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.