On the Determination of Multiply Connected Domains of an Elastic Plane Body, Bounded by Free Boundaries with Constant Tangential Stresses

1952 ◽  
Vol 74 (4) ◽  
pp. 797
Author(s):  
C. Arf
Keyword(s):  
Elastic Plane ◽  
Multiply Connected Domains ◽  
Free Boundaries ◽  
Plane Body ◽  
Multiply Connected ◽  
Tangential Stresses

Thermal Stress Analysis of Multiholed Composite Plates and Cylinders by the Boundary-Point-Least-Squares Method

1974 ◽  
Vol 96 (3) ◽  
pp. 214-219 ◽  
Author(s):  
L. E. Hulbert ◽  
S. G. Sampath
Keyword(s):  
Least Squares ◽  
Boundary Point ◽  
Thermal Stresses ◽  
Least Squares Method ◽  
Composite Plates ◽  
Multiply Connected Domains ◽  
Series Solutions ◽  
Thermally Induced ◽  
Multiply Connected

The paper describes the application of the boundary-point-least-squares method (BPLS) to the determination of the two-dimensional temperatures and thermal stresses in composite multiply connected domains. Series solutions are first determined for the steady-state temperatures. Using these temperature solutions, the solution to the thermally-induced stresses is automatically found in terms of Airy stress function series. Applications are described which illustrate use of the method in specific problems.

Conformal and Quasiconformal Mappings of Close Multiply-Connected Domains

2002 ◽  
Vol 9 (2) ◽  
pp. 367-382
Author(s):  
Z. Samsonia ◽  
L. Zivzivadze
Keyword(s):  
Integral Equations ◽  
Quasiconformal Mappings ◽  
Multiply Connected Domains ◽  
Multiply Connected

Abstract Doubly-connected and triply-connected domains close to each other in a certain sense are considered. Some questions connected with conformal and quasiconformal mappings of such domains are studied using integral equations.

Simultaneous Determination of Steady Temperatures and Heat Fluxes on Surfaces of Three Dimensional Objects Using FEM

2001 ◽  
Author(s):  
Brian H. Dennis ◽  
George S. Dulikravich
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Multiply Connected ◽  
Three Dimensional Objects ◽  
Solid Objects ◽  
System Solution

Abstract A finite element method (FEM) formulation is presented for the prediction of unknown steady boundary conditions in heat conduction on multiply connected three-dimensional solid objects. The present FEM formulation is capable of determining temperatures and heat fluxes on the boundaries where such quantities are unknown or inaccessible, provided such quantities are sufficiently over-specified on other boundaries. Details of the discretization, linear system solution techniques, regularization, and sample results for 3-D problems are presented.

scholarly journals Eigenvalues of the negative Laplacian for arbitrary multiply connected domains

1996 ◽  
Vol 19 (3) ◽  
pp. 581-586
Author(s):  
E. M. E. Zayed
Keyword(s):  
Boundary Conditions ◽  
Spectral Function ◽  
Three Dimensions ◽  
Bounded Domains ◽  
Multiply Connected Domains ◽  
Multiply Connected ◽  
Asymptotic Formulae ◽  
Negative Laplacian

The purpose of this paper is to derive some interesting asymptotic formulae for spectra of arbitrary multiply connected bounded domains in two or three dimensions, linked with variation of positive distinct functions entering the boundary conditions, using the spectral function∑k=1∞{μk(σ1,…,σn)+P}−2asP→∞. Further results may be obtained.

Conformal parameterization for multiply connected domains: combining finite elements and complex analysis

2013 ◽  
Vol 30 (4) ◽  
pp. 441-455 ◽  
Author(s):  
Everett Kropf ◽  
Xiaotian Yin ◽  
Shing-Tung Yau ◽  
Xianfeng David Gu
Keyword(s):  
Finite Elements ◽  
Complex Analysis ◽  
Multiply Connected Domains ◽  
Multiply Connected

A Rapid Method for the Determination of Principal Stresses Across Sections of Symmetry From Photoelastic Data

1938 ◽  
Vol 5 (1) ◽  
pp. A24-A28
Author(s):  
M. M. Frocht
Keyword(s):  
Free Boundary ◽  
Rapid Method ◽  
Circular Hole ◽  
Characteristic Curve ◽  
Principal Stresses ◽  
Recent Improvement ◽  
Tangential Stresses ◽  
Circular Holes ◽  
Photoelastic Data

Abstract The author discusses: (a) Mesnager’s theorem of isoclinics, (b) the characteristic curve of tangential stresses across a section of symmetry, (c) a formula for the maximum tangential stresses for the case of a central circular hole between fields of pure tension, (d) the slope of the p curve at a point corresponding to a cupic point, (e) recent improvement in the determination of free boundary stresses, and (f) formulas for the position of cupic points for two cases. A new method for the determination of the principal stresses across sections of symmetry from photoelastic data is illustrated with three examples: (1) Bars in tension or compression with central circular holes, (2) grooved beams in bending, and (3) rings or disks with circular central holes subjected to two concentrated diametral loads.

Shape Interrogation by Medial Axis Transform

1990 ◽  
Author(s):  
N. M. Patrikalakis ◽  
H. N. Gursoy
Keyword(s):  
Finite Element ◽  
Medial Axis ◽  
Multiply Connected Domains ◽  
Medial Axis Transform ◽  
Curved Boundaries ◽  
Multiply Connected ◽  
Maximum Thickness ◽  
Surface Patches ◽  
Geometric Representations ◽  
Shape Characteristics

Abstract In this paper we develop a new interrogation method based on the medial axis transform to extract some important global shape characteristics from geometric representations. These shape characteristics include constrictions, maximum thickness points, and associated length scales; isolation of holes and their proximity information; and a set of topologically simple subdomains decomposing a complex domain. The algorithm we develop to compute the medial axis transform of planar multiply connected shapes with curved boundaries can automatically identify these characteristics. Higher level algorithms for generation of finite element meshes of planar multiply connected domains, adaptive triangulation and approximation of trimmed curved surface patches and other engineering applications using the medial axis transform are also discussed.

Sign in / Sign up

Export Citation Format

Share Document