Parametric Analysis of Tensegrity Plate-Like Structures: Part 2—Quantitative Analysis
Abstract
:Featured Application
Abstract
1. Introduction
- determination of the minimum and maximum initial prestress levels,
- assessment of the influence of the initial prestress on the structural displacements,
- assessment of the influence of the initial prestress on the effort of the structure, and
- assessment of the influence of the initial prestress on the rigidity of the structure.
2. Mathematical Description
2.1. Geometrical Non-Linear Model of Tensegrity Element
2.2. Model of Tensegrity Structure
3. Influence of the Initial Prestress Level on Static Properties of Tensegrity Structures (Quantitative Analysis)
4. Examples
- for cables (S460N): diameter , moment of inertia , cross-sectional area , load-bearing capacity (calculated with taking into account partial factor for structural resistance): ; the maximum value of the tensile force depends on the self-stress state,
- for struts (made of hot-finished circular hollow section, steel S355J2): diameter: , thickness: , moment of inertia: , cross-sectional area: , load-bearing capacity: ; the maximum value of the compressed force is equal to (—the initial prestress force).
4.1. Single Modified Quartex Module
4.2. Four-Module Tensegrity Plate-Like Structures
4.3. Sixteen-Module Tensegrity Plate-Like Structures and Plate Strips
4.4. Sixty-Four-Module Tensegrity Plate-Like Structures
5. Summary and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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S [kN] | Type of Element | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
0.01 | cables | 26.5 | 0.241 | 1.0 | 35.7 | 0.324 | 1.0 | 44.1 | 0.400 | 1.0 |
struts | −35.6 | 0.184 | −47.8 | 0.246 | 59.1 | 0.305 | ||||
110 | cables | 87.3 | 0.792 | 3.7 | 91.1 | 0.826 | 2.9 | 95.3 | 0.865 | 2.5 |
struts | −117.2 | 0.604 | −122.2 | 0.630 | −128.0 | 0.660 |
S [kN] | Type of Element | Model P4-1 () | Model P4-2 | Model P4-3 | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Smin | cables | 49.54 | 0.450 | 1.0 | 48.8 | 0.443 | 1.0 | 54.4 | 0.493 | 1.0 |
struts | −37.0 | 0.191 | −36.6 | 0.189 | −41.0 | 0.211 | ||||
60 | cables | 100.5 | 0.912 | 2.1 | 101.5 | 0.921 | 2.4 | 105.6 | 0.958 | 1.9 |
struts | −71.2 | 0.367 | −71.93 | 0.371 | −75.4 | 0.389 |
S [kN] | Type of Element | Model P4-4 | Model P4-5 | ||||
---|---|---|---|---|---|---|---|
Smin | cables | 57.7 | 0.524 | 1.0 | 54.1 | 0.491 | 1.0 |
struts | −46.3 | 0.239 | −50.1 | 0.258 | |||
60 | cables | 93.2 | 0.846 | 1.4 | 105.2 | 0.954 | 1.9 |
struts | −73.1 | 0.376 | −77.0 | 0.397 |
Simply Supported | Cantilever | ||||||||
---|---|---|---|---|---|---|---|---|---|
Second Order Theory | Third Order Theory | Second Order Theory | |||||||
S | Plate Strip PS-1x | Plate Model P16-1 | Relative Error | Plate Strip PS-1x | Plate Model P16-1 | Relative Error | Plate Strip PS-2x | Plate Model P16-2 | Relative Error |
[mm] | [mm] | [%] | [mm] | [mm] | [%] | [mm] | [mm] | [%] | |
3 | −156.339 | −156.342 | 0.00 | −17.056 | −17.605 | −3.11 | − | − | − |
10 | −46.965 | −46.967 | −0.01 | −15.672 | −16.131 | −2.85 | − | − | − |
21 | −23.527 | −23.530 | −0.01 | −13.751 | −14.091 | −2.41 | −0.737 | −0.793 | −7.08 |
30 | −15.715 | −15.717 | −0.02 | −11.954 | −12.193 | −1.95 | −0.736 | −0.793 | −7.08 |
40 | −11.808 | −11.811 | −0.02 | −10.345 | −10.505 | −1.52 | −0.736 | −0.792 | −7.07 |
50 | −9.465 | −9.467 | −0.03 | −8.962 | −9.066 | −1.15 | −0.736 | −0.792 | −7.07 |
60 | −7.902 | −7.905 | −0.03 | −7.810 | −7.878 | −0.86 | −0.735 | −0.791 | −7.08 |
S [kN] | Type of Element | Model PS-1x () | Model PS-1y () | ||||
---|---|---|---|---|---|---|---|
Smin | cables | 54.1 | 0.491 | 1.0 | 52.7 | 0.478 | 1.0 |
struts | −40.2 | 0.207 | −39.2 | 0.202 | |||
60 | cables | 103.3 | 0.937 | 2.2 | 102.6 | 0.931 | 2.2 |
struts | −73.0 | 0.377 | −72.5 | 0.374 |
S [kN] | Type of Element | Model P64-1 () | Model P64-2 () | Model P64-3 () | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Smin | cables | 28.9 | 0.262 | 1.0 | 72.5 | 0.658 | 1.0 | 64.8 | 0.588 | 1.0 |
struts | −23.7 | 0.123 | −63.0 | 0.324 | −58.4 | 0.301 | ||||
60 | cables | 91.1 | 0.827 | 3.3 | 94.4 | 0.857 | 1.2 | 97.0 | 0.880 | 1.3 |
struts | −64.6 | 0.333 | −77.9 | 0.402 | 79.9 | 0.412 |
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Obara, P.; Tomasik, J. Parametric Analysis of Tensegrity Plate-Like Structures: Part 2—Quantitative Analysis. Appl. Sci. 2021, 11, 602. https://doi.org/10.3390/app11020602
Obara P, Tomasik J. Parametric Analysis of Tensegrity Plate-Like Structures: Part 2—Quantitative Analysis. Applied Sciences. 2021; 11(2):602. https://doi.org/10.3390/app11020602
Chicago/Turabian StyleObara, Paulina, and Justyna Tomasik. 2021. "Parametric Analysis of Tensegrity Plate-Like Structures: Part 2—Quantitative Analysis" Applied Sciences 11, no. 2: 602. https://doi.org/10.3390/app11020602
APA StyleObara, P., & Tomasik, J. (2021). Parametric Analysis of Tensegrity Plate-Like Structures: Part 2—Quantitative Analysis. Applied Sciences, 11(2), 602. https://doi.org/10.3390/app11020602