A continuum-mechanical theory of redundancy in elastostatic structures

Gade, Jan; Tkachuk, Anton; Scheven, Malte von; Bischoff, Manfred

doi:10.1016/j.ijsolstr.2021.01.022

Cited by 6 publications

(11 citation statements)

References 27 publications

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“…The redundancy matrix has several algebraic and spectral-theoretic properties. For more details, we refer to von Gade et al 2021.…”

Section: Redundancy Distributionmentioning

confidence: 99%

“…The idea of the redundancy matrix was extended to kinematically indeterminate structures (Tibert 2005;Zhou et al 2015;Y. Chen et al 2018) and to continuous representations of structures by a connection between concepts from applied mathematics and classical structural mechanics (Gade et al 2021). Further references for the calculation and application of the redundancy matrix can be found in the work by von Gade et al 2021.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Update of Redundancy Matrices for Truss and Frame Structures

Krake¹,

Scheven²,

Gade³

et al. 2022

Preprint

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Redundancy matrices provide insights into the load carrying behavior of statically indeterminate structures. This information can be employed for the design and analysis of structures with regard to certain objectives, for example reliability, robustness, or adaptability. In this context, the structure is often iteratively examined with the help of slight adjustments. However, this procedure generally requires a high computational effort for the recalculation of the redundancy matrix due to the necessity of costly matrix operations. This paper addresses this problem by providing generic algebraic formulations for efficiently updating the redundancy matrix (and related matrices). The formulations include various modifications like adding, removing, and exchanging elements and are applicable to truss and frame structures. With several examples, we demonstrate the interaction between the formulas and their mechanical interpretation. Finally, a performance test for a scaleable structure is presented.

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“…The redundancy matrix has several algebraic and spectral-theoretic properties. For more details, we refer to von Gade et al 2021.…”

Section: Redundancy Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Efficient Update of Redundancy Matrices for Truss and Frame Structures

Krake¹,

Scheven²,

Gade³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The redundancy matrix has several algebraic and spectral-theoretic properties. For more details, we refer to von Scheven et al ( 2021) and Gade et al (2021).…”

Section: Redundancy Distributionmentioning

confidence: 99%

“…Another more recent work on the redundancy matrix was published by Liu and Liu (2005), who used the redundancy matrix and its counterpart, the 'importance indices', to assess the importance of structural elements in truss and frame structures. The idea of the redundancy matrix was extended to kinematically indeterminate structures (Tibert 2005;Zhou et al 2015;Chen et al 2018) and to continuous representations of structures by a connection between concepts from applied mathematics and classical structural mechanics (Gade et al 2021). Further references for the calculation and application of the redundancy matrix can be found in the works by von and Gade et al (2021).…”

Section: Introductionmentioning

confidence: 99%

“…The idea of the redundancy matrix was extended to kinematically indeterminate structures (Tibert 2005;Zhou et al 2015;Chen et al 2018) and to continuous representations of structures by a connection between concepts from applied mathematics and classical structural mechanics (Gade et al 2021). Further references for the calculation and application of the redundancy matrix can be found in the works by von and Gade et al (2021).…”

Section: Introductionmentioning

confidence: 99%

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Efficient Update of Redundancy Matrices for Truss and Frame Structures

Krake¹,

Scheven²,

Gade³

et al. 2022

Journal of Theoretical, Computational and Applied Mechanics

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Adaptive structures in civil engineering – state of the art

Schwegmann,

Zabel,

Koch

2024

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PurposeAdaptive load-bearing structures pursue the approach of saving mass within a load-bearing structure by adding external energy, thus saving materials and resources. This paper provides an overview of current research developments and shows some examples of existing prototypes.Design/methodology/approachFirst, basic terms and definitions from the research field of adaptive structures are introduced. After a brief historical insight, the numerical methods and prototypes used are presented as examples. The paper concludes with a summary of the state-of-the-art and open questions.FindingsThe current state of the art shows that the idea of adaptive structures offers great potential for more sustainability and resource efficiency in the construction industry. However, it also shows that research is still at the basic stage and that there are still some gaps in research.Originality/valueThe implementation of adaptive load-bearing structures is just one of many different approaches to greater sustainability in the construction sector. The issue of adaptive structures is a highly interdisciplinary field of research. The following paper is a literature review intended to summarize and critically evaluate the state-of-the-art research in this field. In the final section, some open questions are addressed, indicating that this research topic is still evolving.

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A continuum-mechanical theory of redundancy in elastostatic structures

Cited by 6 publications

References 27 publications

Efficient Update of Redundancy Matrices for Truss and Frame Structures

Efficient Update of Redundancy Matrices for Truss and Frame Structures

Efficient Update of Redundancy Matrices for Truss and Frame Structures

Adaptive structures in civil engineering – state of the art

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