2012
DOI: 10.1515/9783110271003
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Integrodifferential Relations in Linear Elasticity

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Cited by 27 publications
(19 citation statements)
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“…The presented paper is devoted to an approach in which the original problem in partial differential equations (PDEs) is approximated by a system of ordinary differential equation (ODEs) based on the method of integro-differential relations (MIDR) [4]. The projection technique developed in [2] was applied to 3D linear elasticity problems with semi-discrete approximations for the displacement vector and the stress tensor.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…The presented paper is devoted to an approach in which the original problem in partial differential equations (PDEs) is approximated by a system of ordinary differential equation (ODEs) based on the method of integro-differential relations (MIDR) [4]. The projection technique developed in [2] was applied to 3D linear elasticity problems with semi-discrete approximations for the displacement vector and the stress tensor.…”
Section: Introductionmentioning
confidence: 99%
“…As compared to the classical Galerkin method, the variational approach described in other studies of the authors [4] possesses some advantages: it guarantees optimality properties of the numerical solution for some approximations, provides explicit error estimates, and supposes the exact implementation of the initial, boundary, and momentum balance conditions. Some drawbacks of the variational method are doubling the dimension of the resulting ODE system and worsening the numerical stability of the results.…”
Section: Introductionmentioning
confidence: 99%
“…Both of these publications are the basis for the experimental case study for a spatially one-dimensional heat transfer process in this paper. For further information concerning the theoretical background of the MIDR, see the work of Kostin and Saurin (2012). Possible extensions of this approach to a problem-oriented modeling of higher-dimensional applications can be found in the works of Rauh et al (2013b) and Kersten et al (2014).…”
mentioning
confidence: 99%
“…In addition, the beams are coupled hingedly by means of two rigid rods. The driver force applied to the carriage is the control input of the structure.The projection approach is based on an integro-differential formulation [3] for the initial-boundary value problem of structure motions with the constitutive relations generalized in the dimensionless form according tow(0, y) = w 0 (y) and p(0, y) = p 0 (y) ; A a w(t, a) + B a s(t, a) = u(t)c a + f a (t) with a ∈ {0, 1} .Here t denotes the time and y is the common coordinate for each structure element. The function w(t, y) ∈ R n is generalizes displacements, p(t, y) ∈ R n is the generalized momentum density, and s(t, y) ∈ R n is the generalized forces.…”
mentioning
confidence: 99%
“…The projection approach is based on an integro-differential formulation [3] for the initial-boundary value problem of structure motions with the constitutive relations generalized in the dimensionless form according to…”
mentioning
confidence: 99%