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Optimization of multibody systems and their structural components Bruls, Olivier ; Lemaire, Etienne ; Duysinx, Pierre et al in Blajer, W.; Arczewski, K.; Fraczek, J. (Eds.) et al Multibody Dynamics: Computational Methods and Applications (2011) This work addresses the optimization of flexible multibody systems based on the dynamic response of the full system with large amplitude motions and elastic deflections. The simulation model involves a ... [more ▼] This work addresses the optimization of flexible multibody systems based on the dynamic response of the full system with large amplitude motions and elastic deflections. The simulation model involves a nonlinear finite element formulation, a time integration scheme and a sensitivity analysis and it can be efficiently exploited in an optimization loop. In particular, the paper focuses on the topology optimization of structural components embedded in multibody systems. Generally, topology optimization techniques consider that the structural component is isolated from the rest of the mechanism and use simplified quasi-static load cases to mimic the complex loadings in service. In contrast, we show that an optimization directly based on the dynamic response of the flexible multibody system leads to a more integrated approach. The method is applied to truss structural components. Each truss is represented by a separate structural universe of beams with a topology design variable attached to each one. A SIMP model (or a variant of the power law) is used to penalize intermediate densities. The optimization formulation is stated as the minimization of the mean compliance over a time period or as the minimization of the mean tip deflection during a given trajectory, subject to a volume constraint. In order to illustrate the benefits of the integrated design approach, the case of a two degrees-of-freedom robot arm is developed. [less ▲] Detailed reference viewed: 92 (15 ULg)Topology Optimization of Structural Components: A Multibody Dynamics-Oriented Approach Bruls, Olivier ; Lemaire, Etienne ; Duysinx, Pierre et al in Proceedings of the Multibody Dynamics ECCOMAS Conference (2009) This work addresses the topology optimization of structural components embedded in multibody systems with large amplitude motions. Generally, topology optimization techniques consider that the structural ... [more ▼] This work addresses the topology optimization of structural components embedded in multibody systems with large amplitude motions. Generally, topology optimization techniques consider that the structural component is isolated from the rest of the mechanism and use simplified quasi-static load cases to mimic the complex loadings in service. In contrast, this paper proposes an optimization procedure based on the dynamic simulation of the full multibody system with large amplitude motions and elastic deflections. We show that the simulation model, which involves a nonlinear finite element formulation, a time integration scheme and a sensitivity analysis, can be efficiently exploited in an optimization loop. The method is applied to truss structural components. Each truss is represented by a separate structural universe of beams with a topology design variable attached to each one. A SIMP model (or a variant of the power law) is used to penalize intermediate densities. The optimization formulation is stated as the minimization of the mean compliance over a time period or as the minimization of the mean tip deflection during a given trajectory, subject to a volume constraint. In order to illustrate the benefits of the integrated design approach, the case of a two degrees-of-freedom robot arm is developed. [less ▲] Detailed reference viewed: 115 (13 ULg)Design of mechanism components using topology optimization and flexible multibody simulation Bruls, Olivier ; Lemaire, Etienne ; et al in Proceedings of the 8th World Congress on Computational Mechanics (2008, July) This work addresses the topology optimization of structural components embedded in multibody systems with large amplitude motions. For example, in deployable space structures, piston engines, automotive ... [more ▼] This work addresses the topology optimization of structural components embedded in multibody systems with large amplitude motions. For example, in deployable space structures, piston engines, automotive suspensions, robots and high-speed machine-tools, the articulated components undergo large displacements and elastic deformations, and are subject to transient loads and nonlinear dynamic effects. The performance of such systems often depends on the mechanical design in a non-intuitive way. <br />Several researchers have addressed the optimization of the geometric parameters of mechanisms and also of the connectivity of mechanisms made of rigid members. In contrast, topology optimization techniques are often based on continuum mechanics assumptions, and usually aim at optimizing the layout of an isolated structural component under the assumption of small displacements and small deflections. In order to apply topology optimization to mechanism components, one may consider that each structural component is isolated from the rest of the mechanism and use simplified quasi-static load cases to mimic the complex loadings in service. However, two main drawbacks are associated with this approach. Firstly, defining the equivalent load cases is a rather difficult task, which is often based on trials and errors and which requires some expertise. Secondly, topology optimization is often sensitive to loading conditions, especially for multiple load cases and stress constraints, so that the optimal character of the resulting design becomes questionable if the loading is approximative. For these reasons, in order to obtain better optimal layouts, this paper proposes an optimization procedure based on dynamic simulations of the full flexible multibody system. <br />For this purpose, the nonlinear finite element approach is selected for the modelling and the simulation of the flexible multibody system. The present work is thus similar to the usual approach used in topology optimization in which the continuum domain is discretized into finite elements. The nonlinear finite element formalism accounts for both large rigid-body motions and elastic deflections of the structural components. The design variables are classically density-like parameters associated to a power law interpolation of effective material properties for intermediate densities, also known as Simply Isotropic Material with Penalization (SIMP). <br />The nonlinear equations of motion are solved using a generalized-alpha time integration scheme, and the sensitivity analysis of mechanical responses is based on a direct differentiation method. The efficient solution of the optimization problem relies on the sequential convex programming concept at the core of the CONLIN software. <br />In the present study, the method is applied to various types of mechanical systems. Firstly, planar mechanisms with truss structural components are considered. Each truss is represented by a structural universe of beams with a topology design variable attached to each one. Secondly, the discussion is extended to similar mechanisms with 3D motions. Finally, the topology optimization of spatial bodies represented by 3D finite element meshes is considered. [less ▲] Detailed