References of "Computer Methods in Applied Mechanics and Engineering"
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See detailBridging proper orthogonal decomposition methods and augmented Newton-Krylov algorithms: An adaptive model order reduction for highly nonlinear mechanical problems
Kerfriden, P.; Gosselet, P.; Adhikari, S. et al

in Computer Methods in Applied Mechanics and Engineering (2011), 200(5-8), 850-866

This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, " on-the-fly ... [more ▼]

This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, " on-the-fly" , the reduced order modelling of highly nonlinear problems undergoing strong topological changes. Damage initiation problems tackled via a corrected hyperreduction method are used as an example. It is shown that the relevancy of reduced order model can be significantly improved with reasonable additional costs when using this algorithm, even when strong topological changes are involved. © 2010. [less ▲]

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See detailA simple and robust three-dimensional cracking-particle method without enrichment
Rabczuk, T.; Zi, G.; Bordas, Stéphane UL et al

in Computer Methods in Applied Mechanics and Engineering (2010), 199(37-40), 2437-2455

A new robust and efficient approach for modeling discrete cracks in meshfree methods is described. The method is motivated by the cracking-particle method (Rabczuk T., Belytschko T., International Journal ... [more ▼]

A new robust and efficient approach for modeling discrete cracks in meshfree methods is described. The method is motivated by the cracking-particle method (Rabczuk T., Belytschko T., International Journal for Numerical Methods in Engineering, 2004) where the crack is modeled by a set of cracked segments. However, in contrast to the above mentioned paper, we do not introduce additional unknowns in the variational formulation to capture the displacement discontinuity. Instead, the crack is modeled by splitting particles located on opposite sides of the associated crack segments and we make use of the visibility method in order to describe the crack kinematics. We apply this method to several two- and three-dimensional problems in statics and dynamics and show through several numerical examples that the method does not show any "mesh" orientation bias. © 2010 Elsevier B.V. [less ▲]

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See detailProjection-based reduction of fluid-structure interaction systems using monolithic space-time modes
Zilian, Andreas UL; Dinkler, D.; Vehre, A.

in Computer Methods in Applied Mechanics and Engineering (2009), 198(47-48), 3795-3805

The focus of this work is the development of reduced models for engineering applications in complex bidirectional fluid-structure interaction. In the simultaneous solution procedure, velocity variables ... [more ▼]

The focus of this work is the development of reduced models for engineering applications in complex bidirectional fluid-structure interaction. In the simultaneous solution procedure, velocity variables are used for both fluid and solid, and the whole set of model equations is discretized by a stabilized time-discontinuous space-time finite element method. Flexible structures are modeled using a three-dimensional continuum approach in a total Lagrangian setting considering large displacements and rotations. In the flow domain the incompressible Navier-Stokes equations describe the Newtonian fluid. A continuous finite element mesh is applied to the entire spatial domain, and the discretized model equations are assembled in a single set of algebraic equations, considering the two-field problem as a whole. The continuous fluid-structure mesh with identical orders of approximation for both solid and fluid in space and time automatically yields conservation of mass, momentum and energy at the fluid-structure interface. A mesh-moving scheme is used to adapt the nodal coordinates of the fluid space-time finite element mesh to the structural deformation. The computational approach for strongly coupled fluid-structure interaction is used to create suitable reduced models of generic nonlinear problems. Reduction is performed with monolithic projection-based space-time modes, ensuring strong coupling of fluid and structure in the reduced model. The contribution discusses results using proper orthogonal decomposition (POD) for determination of monolithic space-time modes in the reduction of fluid-structure systems. © 2009 Elsevier B.V. All rights reserved. [less ▲]

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See detailA smoothed finite element method for plate analysis
Nguyen-Xuan, H.; Rabczuk, T.; Bordas, Stéphane UL et al

in Computer Methods in Applied Mechanics and Engineering (2008), 197(13-16), 1184-1203

