A variational approach to boundary element elastodynamic analysis and extension to multidomain problems

Maier, G.; Diligenti, M.; Carini, Alberto

doi:10.1016/0045-7825(91)90239-3

Cited by 71 publications

(40 citation statements)

References 19 publications

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“…In the second benchmark, we consider the problem (1)-(3) with Γ = x ∈ R 2 |x = (cos β, sin β), β ∈ [0, π] and the Dirichlet boundary datum, taken from [29], (25) g(β, t) = H[t]f (t) cos(β) , with f (·) given in (24). The velocity is still fixed as c = 1.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Space-time BEM has the advantage that it directly yields the unknown time-dependent quantities. In this last approach, the construction of the BIEs, via representation formula in terms of single and double layer potentials, uses the fundamental solution of the hyperbolic partial differential equation and jump relations [23][24][25]. The mathematical background of time-dependent boundary integral equations is summarized by M. Costabel in [26].…”

Section: Introductionmentioning

confidence: 99%

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Energetic BEM for the numerical analysis of 2D Dirichlet damped wave propagation exterior problems

Aimi

Diligenti

Guardasoni

2017

Communications in Applied and Industrial Mathematics

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Time-dependent problems modeled by hyperbolic partial differential equations can be reformulated in terms of boundary integral equations and solved via the boundary element method. In this context, the analysis of damping phenomena that occur in many physics and engineering problems is a novelty. Starting from a recently developed energetic space-time weak formulation for 1D damped wave propagation problems rewritten in terms of boundary integral equations, we develop here an extension of the so-called energetic boundary element method for the 2D case. Several numerical benchmarks, whose numerical results confirm accuracy and stability of the proposed technique, already proved for the numerical treatment of undamped wave propagation problems in several dimensions and for the 1D damped case, are illustrated and discussed.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Energetic BEM for the numerical analysis of 2D Dirichlet damped wave propagation exterior problems

Aimi

Diligenti

Guardasoni

2017

Communications in Applied and Industrial Mathematics

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“…[22][23][24][25][26][27][28]) where both strongly singular and hypersingular kernels have to be addressed.…”

Section: Introductionmentioning

confidence: 99%

Elastodynamics by BEM: a new direct formulation

Frangi

1999

Int. J. Numer. Meth. Engng.

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SUMMARYA new direct BE formulation is proposed for the solution of elastodynamic problems. An analytical regularization procedure is devised via an integration-by-parts technique without introducing any hypothesis about either the discretization of the boundary geometry or the space-time interpolation of the elastic ÿelds involved. The only requirement is for continuity in the displacement ÿeld. The regularization of the integral equations for static elasticity using the same approach, already available in the literature, is presented as a particular case of the general procedure introduced herein. The numerical implementation of this technique is discussed and two-dimensional examples are presented.

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“…Their explicit expressions are presented in the Appendix of Ref. 100. Interpreted as influence or Green's functions, the kernels G hk give in x ∈ Ω∞ at time t the effect specified by the first subscript of G hk (i.e.…”

Section: Linear Elastic Dynamicsmentioning

confidence: 99%

Symmetric Galerkin Boundary Element Method

Bonnet

Maier²,

Polizzotto³

2008

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This review concerns a methodology for solving numerically, to engineering purposes, boundary and initial-boundary value problems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form; the discretization is performed either on a variational basis or by a Galerkin weighted residual procedure, the interpolation and weight functions being chosen so that the variables in the approximate formulation are generalized variables in Prager's sense. As main consequences of the above provisions, symmetry is exhibited by matrices with a key role in the algebraized versions, some quadratic forms have a clear energy meaning, variational properties characterize the solutions and other results, invalid in traditional boundary element methods, enrich the theory underlying the computational applications. The present survey outlines recent theoretical and computational developments of the title methodology with particular reference to linear elasticity, elastoplasticity, fracture mechanics, time-dependent problems, variational approaches, singular integrals, approximation issues, sensitivity analysis, coupling of boundary and finite elements, computer implementations. Areas and aspects which at present require further research are identified and comparative assessments are attempted with respect to traditional boundary integral-element methods.

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A variational approach to boundary element elastodynamic analysis and extension to multidomain problems

Cited by 71 publications

References 19 publications

Energetic BEM for the numerical analysis of 2D Dirichlet damped wave propagation exterior problems

Energetic BEM for the numerical analysis of 2D Dirichlet damped wave propagation exterior problems

Elastodynamics by BEM: a new direct formulation

Symmetric Galerkin Boundary Element Method

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