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Energy conserving balance of explicit time steps to combine implicit and explicit algorithms in structural dynamics Noels, Ludovic ; Stainier, Laurent ; Ponthot, Jean-Philippe in Computer Methods in Applied Mechanics & Engineering (2006), 195(19-22), 21692192 Recent developments have proved the advantage of combining both time implicit and time explicit integration algorithms in structural dynamics. A major problem is to define the initial conditions for the ... [more ▼] Recent developments have proved the advantage of combining both time implicit and time explicit integration algorithms in structural dynamics. A major problem is to define the initial conditions for the implicit simulation on the basis of a solution obtained from an unbalanced explicit resolution. The unbalanced nature of the explicit algorithm leads to oscillations in the fields of interest. Therefore, the values obtained after an explicit computation cannot be used directly as initial conditions for an implicit simulation. In this paper, we develop such initial values that lead to a stable (no numerical creation of energy) and energy-conserving transition. (c) 2005 Elsevier B.V. All rights reserved. [less ▲] Detailed reference viewed: 51 (8 ULg)On the exploitation of chaos to build reduced-order models Kerschen, Gaëtan ; ; Golinval, Jean-Claude in Computer Methods in Applied Mechanics & Engineering (2003), 192(13-14), 1785-1795 The present study focuses on the model reduction of non-linear systems. The proper orthogonal decomposition is exploited to compute eigenmodes from time series of displacement. These eigenmodes, called ... [more ▼] The present study focuses on the model reduction of non-linear systems. The proper orthogonal decomposition is exploited to compute eigenmodes from time series of displacement. These eigenmodes, called the proper orthogonal modes, are optimal with respect to energy content and are used to build a low-dimensional model of the non-linear system. For this purpose, the proper orthogonal modes obtained from a chaotic orbit are considered. Indeed, such an orbit is assumed to cover a portion of the phase space of higher dimension, and hence of greater measure. This higher dimensional data is further assumed to contain more information about the system dynamics than data of a lower-dimensional periodic orbit. In an example, it is shown that the modes for this particular behaviour are more representative of the system dynamics than any other set of modes extracted from a non-chaotic response. This is applied to a buckled beam with two permanent magnets and the reduced-order model is validated using both qualitative and quantitative comparisons. (C) 2003 Elsevier Science B.V. All rights reserved. [less ▲] Detailed reference viewed: 16 (3 ULg)Arbitrary Lagrangian-Eulerian formulation for element-free Galerkin method Ponthot, Jean-Philippe ; in Computer Methods in Applied Mechanics & Engineering (1998), 152 Arbitrary Lagrangian-Eulerian (ALE) formulation of the Element Free Galerkin (EFG) method is presented. EFG is a meshless method for solving partial differential equations in which the trial and test ... [more ▼] Arbitrary Lagrangian-Eulerian (ALE) formulation of the Element Free Galerkin (EFG) method is presented. EFG is a meshless method for solving partial differential equations in which the trial and test functions employed in the discretization process result from moving least square interpolants. The most significant advantage of the method is that it requires only nodes and a description of internal and external boundaries and interfaces, such as cracks, of the model: no element connectivity is needed. However, as for any discretization method, acceptable solutions can only be obtained for a sufficiently refined discretization. In dynamic fracture problems, where the crack path can be arbitrary, and is thus a priori unknown, this necessitates a refined discretization in large parts of the computational domain which can lead to prohibitive computation costs. ALE formulation allows to continuously relocate nodes on the computational domain. By combining EFG with ALE, it is thus possible, in a crack propagation problem, to refine locally the spatial discretization in the neighborhood of a propagating crack-tip. Results are presented for a wave propagation problem as well as for 2-D dynamic crack propagation problems. [less ▲] Detailed reference viewed: 67 (4 ULg)Dual analysis with general boundary conditions Debongnie, Jean-François ; ; Beckers, Pierre in Computer Methods in Applied Mechanics & Engineering (1995), 122(1-2), 183-192 The dual analysis concept was introduced by Fraeijs de Veubeke [1] as a consequence of upper and lower bounds of the energy. As such bounds exist only in those cases where one type of condition is ... [more ▼] The dual analysis concept was introduced by Fraeijs de Veubeke [1] as a consequence of upper and lower bounds of the energy. As such bounds exist only in those cases where one type of condition is homogeneous, it is commonly admitted that a dual error measure does not exist with general boundary conditions. This paper presents a re-examination of the dual error measure by a way which avoids any use of upper and lower bounds of the energy. It is found that such an error measure holds whatever the boundary conditions be. Furthermore, it is not necessary to obtain the approximate solutions by a Rayleigh-Ritz process, so that the second analysis, which seemed necessary in the original dual analysis concept, may be replaced by any admissible approximation. This implies the possibility of a dual error measure at a simple post-processor level. [less ▲] Detailed reference viewed: 35 (8 ULg)AN IMPROVED ONE-POINT INTEGRATION METHOD FOR LARGE-STRAIN ELASTOPLASTIC ANALYSIS Stainier, Laurent ; Ponthot, Jean-Philippe in Computer Methods in Applied Mechanics & Engineering (1994), 118(1-2), 163-177 In this paper, we present a new one-point integration method generalizing Flanagan and Belytschko's method (Internat. J. Numer. Methods Engrg. 