End Effects in a Truncated Semi-Infinite Cone

Thompson, Tommie R.; Little, Robert W.

doi:10.1093/qjmam/23.2.185

Cited by 17 publications

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“…Although they considered no notches or inclusions (/r > x/2), it is easy to check that their solution also applies to these cases. According to equation 2.39 in [4], non-zero solutions of the type (13) …”

Section: (A) Solutiou In Terms Of'legendre Functionsmentioning

confidence: 99%

“…Knowing i, the eigenstates, when desired, can easily be computed from the formulas 2.32 and 2.33 derived in [4] by setting in these formulas C; = C and L? ; = Cx,(I + c~)~~(.~~~~…”

Section: (A) Solution In Terms Of Legendre Functionsmentioning

confidence: 99%

“…Knowing A, the eigenstates, when desired, can easily be computed from the formulas 2.32 and 2.33 derived in [4] Knowledge of the field near the singularity makes it possible to construct a singular finite element for the vertex region of a cone, and thui to solve practical boundary value problems for bodies of finite dimensions.…”

Section: Singularities Of Elastic Stresses and Of Harmonic Functions mentioning

confidence: 99%

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Singularities of elastic stresses and of harmonic functions at conical notches or inclusions

Bažant

Keer

1974

International Journal of Solids and Structures

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Abstract-The nature of singularities at the vertex of conical notches and inclusions is found for problems of potential theory and for elastostatic problems of torsion and of axisymmetric stress. A solution in terms of spherical harmonics and a general numerical solution based upon the field equations are used to determine the power dependence of the field quantities upon the distance from the apex of the cone. Eigenvalues representing the exponent are computed for various values of cone angle and for various Poisson ratios.

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Section: (A) Solutiou In Terms Of'legendre Functionsmentioning

confidence: 99%

“…Knowing i, the eigenstates, when desired, can easily be computed from the formulas 2.32 and 2.33 derived in [4] by setting in these formulas C; = C and L? ; = Cx,(I + c~)~~(.~~~~…”

Section: (A) Solution In Terms Of Legendre Functionsmentioning

confidence: 99%

Section: Singularities Of Elastic Stresses and Of Harmonic Functions mentioning

confidence: 99%

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Singularities of elastic stresses and of harmonic functions at conical notches or inclusions

Bažant

Keer

1974

International Journal of Solids and Structures

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“…Among the numerically determined (real and complex) roots of ref. [14] and [16] together, no pairs of roots )t and )t'=-l-3, occur. But the fact that these roots indeed are present in these pairs is of course easily numerically established by substitution.…”

Section: Recent Investigations On Conical Regionsmentioning

confidence: 96%

“…[14] and [16] the exponents ~ and -1-A always occur together is of course far from a proof of the inversion theorem for general cones and arbitrary (homogeneous) boundary conditions along the generators. But there are some more indications for its validity.…”

Section: Some Further Indications For the Validity Of The Inversion Tmentioning

confidence: 99%

On an inversion theorem for conical regions in elasticity theory

Benthem

1979

J Elasticity

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Two-dimensional stress singularities in wedges have already drawn attention since a long time. An inverse square-root stress singularity (in a 360 ° wedge) plays an important role in fracture mechanics.Recently some similar three-dimensional singularities in conical regions have been investigated, from which one may be also important in fracture mechanics.Spherical coordinates are r, 0, 4~-The conical region occupied by the elastic homogeneous body (and possible anisotropic) has its vertex at r = 0. The mantle of the cone is described by an arbitrary function f(O, qS) = 0. The displacement components be ue. For special values of X (eigenvalues) there exist states of displacements (eigenstates) u~ = r%(X, o, 4)),which may satisfy rather arbitrary homogeneous boundary conditions along the generators.The paper brings a theorem which expresses that if A is an eigenvalue, then also -1-A is an eigenvalue. Though the theorem is related to a known theorem in Potential Theory (Kelvin's theorem), the proof has to be given along quite another line. ZUSAMMENFASSUNGZwei-dimensionale Spannungssingularitiiten in keilf6rmigen Gebieten sind schon liingere Zeit untersucht worden und neuerdings auch iihnliche drei-dimensionale Singularitiiten in konischen Gebieten.Kugelkoordinaten sind r, 0, 4~. Das konische Gebiet hat seine Spitze in r = 0. Der Mantel des Kegels

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Note on the Boussinesq-Papkovich stress-functions

Benthem

1979

J Elasticity

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Boussinesq created already three types of solutions of the Navier-Cauchy equations together involving seven harmonics. Those of 2nd and 3rd type together involve four harmonics which are known today as the Papkovich-Neuber Stress-Functions.Paper brings the dependencies between Boussinesq's seven harmonics in an elucidative form and discusses their relevance to analytical and numerical investigations.

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End Effects in a Truncated Semi-Infinite Cone

Cited by 17 publications

References 0 publications

Singularities of elastic stresses and of harmonic functions at conical notches or inclusions

Singularities of elastic stresses and of harmonic functions at conical notches or inclusions

On an inversion theorem for conical regions in elasticity theory

Note on the Boussinesq-Papkovich stress-functions

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