Selecting a Derivative Boundary Element Formulation for use with Hermitian Interpolation

Tomlinson, Karl A.; Pullan, Andrew J.; Bradley, Chris

doi:10.1007/978-3-642-79654-8_439

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“…n ndof = 1, 2 or 3, for general problems of potential, 2D elasticity and 3D elasticity, respectively. One might in principle develop a formulation with any number of parameters attached to each nodal point [17]. Another possibility would be to have d and p * with no clear mechanical meaning at all, just as discretization parameters [18].…”

Section: Proposition On Stress and Displacement Representationsmentioning

confidence: 99%

Assessment of the spectral properties of the double-layer potential matrix H

Dumont¹

2013

Boundary Elements and Other Mesh Reduction Methods XXXV

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The double-layer potential matrix H of the conventional, collocation boundary element method (CBEM) is singular, as referred to a static problem in a bounded continuum. This means that no rigid body displacements can be transformed between two different reference systems -and that unbalanced forces are to be excluded from a consistent linear algebra contragradient transformation. The properties of H T may become quite informative, as they reflect the topology (concavities, notches, cracks, holes) of the discretized domain as well as material non-homogeneities, which comes from the fact that local stress gradients can be represented by fundamental solutions only in a global sense. Symmetries and antisymmetries are also evidenced in N (H T ) as well as the spectral properties related to simple polynomial solutions that one may propose as patch tests. In the usual implementations of the CBEM with real fundamental solutions, all eigenvalues λ of H are real, λ ∈ R, 0 ≥ λ < 1 for a bounded domain. This means that H is a contraction -a paramount mechanical feature that comes up naturally in the frame of a virtual work investigation of Kelvin's (singular) fundamental solution and is resorted to in a simplified variational implementation of the boundary element method.

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Section: Proposition On Stress and Displacement Representationsmentioning

confidence: 99%

Assessment of the spectral properties of the double-layer potential matrix H

Dumont¹

2013

Boundary Elements and Other Mesh Reduction Methods XXXV

View full text Add to dashboard Cite

show abstract

Selecting a Derivative Boundary Element Formulation for use with Hermitian Interpolation

Cited by 1 publication

References 5 publications

Assessment of the spectral properties of the double-layer potential matrix H

Assessment of the spectral properties of the double-layer potential matrix H

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