A quadrilateral element with smoothed curvatures for Mindlin-Reissner plates is proposed. The curvature at each point is obtained by a non-local approximation via a smoothing function. The bending ... [more ▼]

A quadrilateral element with smoothed curvatures for Mindlin-Reissner plates is proposed. The curvature at each point is obtained by a non-local approximation via a smoothing function. The bending stiffness matrix is calculated by a boundary integral along the boundaries of the smoothing elements (smoothing cells). Numerical results show that the proposed element is robust, computational inexpensive and simultaneously very accurate and free of locking, even for very thin plates. The most promising feature of our elements is their insensitivity to mesh distortion. [less ▲]

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See detailA smoothed finite element method for shell analysis
Nguyen-Thanh, N.; Rabczuk, T.; Nguyen-Xuan, H. et al

in Computer Methods in Applied Mechanics and Engineering (2008), 198(2), 165-177

A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on ... [more ▼]

A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples. [less ▲]

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See detailDerivative recovery and a posteriori error estimate for extended finite elements
Bordas, Stéphane UL; Duflot, M.

in Computer Methods in Applied Mechanics and Engineering (2007), 196(35-36), 3381-3399

This paper is the first attempt at error estimation for extended finite elements. The goal of this work is to devise a simple and effective local a posteriori error estimate for partition of unity ... [more ▼]

This paper is the first attempt at error estimation for extended finite elements. The goal of this work is to devise a simple and effective local a posteriori error estimate for partition of unity enriched finite element methods such as the extended finite element method (XFEM). In each element, the local estimator is the L2 norm of the difference between the raw XFEM strain field and an enhanced strain field computed by extended moving least squares (XMLS) derivative recovery obtained from the raw nodal XFEM displacements. The XMLS construction is tailored to the nature of the solution. The technique is applied to linear elastic fracture mechanics, in which near-tip asymptotic functions are added to the MLS basis. The XMLS shape functions are constructed from weight functions following the diffraction criterion to represent the discontinuity. The result is a very smooth enhanced strain solution including the singularity at the crack tip. Results are shown for two- and three-dimensional linear elastic fracture mechanics problems in mode I and mixed mode. The effectivity index of the estimator is close to 1 and improves upon mesh refinement for the studied near-tip problem. It is also shown that for the linear elastic fracture mechanics problems treated, the proposed estimator outperforms one of the superconvergent patch recovery technique of Zienkiewicz and Zhu, which is only C0. Parametric studies of the general performance of the estimator are also carried out. © 2007 Elsevier B.V. All rights reserved. [less ▲]

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See detailNumerical simulation of a motion of non-sherical granular material using object-orientated techniques.
Peters, Bernhard UL; Dzuigys, A.

in Computer Methods in Applied Mechanics and Engineering (2002), 191

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See detailCoarsen Graining: A Renewal Concept of Efficient Adaptivity Techniques for Multiscale Models
Shih-Wei, Yang; Pattabhi Ramaiah, Budarapu; Roy Mahapatra, Debiprasad et al

in Computer Methods in Applied Mechanics and Engineering (n.d.)

This paper presents a multiscale method for the quasi-static crack propagation. The coarse region is modeled by the di erential reproducing kernel particle(DRKP) method. The coupling between the coarse ... [more ▼]

This paper presents a multiscale method for the quasi-static crack propagation. The coarse region is modeled by the di erential reproducing kernel particle(DRKP) method. The coupling between the coarse scale and ne scale is realized through ghost atoms. The ghost atoms positions are interpolated from the coarse scale solution and enforced as boundary conditions on the ne scale. The ne scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened. The centro symmetry parameter(CSP) is used to detect the crack tip location. The triangular lattice corresponds to the lattice structure of the (111) plane of an FCC crystal in the ne scale region. The Lennard-Jones potential is used to model the atom-atom interactions. The method is implemented in two dimensions. The results are compared to pure atomistic simulations and show excellent agreement. [less ▲]

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