An investigation of beam theory using the Airy stress function coupled with analytic function theory

1986 ◽  
Vol 20 (1) ◽  
pp. 73-79
Author(s):  
D. E. Jesson ◽  
W. N. Cottingham
1973 ◽  
Vol 40 (3) ◽  
pp. 767-772 ◽  
Author(s):  
O. L. Bowie ◽  
C. E. Freese ◽  
D. M. Neal

A partitioning plan combined with the modified mapping-collocation method is presented for the solution of awkward configurations in two-dimensional problems of elasticity. It is shown that continuation arguments taken from analytic function theory can be applied in the discrete to “stitch” several power series expansions of the stress function in appropriate subregions of the geometry. The effectiveness of such a plan is illustrated by several numerical examples.


Author(s):  
Masaaki Miki ◽  
Emil Adiels ◽  
William Baker ◽  
Toby Mitchell ◽  
Alexander Sehlstrom ◽  
...  

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.


2019 ◽  
Vol 2019 ◽  
pp. 1-1
Author(s):  
Serap Bulut ◽  
Stanislawa Kanas ◽  
Pranay Goswami

1965 ◽  
Vol 8 (1) ◽  
pp. 59-71
Author(s):  
H. L. Jackson

The field of boundary limit theorems in analytic function theory is usually considered to have begun about 1906, with the publication of Fatou's thesis [8]. In this remarkable memoir a theorem is proved, that now bears the author's name, which implies that any bounded holomorphic function defined on the unit disk possesses an angular limit almost everywhere (Lebesgue measure) on the frontier. Outstanding classical contributions to this field can be attributed to F. and M. Riesz, R. Nevanlinna, Lusin, Privaloff, Frostman, Plessner, and others.


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