Numerical solutions in axisymmetric elasticity

Cruse, T. A.; Snow, D. W.; Wilson, R. B.

doi:10.1016/0045-7949(77)90081-5

Cited by 177 publications

(30 citation statements)

References 5 publications

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“…The line integral is with respect to the point (r, z) (subsequently the subscript on will be omitted), and the boundary contour is the x > 0 section of the intersection of the three-dimensional boundary surface with the y = 0 plane. For what is to follow, it is worth noting that the integral is over a circle of radius r, and thus the r factor in Equation (1) comes from the Jacobian of this integration. The axisymmetric Green's function G(r,ẑ; r, z) and its normal derivative are defined in terms of the complete elliptic integrals of the first and second kind, K(m) and E(m)…”

Section: Axisymmetric Formulationmentioning

confidence: 99%

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Galerkin boundary integral analysis for the axisymmetric Laplace equation

Gray

Garzon

Mantič

et al. 2006

Numerical Meth Engineering

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SUMMARYThe boundary integral equation for the axisymmetric Laplace equation is solved by employing modified Galerkin weight functions. The alternative weights smooth out the singularity of the Green's function at the symmetry axis, and restore symmetry to the formulation. As a consequence, special treatment of the axis equations is avoided, and a symmetric-Galerkin formulation would be possible. For the singular integration, the integrals containing a logarithmic singularity are converted to a non-singular form and evaluated partially analytically and partially numerically. The modified weight functions, together with a boundary limit definition, also result in a simple algorithm for the post-processing of the surface gradient.

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Section: Axisymmetric Formulationmentioning

confidence: 99%

“…Beginning in the mid-1970s [1][2][3], collocation solutions of integral equations for axisymmetric problems have been extensively considered in the literature [4]. Recent work has focused on axisymmetric elasticity [5][6][7][8], in particular for fracture and contact analysis.…”

Section: Introductionmentioning

confidence: 99%

Galerkin boundary integral analysis for the axisymmetric Laplace equation

Gray

Garzon

Mantič

et al. 2006

Numerical Meth Engineering

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“…where the free term coe cient C ij (^), for case a, is given by Cruse et al [3], and the sign on the second integral indicates Cauchy Principal Value. Di erentiating the displacement equation (1) with respect to directions r and z, substituting into the linear strain-displacement equations and these into Hooke's law, the following integral equation for stresses at interior points is obtained:…”

Section: Brief Review Of Axisymmetric Standard Bie Let a 2-d Body B Rmentioning

confidence: 99%

“…The pioneering applications of these methods to axisymmetric elasticity date back to the mid-1970s with the works of Kermanidis [1], Mayr [2] and Cruse et al [3]. Rizzo and Shippy [4] and Mayr et al [5] considered general boundary conditions applied to axisymmetric geometries.…”

Section: Introductionmentioning

confidence: 99%

Hypersingular boundary integral equation for axisymmetric elasticity

Lacerda

Wrobel

2001

Numerical Meth Engineering

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SUMMARYAn axisymmetric hypersingular boundary integral formulation for elasticity problems is presented in this paper. The hypersingular and strong-singular fundamental solutions are derived and their singular behaviour is discussed in detail for di erent locations of the source point. Several free terms arise from the limiting process when generating hypersingular boundary integral equations, including an extra one speciÿc to the axisymmetric formulation which does not appear in two and three dimensional cases. The singularity subtraction technique is used to regularize all strong-singular and hypersingular integrals, and their evaluation procedure is explained. Finally, the developed formulation is assessed through simple numerical tests.

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“…It is wellknown that three-dimensional BEM is useful to efficiently analyze the stress fields in three-dimensional joints, since only surfaces are divided into meshes for analysis. Cruse et al [1977] and Rizzo and Shippy [1977] determined the boundary integral equation for three-dimensional thermoelasticity. The thermoelastic integral equation was also derived using the body force analogy [Karami and Kuhn 1992;Cheng et al 2001].…”

Section: Introductionmentioning

confidence: 99%

Untitled

2007

JOMMS

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See inside back cover or http://www.jomms.org for submission guidelines.Regular subscription rate: $500 a year. It is established that upper and lower bounds predict results far apart from each other for the effective elastic properties of semicrystalline polymers such as polyethylene. This is manly due to the high anisotropy of the elastic properties of the crystals. Composite modeling has been used to predict intermediate results between the bounds. Here, we show the details of composite modeling based on a two phase inclusion (crystalline lamella and amorphous domain) as the local representative element of a semicrystalline polymer. Three approaches, two composite bounds, and a composite self-consistent model, are used to compute the overall elastic properties. Details of the development of these approaches are given in this paper. We find good agreement between results from these approaches and experimental results for polyethylene.

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Numerical solutions in axisymmetric elasticity

Cited by 177 publications

References 5 publications

Galerkin boundary integral analysis for the axisymmetric Laplace equation

Galerkin boundary integral analysis for the axisymmetric Laplace equation

Hypersingular boundary integral equation for axisymmetric elasticity

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