Nonlinear Geometric Thermoelastic Response of Structures with Uncertain Thermal and Structural Properties

Abstract

The focus of this investigation is on modeling uncertainties on the structural and thermal properties of heated structures and assessing their effects on the resulting temperature distributions and structural response. This effort is accomplished within the framework of reduced-order models (ROMs) of both the thermal (heat conduction) and structural (nonlinear geometric response) problems relying on the maximum entropy nonparametric approach. Uncertainties are introduced on both the heat conduction and the structural response problems. In the latter, it is in particular shown that the purely structural terms of the ROM governing equations and those associated with the structural–thermal coupling should be randomized jointly. Moreover, this can be done through the construction of a large matrix that includes all of these terms and is shown to be symmetric and positive definite. Several challenges in applying this approach are identified and resolved. Finally, the applicability of the methodology is demonstrated on the response of a simple panel subjected to an oscillating heating flux as an example of strongly coupled thermal–structural problems.