A continuum-mechanical theory of redundancy in elastostatic structures

In the present paper, theoretical foundations of redundancy in spatially continuous, elastostatic, and lin -ear representations of structures are derived. Adopting an operator-theoretical perspective, the redun-dancy operator is introduced, inspired by the concept of redundancy matrices, previously described for spatially discrete representations of structures. Studying symmetry, trace, rank, and spectral properties of this operator as well as revealing the relation to the concept of statical indeterminacy, a continuum-mechanical theory of redundancy is proposed. Here, the notion "continuum-mechanical" refers to the representation being spatially continuous. Apart from the theory itself, the novel outcome is a clear con-cept providing information on the distribution of statical indeterminacy in space and with respect to dif-ferent load carrying mechanisms. The theoretical findings are confirmed and illustrated within exemplary rod, plane beam, and plane frame structures. The additional insight into the load carrying behavior may be valuable in numerous applications, including robust design of structures, quantification of imperfection sensitivity, assessment of adaptability, as well as actuator placement and optimized con-trol in adaptive structures. (c) 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).