Quadratic Stress Failure Constraints for Structures Under Combined Steady and Random Excitation

Constraint functions are formulated and their analytical sensitivities are derived for multiaxial states of stress arising in actively controlled airplane structures from combined maneuver loads and random gust responses. The stress failure criteria of von Mises for isotropic materials and Tsai-Wu for composite materials are considered. These criteria are nonlinear in nature and involve interactions between the multiaxial stress components. The gust response is based on random gust analysis using state-space mathematical models and statistical properties of gusts in the atmosphere. The covariance matrix of the stress components at a point is used to define a quadratic surface representing stress combinations of equal probability. It is shown how a single critical stress combination can be determined analytically for all stress combinations on the equal-probability stress surface. Analytic sensitivities of the resulting stress constraint with respect to design variables are derived. A constraint function approximation is also derived to reduce computational effort in an approximation-concepts-based optimization strategy. The constraint, analytic sensitivities, and approximations are then integrated into a multidisciplinary aeroservoelastic optimization capability, and results for a large flexible commercial transport airplane are presented.