Multi-structures: asymptotic analysis and singular perturbation problems

Movchan, Alexander

doi:10.1016/j.euromechsol.2006.05.006

Cited by 8 publications

(3 citation statements)

References 22 publications

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“…[11,31] and reference therein). Moreover, this topic is also related with engineering problems, such as elasticity and multi-structure problems, as well explained in surveys [16,34].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Sharp convergence rate of eigenvalues in a domain with a shrinking tube

Felli

Ognibene

2020

Journal of Differential Equations

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“…[11,31] and reference therein). Moreover, this topic is also related with engineering problems, such as elasticity and multi-structure problems, as well explained in surveys [16,34].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Sharp convergence rate of eigenvalues in a domain with a shrinking tube

Felli

Ognibene

2020

Journal of Differential Equations

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“…We refer to Refs. [1][2][3][4][5][6] and references therein for mathematical modeling and numerical solutions for simple elastic multi-structures composed of only two elastic members. For general elastic multi-structure problems, we refer to Ref.…”

Section: Introductionmentioning

confidence: 99%

Adini-Q₁-P₃FEM for general elastic multi-structure problems

Guo

Huang

2010

Numer. Methods Partial Differential Eq.

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An Adini-Q 1 -P 3 finite element method is introduced to solve general elastic multi-structure problems, where displacements on bodies, longitudinal displacements on plates, longitudinal displacements and rotational angles on rods are discretized by conforming linear (bilinear or trilinear) elements, and transverse displacements on plates and rods are discretized by Adini elements and Hermite elements of third order, respectively. The unique solvability and optimal error estimates in the energy norm are established for the discrete method, whose numerical performance is illustrated by some numerical examples.

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“…We refer to [6,7] for details along this line. Kozlov et al [8][9][10] presented asymptotic theory and spectral analysis of boundary value problems in multi-structures with junctions between one-dimensional and threedimensional substructures.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis for elastic multi‐beam structures by the C⁰‐continuous time‐stepping finite element method

Lai

Huang

Shi

2008

Numer Methods Biomed Eng

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SUMMARYSome C 0 -continuous time-stepping finite element method is proposed for investigating vibration analysis of elastic multi-beam structures. In the time direction, the C 0 -continuous Galerkin method is used to discretize the generalized displacement field. In the space directions, the longitudinal displacements and rotational angles on beams are discretized using conforming linear elements, while the transverse displacements on beams are discretized by the Hermite elements of third order. The error of the method in the energy norm is proved to be O(h +k 3 ), where h and k denote the mesh sizes of the subdivisions in the space and time directions, respectively. The finite difference analysis in time is developed to discuss the spectral behavior of the algorithms as well as their dissipation and dispersion properties in the low-frequency regime. The method has also been extended to study some nonlinear problems. A number of numerical tests are included to illustrate the computational performance of the method.

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Multi-structures: asymptotic analysis and singular perturbation problems

Cited by 8 publications

References 22 publications

Sharp convergence rate of eigenvalues in a domain with a shrinking tube

Sharp convergence rate of eigenvalues in a domain with a shrinking tube

Adini-Q₁-P₃FEM for general elastic multi-structure problems

Vibration analysis for elastic multi‐beam structures by the C⁰‐continuous time‐stepping finite element method

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Multi-structures: asymptotic analysis and singular perturbation problems

Cited by 8 publications

References 22 publications

Sharp convergence rate of eigenvalues in a domain with a shrinking tube

Sharp convergence rate of eigenvalues in a domain with a shrinking tube

Adini-Q1-P3FEM for general elastic multi-structure problems

Vibration analysis for elastic multi‐beam structures by the C0‐continuous time‐stepping finite element method

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Product

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About

Adini-Q₁-P₃FEM for general elastic multi-structure problems

Vibration analysis for elastic multi‐beam structures by the C⁰‐continuous time‐stepping finite element method