The degree of statical indeterminacy is a fundamental property in structural mechanics of discrete truss and beam structures, exploitable in analysis and design. While further specifications, like.e.g. subdivision into an internal and external part or determination w.r.t. special load directions, are well-established, the property is today mainly understood as an integral property of an entire structure (or entire substructures), without quantified information about its distribution in space and w.r.t. load-carrying types. The redundancy matrix, introduced in [1, 2] and extended in [3], provides information about the distribution of statical indeterminacy in discrete truss and beam structures. This gives an additional valuable insight into the load-carrying behavior. In [3] also the redundancy distribution for one-dimensional continua is introduced and computed analogously to the redundancy matrix in discrete truss structures. A generalization of the redundancy concept to spatially continuous, linear, elastostatic representations of structures is given in [4]. The quantity cation of redundancy distribution considering geometrically non-linear behavior is approached in [2, 5]. These works are limited to discrete representations of truss structures with prestressing. We present an extension of the concept of redundancy to beam and surface structures using a finite element framework. We also discuss ideas on how to consider geometrically non-linear behaviour. There are numerous applications like e.g. robust design of structures, quantification of imperfection sensitivity, evaluation of adaptability, assessment of actuator placement as well as optimal control in adaptive structures.
REFERENCES
[1] Bahndorf, J.: Zur Systematisierung der Seilnetzberechnung und zur Optimierung vonSeilnetzen. Doctoral Thesis, Universitat Stuttgart, Stuttgart, 1991.
[2] Strobel, D.: Die Anwendung der Ausgleichungsrechnung auf elastomechanische Systeme.Doctoral Thesis, Universitat Stuttgart, Stuttgart, 1995.
[3] von Scheven, M., Ramm, E. and Bischoff, M.: Quanti cation of the Redundancy Distributionin Truss and Beam Structures. Int. J. Sol. Str., 2020.
[4] Gade, J., Tkachuk, A., von Scheven, M. and Bischoff, M.: A continuum-mechanical theory of redundancy in elastostatic structures. Int. J. Sol. Str., under review, 2020.
[5] Zhou, J., Chen, W., Zhao, B. and Gao, C.: A uni ed formulation for redundancy of cable-strut structures considering the effect of pre-stresses. Proc. IASS Ann. Symp. 2016, Tokyo, Japan.