Funicularity in elastic domes: Coupled effects of shape and thickness
An historical overview is presented concerning the theory of shell structures and thin domes. Early conjectures proposed, among others, by French, German, and Russian Authors are discussed. Static and kinematic matrix operator equations are formulated explicitly in the case of shells of revolution a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2021-05-01
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| Series: | Curved and Layered Structures |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/cls-2021-0017 |
| _version_ | 1818735747366125568 |
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| author | Accornero Federico Carpinteri Alberto |
| author_facet | Accornero Federico Carpinteri Alberto |
| author_sort | Accornero Federico |
| collection | DOAJ |
| description | An historical overview is presented concerning the theory of shell structures and thin domes. Early conjectures proposed, among others, by French, German, and Russian Authors are discussed. Static and kinematic matrix operator equations are formulated explicitly in the case of shells of revolution and thin domes. It is realized how the static and kinematic matrix operators are one the ad-joint of the other, and, on the other hand, it can be rigorously demonstrated through the definition of stiffness matrix and the application of virtual work principle. In this context, any possible omission present in the previous approaches becomes evident. As regards thin shells of revolution (thin domes), the elastic problem results to be internally statically-determinate, in analogy to the case of curved beams, being characterized by a system of two equilibrium equations in two unknowns. Thus, the elastic solution can be obtained just based on the equilibrium equations and independently of the shape of the membrane itself. The same cannot be affirmed for the unidimensional elements without ‚exural stiffness (ropes). Generally speaking, the static problem of elastic domes is governed by two parameters, the constraint reactions being assumed to be tangential to meridians at the dome edges: the shallowness ratio and the thickness of the dome. On the other hand, when the dome thickness tends to zero, the funicularity emerges and prevails, independently of the shallowness ratio or the shape of the dome. When the thickness is finite, an optimal shape is demonstrated to exist, which minimizes the flexural regime if compared to the membrane one. |
| first_indexed | 2024-12-18T00:26:10Z |
| format | Article |
| id | doaj.art-4d45f3a284794aca9a927cb033b0b921 |
| institution | Directory Open Access Journal |
| issn | 2353-7396 |
| language | English |
| last_indexed | 2024-12-18T00:26:10Z |
| publishDate | 2021-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Curved and Layered Structures |
| spelling | doaj.art-4d45f3a284794aca9a927cb033b0b9212022-12-21T21:27:15ZengDe GruyterCurved and Layered Structures2353-73962021-05-018118118710.1515/cls-2021-0017Funicularity in elastic domes: Coupled effects of shape and thicknessAccornero Federico0Carpinteri Alberto1Politecnico di Torino, DISEG, 24 C.so Duca degli Abruzzi, 10129Torino, ItalyPolitecnico di Torino, DISEG, 24 C.so Duca degli Abruzzi, 10129Torino, ItalyAn historical overview is presented concerning the theory of shell structures and thin domes. Early conjectures proposed, among others, by French, German, and Russian Authors are discussed. Static and kinematic matrix operator equations are formulated explicitly in the case of shells of revolution and thin domes. It is realized how the static and kinematic matrix operators are one the ad-joint of the other, and, on the other hand, it can be rigorously demonstrated through the definition of stiffness matrix and the application of virtual work principle. In this context, any possible omission present in the previous approaches becomes evident. As regards thin shells of revolution (thin domes), the elastic problem results to be internally statically-determinate, in analogy to the case of curved beams, being characterized by a system of two equilibrium equations in two unknowns. Thus, the elastic solution can be obtained just based on the equilibrium equations and independently of the shape of the membrane itself. The same cannot be affirmed for the unidimensional elements without ‚exural stiffness (ropes). Generally speaking, the static problem of elastic domes is governed by two parameters, the constraint reactions being assumed to be tangential to meridians at the dome edges: the shallowness ratio and the thickness of the dome. On the other hand, when the dome thickness tends to zero, the funicularity emerges and prevails, independently of the shallowness ratio or the shape of the dome. When the thickness is finite, an optimal shape is demonstrated to exist, which minimizes the flexural regime if compared to the membrane one.https://doi.org/10.1515/cls-2021-0017static-kinematic dualityshell of revolutionthin domesmembranesshallowness ratiodome thicknessfunicularity |
| spellingShingle | Accornero Federico Carpinteri Alberto Funicularity in elastic domes: Coupled effects of shape and thickness Curved and Layered Structures static-kinematic duality shell of revolution thin domes membranes shallowness ratio dome thickness funicularity |
| title | Funicularity in elastic domes: Coupled effects of shape and thickness |
| title_full | Funicularity in elastic domes: Coupled effects of shape and thickness |
| title_fullStr | Funicularity in elastic domes: Coupled effects of shape and thickness |
| title_full_unstemmed | Funicularity in elastic domes: Coupled effects of shape and thickness |
| title_short | Funicularity in elastic domes: Coupled effects of shape and thickness |
| title_sort | funicularity in elastic domes coupled effects of shape and thickness |
| topic | static-kinematic duality shell of revolution thin domes membranes shallowness ratio dome thickness funicularity |
| url | https://doi.org/10.1515/cls-2021-0017 |
| work_keys_str_mv | AT accornerofederico funicularityinelasticdomescoupledeffectsofshapeandthickness AT carpinterialberto funicularityinelasticdomescoupledeffectsofshapeandthickness |