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]

Stress Function Interface and Boundary Conditions in Anisotropic Materials

1982 ◽  
Vol 49 (4) ◽  
pp. 787-791 ◽  
Author(s):  
E. E. Gdoutos ◽  
M. Kattis
Keyword(s):  
Boundary Conditions ◽  
Stress Function ◽  
Anisotropic Media ◽  
Anisotropic Materials ◽  
Function Approach ◽  
Airy Stress Function ◽  
Stress Functions ◽  
The Media

The stress and displacement continuity conditions for interfaces between two different anisotropic media were formulated in terms of the Airy stress functions of the media. It was shown that such formulation greatly facilitates the solution of the problems of composite anisotropic materials by the Airy stress function approach. Two examples were given to demonstrate the potentiality of the method.

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.

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