Distributed redundancy in elastostatics for the design of adaptive structures

Abstract

The present thesis is concerned with the concept of distributed redundancy in linear elastostatics of load-carrying structures. This concept addresses supernumerous self-equilibrating force states in a statically indeterminate structure activated by internal constraint due to geometric compatibility. The redundancy distribution in a truss or frame system can be considered for investigations on failure safety. A continuum-mechanical theory on distributed redundancy for statically determinate structural theories is presented. Here, the redundancy relation appears as an integral equation with a special influence function as integral kernel. From this influence function, the redundancy density function can be derived. Furthermore, the concept of distributed redundancy is introduced for finite element models. The redundancy matrix inherently appears in a hybrid-mixed displacement-stress formulation based on the Hellinger-Reissner variational principle. Moreover, the redundancy concept reflects the elastic response of a structural system due to prescribed inelastic strain quantities such as temperature loads or actuation. This reflection allows for the application of the concept for analysis and design of adaptive structures. A deeper understanding of the redundancy distribution and space of self-stress states based on the redundancy matrix can be employed for redistribution of forces and adaptation of displacements in adaptive trusses. As design aspects for adaptive trusses, two methods for load-case-independent actuator placement are described. Formulations for compensation of displacements or forces or a combination of both are presented. Finally, a novel formulation of displacement control minimizing the actuation work is developed. Its application in an exemplary adaptive truss bridge system shows significant potential for reducing actuation work compared to a conventional displacement control.