Optimization of Multibody Systems and Their Structural Components

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.

[1]  Claude Fleury,et al.  CONLIN: An efficient dual optimizer based on convex approximation concepts , 1989 .

[2]  C. Bottasso,et al.  On the Solution of Inverse Dynamics and Trajectory Optimization Problems for Multibody Systems , 2004 .

[3]  O. Sigmund,et al.  Stiffness design of geometrically nonlinear structures using topology optimization , 2000 .

[4]  Martin P. Bendsøe,et al.  Equivalent displacement based formulations for maximum strength truss topology design , 1992, IMPACT Comput. Sci. Eng..

[5]  M. Géradin,et al.  Flexible Multibody Dynamics: A Finite Element Approach , 2001 .

[6]  P. Eberhard,et al.  Augmented Lagrangian Particle Swarm Optimization in Mechanism Design , 2007 .

[7]  José Herskovits,et al.  Mathematical programming models and algorithms for engineering design optimization , 2005 .

[8]  Albert Albers,et al.  Structural Optimization of Components in Controlled Mechanical Systems , 2007 .

[9]  M. Bendsøe,et al.  Optimization methods for truss geometry and topology design , 1994 .

[10]  Noboru Kikuchi,et al.  TOPOLOGY OPTIMIZATION OF COMPLIANT MECHANISMS USING THE HOMOGENIZATION METHOD , 1998 .

[11]  Uri Kirsch,et al.  Optimal topologies of truss structures , 1989 .

[12]  John M. Hansen.  Synthesis of Mechanisms Using Time-Varying Dimensions , 2002 .

[13]  Peter Eberhard,et al.  Sensitivity analysis for dynamic mechanical systems with finite rotations , 2008 .

[14]  Krister Svanberg,et al.  A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations , 2002, SIAM J. Optim..

[15]  M. Bendsøe.  Optimal shape design as a material distribution problem , 1989 .

[16]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[17]  Alberto Cardona,et al.  Design of a new finite element programming environment , 1994 .

[18]  Paul Fisette,et al.  Contribution to the Optimization of Closed-Loop Multibody Systems: Application to Parallel Manipulators , 2005 .

[19]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[20]  E. Ramm,et al.  Adaptive topology optimization of elastoplastic structures , 1998 .

[21]  C. Fleury,et al.  A family of MMA approximations for structural optimization , 2002 .

[22]  Martín A. Pucheta,et al.  An automated method for type synthesis of planar linkages based on a constrained subgraph isomorphism detection , 2007 .

[23]  Peter Eberhard,et al.  Automatic differentiation of numerical integration algorithms , 1999, Math. Comput..

[24]  Ole Sigmund,et al.  Articulated mechanism design with a degree of freedom constraint , 2004 .

[25]  M. Arnold,et al.  Convergence of the generalized-α scheme for constrained mechanical systems , 2007 .

[26]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[27]  Gyung-Jin Park,et al.  Optimization of Flexible Multibody Dynamic Systems Using the Equivalent Static Load Method , 2005 .

[28]  C B W Pedersen.  Topology optimization for crashworthiness of frame structures , 2003 .

[29]  Ole Sigmund,et al.  On the Design of Compliant Mechanisms Using Topology Optimization , 1997 .

[30]  Olivier Bruls,et al.  The generalized‐α method in mechatronic applications , 2006 .

[31]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[32]  Jasbir S. Arora,et al.  Introduction to Optimum Design , 1988 .

[33]  D. Bestle,et al.  Sensitivity analysis of constrained multibody systems , 1992, Archive of Applied Mechanics.

[34]  D. Bestle,et al.  Analyzing and Optimizing Multibody Systems , 1992 .

[35]  Albert Albers,et al.  Automated coupling of MDI/ADAMS and MSC.CONSTRUCT for the topology and shape optimization of flexible mechanical systems , 1999 .

[36]  A. Michell.  LVIII. The limits of economy of material in frame-structures , 1904 .

[37]  Harvey J. Greenberg,et al.  Automatic design of optimal structures , 1964 .

[38]  Ole Sigmund,et al.  Topology synthesis of large‐displacement compliant mechanisms , 2001 .