17 (1981) 679-706) and a modification of Belytschko and ... [more ▼] In this paper, we present a new one-point integration method generalizing Flanagan and Belytschko's method (Internat. J. Numer. Methods Engrg. 17 (1981) 679-706) and a modification of Belytschko and Bindeman's method (Comput. Methods Appl. Mech. Engrg. 88 (1991) 311-340), both in the frame of large deformation elastoplastic analysis. These stabilization methods are combined with the radial return method used to integrate the constitutive law. Plane strain problems are first considered, and the method is then generalized to axisymmetrical situations. The explicit time integration scheme with its critical timestep is also considered. A few examples are presented that show the great time savings that can be obtained with reduced integration without any loss of accuracy, and even with a gain in the solution quality, since the underintegrated elements prove to be 'flexurally superconvergent'. [less ▲] Detailed reference viewed: 41 (12 ULg)Automatic adaptive remeshing for numerical simulations of metalforming ; Habraken, Anne ; Cescotto, Serge in Computer Methods in Applied Mechanics & Engineering (1992), 101 Detailed reference viewed: 10 (3 ULg)On a purely lagrangian formulation of sloshing and fluid-induced vibrations of tanks Debongnie, Jean-François in Computer Methods in Applied Mechanics & Engineering (1986), 58(1), 1-18 A general variational principle for fluid-structure interactions is obtained from a purely Lagrangian point of view, thus avoiding any difficulty at the fluid-structure interaction. This rather general ... [more ▼] A general variational principle for fluid-structure interactions is obtained from a purely Lagrangian point of view, thus avoiding any difficulty at the fluid-structure interaction. This rather general variational principle is shown to degenerate, when suitable restrictions are made, in two known formulations, whose range of applicability is defined with the aid of three nondimensional numbers. [less ▲] Detailed reference viewed: 26 (5 ULg)Shape optimal-design using B-splines ; Fleury, Claude in Computer Methods in Applied Mechanics & Engineering (1984), 44(3), 247-267 Shape optimal design of an elastic structure is formulated using a design element technique. It is shown that Bezier and B-spline curves, typical of the CAD philosophy, are well suited to the definition ... [more ▼] Shape optimal design of an elastic structure is formulated using a design element technique. It is shown that Bezier and B-spline curves, typical of the CAD philosophy, are well suited to the definition of design elements. Complex geometries can be described in a very compact way by a small set of design variables and a few design elements. Because of the B-splines flexibility, it is no longer necessary to piece design elements together in order to agree with the shape complexity, nor to restrict the shape variations. Moreover, the additional optimization constraints that are most often needed to avoid unrealistic designs when the shape variables are the nodal coordinates of a finite element mesh, are automatically taken into account in the new formulation. An analytical derivation of the sensitivity analysis will be established, giving rise to numerical efficiency. It will be seen that the resulting optimization problem does not involve highly nonlinear functions with respect to the shape variables, so that simple mathematical programming algorithms can be applied to solve it. Some numerical examples are offered to demonstrate the power and generality of the new approach presented in this paper. [less ▲] Detailed reference viewed: 101 (5 ULg)Dual methods for optimizing finite element flexural systems Fleury, Claude ; in Computer Methods in Applied Mechanics & Engineering (1983), 37(3), 249-275 Modern numerical methods for the optimization of large discretized systems are now well developed and highly efficient in the case of thin walled elastic structures modeled by finite elements. However ... [more ▼] Modern numerical methods for the optimization of large discretized systems are now well developed and highly efficient in the case of thin walled elastic structures modeled by finite elements. However, this is not yet true for structures whose components are subject simultaneously to bending and extension loads. In this paper, the idea of Generalized Optimality Criterion (GOC), set forth in previous papers for bar, membrane, and pure bending elements, is extended to deal with general beam and flat shell elements. The modifications brought to the GOC result in explicit approximations for the behavior constraints that are correct up to the first order, but that exhibit a more complex algebraic form. Indeed these explicit expressions are no longer merely linear in the reciprocal design variables. However, they continue to be additively separable, and therefore dual methods remain fully applicable, just as in the original statement of the GOC approach. Numerical examples will be offered to demonstrate the efficiency of the method presented. [less ▲] Detailed reference viewed: 14 (1 ULg) |
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