (your FE solver of choice) using imperfection amplitudes drawn from the MDC shell-imperfection database. Recovers margin compared to Level 0 by using realistic — rather than worst-case — fabrication assumptions. The right level for preliminary design once geometry is fixed.
Numerical analysis using physically measured imperfection data from the actual shell or a fabrication-equivalent specimen. Recovers further margin by removing statistical conservatism. The right level for verification before qualification testing or for shells already in production.
Numerical analysis combined with geometry modification to push the shell into a more favourable regime — typically increasing length to lower Z, improving fabrication tolerance to lower w/t, or accepting Z-raising stiffeners as a deliberate trade. MDC quantifies the regime shift and its KDF impact, replacing intuition with physics-based optimisation. The right level for mass-critical structures and unfavourable starting geometries.
Illustrative analyses prepared during the MDC Codex beta program. Public case studies with named partners will follow general availability.
Four representative structures spanning aerospace, energy, process engineering, and launch-vehicle hardware. Each analysed end-to-end in MDC Codex — multi-standard, imperfection-aware, with the recoverable margin quantified explicitly.
CFRP-stiffened conical interstage, compared across NASA SP-8019, Eurocode 1993-1-6 (2025), ECSS-HB-32-24, and MDC B-basis. Imperfection sensitivity swept from Q=A to Q=C. Governing standard identified per load case.
Illustrative analysis based on publicly-available Ariane-class launcher reference geometry. Not affiliated with or endorsed by ArianeGroup or ESA.
130 m steel monopile, bending-dominated with axial from tower mass. Compared against Eurocode 1993-1-6 (2025), DNV RP-C202, and MDC A-basis. Fatigue excluded — focus on ultimate stability. Ring stiffener spacing optimised.
Illustrative analysis based on generic onshore wind-tower reference geometry. Not affiliated with or endorsed by Vestas, Siemens Gamesa, or any specific OEM.
ASME/PD 5500 torisphere for a 12 bar process vessel. Plastic buckling governed — not elastic. Compared against PD 5500, GOST 34233-2, Eurocode, and MDC A-basis. Crown-to-knuckle transition plastic-zone flagged automatically.
Illustrative analysis based on publicly-available process-vessel reference geometry. Not affiliated with or endorsed by any specific OEM.
Ring-plus-stringer CFRP cylinder, local skin buckling and global stability evaluated together. Compared against NASA SP-8007/8019, Eurocode 1993-1-6 (2025), ECSS-HB-32-24, and MDC B-basis. Stiffener spacing co-optimised with skin thickness.
Illustrative analysis based on publicly-available Vega-class small-launcher reference geometry. Not affiliated with or endorsed by Avio or ESA.
Typical savings enabled by MDC exceed the annual software cost by one to two orders of magnitude. A single sizing decision on one structure pays for the license many times over.
Beta pricing — locked in for early-access subscribers through general availability.
For programs requiring numerical analysis under MDC methodology — beyond the Codex self-service capability.
Large aerospace, defence, and energy organisations cannot procure a credit-card subscription — and the Professional tier is not built for their workflow. The Enterprise package exists to meet the concrete, often non-negotiable requirements these organisations bring to any external tool.
Enterprise capabilities are scoped and delivered on a per-customer basis. The list below describes what we build with you — most items are engineered to your environment rather than shipped off the shelf. Concrete timelines, pricing, and reference architectures are part of the scoping conversation.
Your engineers drive MDC directly from Python, MATLAB, or their optimisation pipeline — no browser required. Typical use: sweep 10,000 geometry candidates inside an Ansys or Nastran workflow, pull MDC allowables for each, feed them into your mass-optimiser.
Embed your company’s internal knockdown factors, fabrication-quality classes, or proprietary design handbook alongside the public standards. Ideal for organisations with decades of in-house test data or bespoke mission-specific reduction factors (e.g. ESA-ECSS plus your internal amendments).
