Constrained finite rotations in dynamics of shells and Newmark implicit time‐stepping schemes

Brank, Boštjan; Mamouri, Said; Ibrahimbegović, Adnan

doi:10.1108/02644400510602998

Cited by 9 publications

(9 citation statements)

References 23 publications

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“…The presented work concerns only plates with moderate rotations, but complex models of plates and shells could be investigated [28] by taking into account large displacements and rotations. This has already been done in the static case [29,30] by use of a particular formulation and finite element of type RAMM.…”

Section: Resultsmentioning

confidence: 99%

Nonlinear forced vibration of damped plates by an asymptotic numerical method

Boumediene

Miloudi

Cadou

et al. 2009

Computers & Structures

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a b s t r a c tThis work deals with damped nonlinear forced vibrations of thin elastic rectangular plates subjected to harmonic excitation by an asymptotic numerical method. Using the harmonic balance method and Hamilton's principle, the governing equation is converted into a static formulation. A mixed formulation is used to transform the problem from cubic nonlinearity to quadratic one sequence. Displacement, stress and frequency are represented by power series with respect to a path parameter. Equating the like powers of this parameter, the nonlinear governing equation is transformed into a sequence of linear problems with the same stiffness matrix. Through a single matrix inversion, a considerable number of terms of the perturbation series can easily be computed with a limited computation time. The starting point, corresponding to a regular solution, is obtained by the Newton-Raphson method. In order to increase the step length, Padé approximants are used. Numerical tests are presented and compared with numerical and analytical results in the literature, for different boundary conditions, excitations and damping coefficients.

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Section: Resultsmentioning

confidence: 99%

Nonlinear forced vibration of damped plates by an asymptotic numerical method

Boumediene

Miloudi

Cadou

et al. 2009

Computers & Structures

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“…where Similar developments and constraints on rotation vector can be carried out in the spatial representation (see Brank, Mamouri and Ibrahimbegovi c [8] and Brank and Ibrahimbegovi c [7]) with the spatial rotation vector . The natural relationship of di erent velocity parameters can be expressed by the commutative diagram in Figure 2, where…”

Section: Finite Rotations Of the Shell Directormentioning

confidence: 94%

“…In closing this section we turn to deriving expressions for the shell-director acceleration, where by taking time derivative of (3.8) and (3.11), we get (see Brank, Mamouri and Ibrahimbegovi c [8])…”

Section: Finite Rotations Of the Shell Directormentioning

confidence: 99%

Dynamics and time-stepping schemes for elastic shells undergoing finite rotations

Brank

Korelc

Ibrahimbegović

2003

Computers & Structures

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“…In practice, the potential crack paths will be located on inter-element edges. The critical condition for cohesive zone activation is specified in terms of the resultant tractions on the edge n := n α ν α (27)…”

Section: Specialization Of the Cohesive Zone Constitutive Relationsmentioning

confidence: 99%

“…Specialized numerical integration algorithms of the equations of motion for directed surfaces has been investigated by a number of authors, see e.g., [26][27][28]. These schemes have been designed with various goals in mind, such as exactly preserving certain integrals of the motion.…”

Section: Newmark Time Integration Schemementioning

confidence: 99%

A parallel discontinuous Galerkin/cohesive-zone computational framework for the simulation of fracture in shear-flexible shells

Talamini

Radovitzky

2017

Computer Methods in Applied Mechanics and Engineering

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We propose a computational framework for the simulation of deformation and fracture in shells that is well suited to situations with widespread damage and fragmentation due to impulsive loading. The shell is modeled with a shear-flexible theory and discretized with a discontinuous Galerkin finite element method, while fracture is represented with a cohesive zone model on element edges. A key feature of the method is that the underlying shear-flexible shell theory enables the description of transverse shear fracture modes, in addition to the in-plane and bending modes accessible to Kirchhoff-Love thin shell formulations. This is especially important for impulsive loading conditions, where shear-off failure near stiffeners and supports is common. The discontinuous Galerkin formulation inherits the scalability properties demonstrated previously for large-scale simulation of fracture in solids, while avoiding artificial elastic compliance issues that are common in other cohesive model approaches. We demonstrate the ability of the framework to capture the transverse shear fracture mode through numerical examples, and the parallel computation capabilities of the method through the simulation of explosive decompression of the skin of a full-scale passenger aircraft fuselage.

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Constrained finite rotations in dynamics of shells and Newmark implicit time‐stepping schemes

Cited by 9 publications

References 23 publications

Nonlinear forced vibration of damped plates by an asymptotic numerical method

Nonlinear forced vibration of damped plates by an asymptotic numerical method

Dynamics and time-stepping schemes for elastic shells undergoing finite rotations

A parallel discontinuous Galerkin/cohesive-zone computational framework for the simulation of fracture in shear-flexible shells

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