reference viewed: 109 (11 ULg)Sensitivity analysis for dynamic mechanical systems with finite rotations Bruls, Olivier ; in International Journal for Numerical Methods in Engineering (2008), 74(13), 1897-1927 This paper presents a sensitivity analysis for dynamic systems with large rotations using a semi-analytical direct differentiation technique. The choice of a suitable time integration strategy for the ... [more ▼] This paper presents a sensitivity analysis for dynamic systems with large rotations using a semi-analytical direct differentiation technique. The choice of a suitable time integration strategy for the rotation group appears to be critical for the development of an efficient sensitivity analysis. Three versions of the generalized-alpha time integration scheme are considered: a residual form, a linear form, and a geometric form. Their consistency is discussed, and we show that the residual form, which is the most direct extension of the generalized-alpha algorithm defined in structural dynamics, should not be used for problems with large rotations. The sensitivity analysis is performed and close connections are highlighted between the structure of the sensitivity equations and of the linearized dynamic equations. Hence, algorithms developed for the original problem can be directly reused for the sensitivities. Finally, a numerical example is analysed in detail. [less ▲] Detailed reference viewed: 93 (15 ULg)Topology Optimization of Structural Components Included in Flexible Multibody Systems Bruls, Olivier ; Lemaire, Etienne ; et al in Proceedings of the 7th World Congress on Structural and Multidisciplinary Optimization (2007, May) This work addresses the topology optimization of structural components embedded in multibody systems with large amplitude motions. Generally, topology optimization techniques consider that the structural ... [more ▼] This work addresses the topology optimization of structural components embedded in multibody systems with large amplitude motions. Generally, topology optimization techniques consider that the structural component is isolated from the rest of the mechanism and use simplified quasi-sta tic load cases to mimic the complex loadings in service. In contrast, this paper proposes an optimization procedure based on the dynamic simulation of the full multibody system with large amplitude motions and elastic deflections. We show that the simulation model, which involves a nonlinear finite element formulation, a time integration scheme and a sensitivity analysis, can be efficiently exploited in an optimization loop. The method is applied to truss structural components. Each truss is represented by a structural universe of beams with a topology design variable attached to each one. A SIMP model (or a variant of the power law) is used to penalize intermediate densities. The optimization formulation is stated as the minimization of the mean compliance over a time period or as the minimization of the mean tip deflection during a given trajectory, subject to a volume constraint. In order to illustrate the benefits of the integrated design approach, the case of a two degrees-of-freedom robot arm is developed. [less ▲] Detailed reference viewed: 64 (12 ULg)Direct differentiation of time integrators for multibody systems with absolute rotations Bruls, Olivier ; in Proceedings of the ECCOMAS Thematic Conference - Multibody Dynamics 2007 (2007) Gradient-based optimization methods require efficient algorithms to compute the sensitivities of the simulation results with respect to design parameters. Compared to finite difference schemes, the direct ... [more ▼] Gradient-based optimization methods require efficient algorithms to compute the sensitivities of the simulation results with respect to design parameters. Compared to finite difference schemes, the direct differentiation technique leads to a significant reduction in the computational cost of the sensitivities while keeping a good accuracy. In particular, this paper focuses on the optimization of multibody systems with large rotations. In this framework, two versions of the generalized-alpha time integration scheme are considered: the first one is based on a parameterized treatment of the rotations, whereas the second one is formulated in a geometric setting. We show that the sensitivity analysis is much simpler and computationally more efficient in the second case than in the first case. The performance of both algorithms is compared for a numerical example. [less ▲] Detailed reference viewed: 23 (3 ULg)On the implementation of a sensitivity analysis in a flexible multibody dynamics environment Bruls, Olivier ; Duysinx, Pierre ; Conference (2006, June) The dynamic performance of complex mechanisms, such as machine tools, manipulators, vehicles, engines or foldable structures, can be strongly affected by flexible phenomena. Therefore, the deformation ... [more ▼] The dynamic performance of complex mechanisms, such as machine tools, manipulators, vehicles, engines or foldable structures, can be strongly affected by flexible phenomena. Therefore, the deformation effects should be considered as soon as possible in the design procedure, which motivates the development of automatic optimization techniques for flexible multibody systems. Advanced software tools are able to simulate the dynamic behaviour of such systems, but they typically involve extensive numerical treatments. Hence, gradient-based optimization methods are of special interest since they require a quite low number of simulations, but an important problem is to obtain the sensitivities of the objective function with respect to the design parameters. Since finite difference approaches lack robustness and computational efficiency, we propose to investigate analytical or semi-analytical sensitivity analysis. Several difficulties are inherent to the simulation of flexible mechanisms. A consistent geometric formulation is necessary to describe large amplitude motion as well as possible large deformations. Here, according to the nonlinear finite element formulation, the motion is parameterized using absolute nodal coordinates, and an updated Lagrangian point of view is adopted for the rotation parameters. The joints and the rigid-body conditions are represented by algebraic constraints between the nodal coordinates, leading to differential algebraic equations of motion (DAEs). Finally, the computation of the trajectories requires a reliable simulation algorithm for nonlinear DAEs. A strong advantage of the finite element method comes from its very systematic implementation, which facilitates the development of a semi-analytical sensitivity analysis. In this work, sensitivity analysis is performed for beam elements, rigid bodies and ideal joints. The global sensitivity is then obtained by numerical assembly of the elementary contributions and by integration in the time domain. Thus, a single but extended simulation is sufficient to compute the sensitivities with respect to all parameters. In order to illustrate the method and to demonstrate its efficiency, we consider the optimal design of a car engine, where the flexibility of the connecting rods between the crankshaft and the pistons is taken into account. The objective is to find a feasible mechanical design which minimizes the level of vibrations. [less ▲] Detailed reference viewed: 36 (1 ULg) |
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