Design of tension structures and shells using the Airy stress function

2021 ◽  
pp. 095605992110641
Author(s):  
Alexander Sehlström ◽  
Karl-Gunnar Olsson ◽  
Chris JK Williams
Keyword(s):  
Stress Function ◽  
Bending Moment ◽  
Internal Stresses ◽  
Airy Stress Function ◽  
Membrane Action ◽  
Form Finding ◽  
Support Design ◽  
Beam Bending ◽  
Cable Nets ◽  
Curved Membrane

Discontinuities in the Airy stress function for in-plane stress analysis represent forces and moments in connected one-dimensional elements. We expand this representation to curved membrane-action structures, such as shells and cable nets, and graphically visualise the internal stresses and section forces at the boundary necessary for equilibrium. The approach enhances understanding of the interplay between form and forces and can support design decisions related to form-finding and force efficiency. As illustrative examples, the prestressing needed for three existing cable nets is determined, and its influence on the edge-beam bending moment is explored.

scholarly journals Form-Finding of Shells Containing Both Tension and Compression Using the Airy Stress Function

2020 ◽  
Author(s):  
Masaaki Miki ◽  
Emil Adiels ◽  
William Baker ◽  
Toby Mitchell ◽  
Alexander Sehlstrom ◽  
...  
Keyword(s):  
Stress Function ◽  
Mixed Type ◽  
Airy Stress Function ◽  
Form Finding ◽  
Graphic Statics ◽  
Tension And Compression ◽  
Stress Functions ◽  
Complete Set ◽  
Pure Compression ◽  
Asymptotic Lines

Pure-compression shells have been the central topic in the form-finding of shells. This paper studies tension-compression mixed type shells by utilizing a NURBS-based isogeometric form-finding approach that analyzes Airy stress functions to expand the possible plan geometry. A complete set of smooth version graphic statics tools is provided to support the analyses. The method is validated using examples with known solutions, and a further example demonstrates the possible forms of shells that the proposed method permits. Additionally, a guideline to configure a proper set of boundary conditions is presented through the lens of asymptotic lines of the stress functions.

scholarly journals Form-Finding of Shells Containing Both Tension and Compression Using the Airy Stress Function

2020 ◽  
Author(s):  
Masaaki Miki ◽  
Emil Adiels ◽  
William Baker ◽  
Toby Mitchell ◽  
Alexander Sehlstrom ◽  
...  
Keyword(s):  
Stress Function ◽  
Mixed Type ◽  
Airy Stress Function ◽  
Form Finding ◽  
Graphic Statics ◽  
Tension And Compression ◽  
Stress Functions ◽  
Complete Set ◽  
Pure Compression ◽  
Asymptotic Lines

Pure-compression shells have been the central topic in the form-finding of shells. This paper studies tension-compression mixed type shells by utilizing a NURBS-based isogeometric form-finding approach that analyzes Airy stress functions to expand the possible plan geometry. A complete set of smooth version graphic statics tools is provided to support the analyses. The method is validated using examples with known solutions, and a further example demonstrates the possible forms of shells that the proposed method permits. Additionally, a guideline to configure a proper set of boundary conditions is presented through the lens of asymptotic lines of the stress functions.

Application of the Generalized Airy Stress Function to Problems on Elastic Vibrations of Hollow Cylinders

1973 ◽  
Vol 40 (4) ◽  
pp. 1140-1141
Author(s):  
R. A. Bourgois
Keyword(s):  
Stress Function ◽  
Laplace Transformation ◽  
Stress Waves ◽  
Elastic Response ◽  
Impact Loads ◽  
Airy Stress Function ◽  
Hollow Cylinders ◽  
Thick Cylinder ◽  
Basic Equations ◽  
Dynamic Plane

This Note concerns the use of the generalized Airy stress function, introduced by Radok [1], for dynamic plane-stress and plane-strain problems with axial symmetry. The solution of the basic equations for stress waves may be accomplished by Laplace transformation. The case of the dynamic elastic response of a thick cylinder to internal axial symmetric impact loads will be studied.

Alternative Derivation of Marguerre’s Displacement Solution in Plane Isotropic Elasticity

1999 ◽  
Vol 67 (2) ◽  
pp. 419-421 ◽  
Author(s):  
X.-L. Gao
Keyword(s):  
Stress Function ◽  
Present Approach ◽  
Function Approach ◽  
Airy Stress Function ◽  
Green's Theorem ◽  
Alternative Derivation ◽  
Green’S Theorem ◽  
Isotropic Elasticity

An alternative derivation of Marguerre’s solution for displacements in plane isotropic elasticity is provided. It is shown that the present approach, which is based on Green’s theorem and parallel to the Airy stress function approach, is straightforward. Also, the current derivation establishes the completeness of the Marguerre solution. [S0021-8936(00)00302-0]

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