A Trigonometry Based Linear Form- Finding Method For Irregular Multi-Layer Prism Tensegrity
Prism tensegrity is one type of tensegrity system, is suitable for possible application in the field of civil and architectural engineering. The form-finding process of an irregular prism tensegrity is normally nonlinear due to the reason that the number of force equilibrium equations are less th...
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my-usm-ep.460712021-11-17T03:42:15Z A Trigonometry Based Linear Form- Finding Method For Irregular Multi-Layer Prism Tensegrity 2017-05-01 Moghaddas, Mohammad T Technology TA1-2040 Engineering (General). Civil engineering (General) Prism tensegrity is one type of tensegrity system, is suitable for possible application in the field of civil and architectural engineering. The form-finding process of an irregular prism tensegrity is normally nonlinear due to the reason that the number of force equilibrium equations are less than the number of unknown parameters. The review of previously proposed methods of form-finding shows that none of them is practical for the form-finding of irregular prism tensegrity with a large number of members. Therefore, this study was carried out with the aim of presenting a practical form-finding method which is fast, accurate and able to satisfy designers’ requirements. Moreover, self-weight and external loads are known to affect final configuration of prism tensegrity which is neglected in the form-finding analysis. Prism tensegrities applied in the field of civil and architectural engineering are subjected to specified practical requirement of structure displacement and member deflection. Hence, this study also aimed at investigating the effect of initial stress and configuration on deformation of prism tensegrity under self-weight. In this research, trigonometry relation is used to connect length relation condition and force equilibrium equations in order to establish a linear approach of form-finding called trigonometry approach. The novel trigonometry approach for form-finding of irregular single layer prism tensegrity is firstly introduced. Then, the concept of connection and conjunction polygons necessary for form-finding of multi-layer prism tensegrity are presented, where a connection polygon is used to connect single layer prism tensegrities to form a multi-layer prism tensegrity. The established trigonometry approach for the form- finding of the single layer prism tensegrity is extended to form-finding of multi-layer prism tensegrity. A computational Excel tool for form-finding is developed based on the trigonometry approach. Eight numerical examples for irregular single layer and ten numerical examples for irregular multi-layer prism tensegrity were designed successfully using the developed computational Excel tool. In all of these examples, new configurations of prism tensegrities are presented for the first time and most of them are unsolvable by other available approaches. Nine numerical examples with variable configurations were designed by using the trigonometry approach proposed in this study and analysed using the Robot Structural Analysis. The self-weight and the external loads are applied on the models as distributed and nodal loads, respectively. The effect of initial stress and configuration on deformation of practically designed prism tensegrity under self-weight is investigated. Geometrical nonlinear analysis was carried out on nine different regular and irregular examples with different base polygon, number of layer and configuration under four different sets of initial member force and four different member cross sections. From the results of analysis, effects of number of side of the base polygon, number of layers, configuration, initial member force and member cross section of prism tensegrity on maximum joint displacement, member deflection, tensile and compression stress of members are obtained. 2017-05 Thesis http://eprints.usm.my/46071/ http://eprints.usm.my/46071/1/A%20Trigonometry%20Based%20Linear%20Form-%20Finding%20Method%20For%20Irregular%20Multi-Layer%20Prism%20Tensegrity.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Kejuruteraan Awam |
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T Technology T Technology Moghaddas, Mohammad A Trigonometry Based Linear Form- Finding Method For Irregular Multi-Layer Prism Tensegrity |
| description |
Prism tensegrity is one type of tensegrity system, is suitable for possible
application in the field of civil and architectural engineering. The form-finding process
of an irregular prism tensegrity is normally nonlinear due to the reason that the number
of force equilibrium equations are less than the number of unknown parameters. The
review of previously proposed methods of form-finding shows that none of them is
practical for the form-finding of irregular prism tensegrity with a large number of
members. Therefore, this study was carried out with the aim of presenting a practical
form-finding method which is fast, accurate and able to satisfy designers’
requirements. Moreover, self-weight and external loads are known to affect final
configuration of prism tensegrity which is neglected in the form-finding analysis.
Prism tensegrities applied in the field of civil and architectural engineering are
subjected to specified practical requirement of structure displacement and member
deflection. Hence, this study also aimed at investigating the effect of initial stress and
configuration on deformation of prism tensegrity under self-weight. In this research,
trigonometry relation is used to connect length relation condition and force equilibrium
equations in order to establish a linear approach of form-finding called trigonometry
approach. The novel trigonometry approach for form-finding of irregular single layer
prism tensegrity is firstly introduced. Then, the concept of connection and conjunction
polygons necessary for form-finding of multi-layer prism tensegrity are presented,
where a connection polygon is used to connect single layer prism tensegrities to form
a multi-layer prism tensegrity. The established trigonometry approach for the form-
finding of the single layer prism tensegrity is extended to form-finding of multi-layer
prism tensegrity. A computational Excel tool for form-finding is developed based on
the trigonometry approach. Eight numerical examples for irregular single layer and ten
numerical examples for irregular multi-layer prism tensegrity were designed
successfully using the developed computational Excel tool. In all of these examples,
new configurations of prism tensegrities are presented for the first time and most of
them are unsolvable by other available approaches. Nine numerical examples with
variable configurations were designed by using the trigonometry approach proposed
in this study and analysed using the Robot Structural Analysis. The self-weight and
the external loads are applied on the models as distributed and nodal loads,
respectively. The effect of initial stress and configuration on deformation of practically
designed prism tensegrity under self-weight is investigated. Geometrical nonlinear
analysis was carried out on nine different regular and irregular examples with different
base polygon, number of layer and configuration under four different sets of initial
member force and four different member cross sections. From the results of analysis,
effects of number of side of the base polygon, number of layers, configuration, initial
member force and member cross section of prism tensegrity on maximum joint
displacement, member deflection, tensile and compression stress of members are
obtained. |
| format |
Thesis |
| qualification_name |
Doctor of Philosophy (PhD.) |
| qualification_level |
Doctorate |
| author |
Moghaddas, Mohammad |
| author_facet |
Moghaddas, Mohammad |
| author_sort |
Moghaddas, Mohammad |
| title |
A Trigonometry Based Linear Form- Finding Method For Irregular Multi-Layer Prism Tensegrity |
| title_short |
A Trigonometry Based Linear Form- Finding Method For Irregular Multi-Layer Prism Tensegrity |
| title_full |
A Trigonometry Based Linear Form- Finding Method For Irregular Multi-Layer Prism Tensegrity |
| title_fullStr |
A Trigonometry Based Linear Form- Finding Method For Irregular Multi-Layer Prism Tensegrity |
| title_full_unstemmed |
A Trigonometry Based Linear Form- Finding Method For Irregular Multi-Layer Prism Tensegrity |
| title_sort |
trigonometry based linear form- finding method for irregular multi-layer prism tensegrity |
| granting_institution |
Universiti Sains Malaysia |
| granting_department |
Pusat Pengajian Kejuruteraan Awam |
| publishDate |
2017 |
| url |
http://eprints.usm.my/46071/1/A%20Trigonometry%20Based%20Linear%20Form-%20Finding%20Method%20For%20Irregular%20Multi-Layer%20Prism%20Tensegrity.pdf |
| _version_ |
1747821604819173376 |