Variational Coupled Loads Analysis

The impact of structural component parameter uncertainties such as frequencies, stiffness, mass, damping, interface deadband sizes, friction, interface springs/dampers (isolation system) on the component’s dynamic response in a coupled system is most accurately ascertained by conducting what ASD has termed a variational coupled loads analyses (VCLA). A VCLA consists of multiple CLA executions with a range of parameter(s) being varied by a specified increment in each CLA. The VCLA becomes a Monte Carlo analysis if variation parameters are statistically selected.

The objective of a VCLA is to rigorously ascertain the impact of component parameter uncertainties on component loads. By doing so, the risk of structural certification issues later in the design cycle is greatly reduced. The VCLA is a powerful tool in preliminary design where it can be utilized in lieu of uncertainty factors. Unlike uncertainty factor application, a VCLA identifies the structural members (typically few) most sensitive to the parameter uncertainties and therefore does not penalize the remainder of the structure. In addition, frequency variation VCLAs have been utilized to ascertain the impact of a component frequency deviations from the modal survey test.

The increment by which the parameter uncertainty is varied from one CLA to the next in a VCLA must be fine enough not to skip over the component’s sensitive response items peak resonant response. Therefore, typically numerous CLAs are utilized to provide granularity for the “variational spectra”, i.e., the absolute max response of a component recovery item versus the parameter variation.

Clearly, a software tool capable of very fast and accurate CLA executions is a necessary requirement for a successful and cost-effective VCLA that can be completed within the desired schedule. The long schedules required to complete a single CLA in commercially available heritage tools have played a major role in disallowing VCLAs.

The enabling capabilities in ASD’s commercially available software tool ASD/CLAS, namely fast coupled loads analysis (CLA) executions and highly accurate linear/nonlinear CLAs, have enabled our clients to rigorously ascertain the impact of component parameter uncertainties in coupled loads analyses upfront and in the early design process, resulting in significant cost, schedule, and risk reductions.

Case Histories

  • ICC-G Cargo Loads Environment Variational CLAs (EADS): ASD conducted 1,144 CLAs to characterize the impact of ICC-G cargo weight variations (up to 5000 lbs in 5% increments) coupled with MPLM (pressurized payload carrier) weight variations (up to 10,000 lbs in 5% increments).
  • Minotaur VCLAs (ORS, NASA, DesignNet, Instar, Orbital): ASD was tasked to develop payload envelopes for certain classes of DoD payloads, the goal being that such payloads could benefit from a greatly simplified flight certification process. Payload variations included mass, C.G., and frequencies for both isolated and hard mounted payloads. Flight events included pre-ignition, liftoff, transonic, supersonic and second stage ignition. ASD conducted over 600 CLAs, made possible only by the enabling technologies in its ASD/CLAS software, in a short period of time. The payload envelopes are germane to a particular launch vehicle.
  • STS-114 Variational CLAs (Boeing, Spacehab, NASA): ASD conducted 9 CLAs to characterize the impact of CMG and FHRC ORU payload stiffness (frequency) variations (uncertainty) of +/- 20% of nominal in 5% increments in order to determine worst case loads.
  • PFAP Variational CLAs (Spacehab): ASD conducted 9 CLAs to characterize the impact of frequency variation of +/- 20% of nominal in 5% increments to determine the worst-case loads
  • Cargo Transport Container (CTC) Variational CLAs (Oceaneering Space Systems): ASD conducted 22 CLAs to characterize the CTC loads a a function of payload weight variations and isolation parameters. Repeated the analysis for CTC without isolation.
  • Space Shuttle Mission 1E (EADS): ASD conducted 114 CLAs to develop the worst-case preliminary design loads for EuTEF and SOLAR science payloads on the new ICC-L carrier accounting for +/- 20% frequency variation on the science payloads.
  • Space Shuttle Mission STS-121 (NASA, Lockheed Martin, Spacehab): ASD conducted 21 CLAs to determine the worst-case impact of DDCU and MBSU cold plates foam stiffness uncertainty of +/- 50% in 5% increments on loads.
  • Space Shuttle Mission STS-121 (Cycle-2) (NASA, Lockheed Martin, Spacehab): ASD conducted 21 CLAs to determine the worst-case impact of DDCU and MBSU cold plates foam stiffness uncertainty of +/- 50% in 5% increments on loads.
  • Space Shuttle Mission STS-121 (Cycle-2A) (NASA, Lockheed Martin, Spacehab): ASD conducted 21 CLAs to determine the worst-case impact of DDCU and MBSU cold plates foam stiffness uncertainty of +/- 50% in 5% increments on loads.
  • Space Shuttle Mission STS-121 (Cycle-2A; include specific foam damping properties) (NASA, Lockheed Martin, Spacehab): ASD conducted 21 CLAs to determine the worst-case impact of DDCU and MBSU cold plates foam stiffness uncertainty of +/- 50% in 5% increments on loads.
  • Space Shuttle Mission STS-121 (Spacehab): ASD conducted 12 CLAs to assess the impact of potential mass variability in the newly designed FGB/FSE payload
  • Space Shuttle Mission STS-121 (Cycle-3) (NASA, Lockheed Martin, Spacehab): ASD conducted 21 CLAs to determine the worst-case impact of DDCU and MBSU cold plates foam stiffness uncertainty of +/- 50% in 5% increments on loads.
  • Space Shuttle Mission STS-121 (Cycle-3; include specific foam damping properties) (NASA, Lockheed Martin, Spacehab): ASD conducted 21 CLAs to determine the worst-case impact of DDCU and MBSU cold plates foam stiffness uncertainty of +/- 50% in 5% increments on loads.