Your staff sign in once with their corporate identity (Azure AD, Okta, Keycloak). No separate MDC passwords, no shadow accounts, instant de-provisioning when an employee leaves. Required by every IT security department above a certain size.
Run MDC entirely inside your firewall — on your own servers, in your own data centre, or in a controlled cloud tenant (AWS GovCloud, OVH SecNumCloud, Bleu, private Azure). Mandatory for ITAR, export-controlled, classified, or IP-sensitive programmes where geometry data must never leave the organisation.
A named engineer (not a ticket queue) is assigned to your account. Direct email & phone contact, scheduled review calls, support for internal tool-qualification exercises (ECSS-E-ST-40, DO-330), and bespoke validation studies against your reference cases.
Contractual availability guarantee — maximum 8.76 hours of unplanned downtime per year. Defined maintenance windows, status page, incident reporting, and service credits if we miss the target. Enterprise procurement requires this in writing.
Formal quotation with VAT-ID, purchase-order workflow, annual framework agreement, NDA, Auftragsverarbeitungsvertrag (DPA under GDPR Art. 28), supplier-qualification questionnaires, export-control declarations. The things large buyers cannot close a deal without.
Optional pricing model tied to delivered value rather than seats. Example: a programme saves 5 % structural mass on a launcher upper stage → licence fee is a fraction of the demonstrated launch-cost saving. Aligns incentives on both sides.
The Professional tier (€990 / named user / month) is the right choice for individual structural engineers, small consultancies, and early evaluation inside larger organisations. It covers the full analytical capability, all bases, certifiable reports, and the complete standards set.
You need Enterprise as soon as any of the following apply:
→ Talk to us — we’ll scope the right setup, share a reference architecture, and prepare the paperwork your procurement team will ask for.
NASA SP-8007 applies a single empirical knockdown factor to all cylindrical shells regardless of their imperfection signature, fabrication quality, or geometric parameters. MDC computes the knockdown factor as a continuous function of the Batdorf parameter (Z) and the imperfection-to-thickness ratio (w/t), based on mechanistic models validated against experimental data. The result is a less conservative, but equally safe, design allowable — with full transparency into the margin being recovered.
MDC Codex produces fully traceable outputs: input parameters, applicable standard, statistical basis, intermediate values, and design verdict. Reports are structured for inclusion in design review packages. The applicable standard (Eurocode, NASA, DNV, etc.) defines the certification pathway — MDC Codex computes the values with the traceability that certification processes require.
The Validation Hub contains 1,000+ experimental buckling records from published literature spanning 60+ years. Each record includes specimen geometry, material properties, test procedure, and measured collapse load. MDC predictions can be directly overlaid against these measurements — discrepancies are visible and auditable. The methodology itself is published in the Proceedings of the Royal Society A (2025).
No. MDC Codex is a pre-design and verification platform. It operates at the analytical level — fast, standards-compliant, and traceable. Use it to size structures, compare design codes, and identify critical load cases before committing to a nonlinear FE campaign. It reduces the number of FE iterations required, not the need for FEA itself. Teams typically report 60–80% fewer required GNIA/GMNIA runs after implementing MDC in their workflow.
MDC Codex supports cylinders, cones, spheres, and torispherical heads under 20+ load cases and combinations. The primary industries are aerospace (launch vehicles, satellite structures), offshore and subsea (pipelines, pressure housings), and pressure vessel manufacturing (heads, caps, closures). The tool includes both isotropic metallic and composite shell analysis.
Yes. The Enterprise tier includes the ability to integrate custom KDF curves (e.g., from proprietary test campaigns or internal FE parametric studies) and custom design norms. API access is available for integration into existing engineering workflows. On-premise deployment and SSO are also supported for organizations with strict compliance requirements.
Subscribe for the months you need it. There is no minimum commitment and no cancellation fee. One month of Professional costs less than two hours of structural consulting.
MDC Codex gives structural teams the analytical foundation to design lighter, validate faster, and certify with full traceability. Start with the Free tier — no commitment, no credit card.
Read the Publication — Proc. R. Soc. A, 2025