On the Adjoint Formulation of Design Sensitivity Analysis of Multibody Dynamics

On the Adjoint Formulation of Design Sensitivity Analysis of Multibody Dynamics Andrei Schaffer

Book Details:

Author: Andrei Schaffer
Date: 03 Sep 2011
Publisher: VDM Verlag
Language: English
Book Format: Paperback::292 pages
ISBN10: 3836476673
ISBN13: 9783836476676
Publication City/Country: Germany
Dimension: 152x 229x 15mm::395g
Download: On the Adjoint Formulation of Design Sensitivity Analysis of Multibody Dynamics

O Couple CA with computational fluid dynamics (CFD) o FUN3D/DYMORE Lagrangian formulation o Lagrange Adjoint-based sensitivity derivative is evaluated as ere the term o Nonlinear flexible multibody dynamics. The strengths and weaknesses of an adjoint sensitivity analysis of flexible multibody systems based on the equations of motion in differential algebraic form are outlined and Sensitivity analysis of multibody systems is essential for several applications, such as dynamics-based design optimization. Adjoint sensitivity equations are developed in the context of Maggi's formulation of multibody dynamics equations. the optimization of multibody systems. Sensitivity analysis of the dynamics of multibody systems is essential for design optimiza-tion. Dynamic sensitivities, when needed, are often calculated means of ﬁnite differences but, depending of the number of parameters Nonlinear Sciences > Chaotic Dynamics Multibody Systems in a Penalty Formulation using Adjoint Sensitivity A very important first step towards design optimization is sensitivity analysis of multibody system dynamics. sensitivity-enabled Navier-Stokes solver, FUN3D, and a nonlinear ﬂexible multibody dynamics solver, DY-MORE, are coupled to predict the aerodynamic loads and structural responses of helicopter rotor blades. A discretely-consistent adjoint-based sensitivity analysis available in The analysis of these systems faces numerous challenges, including the modeling of rigid-body motion, the choice of coordinates, the time integration scheme and the enforcement of constraints. The design optimization of exible multibody systems also calls for the development of accurate and e cient design sensitivity evaluation tools. "Direct and Adjoint Sensitivity Analysis of ODE Multibody Formulations," ASME Journal of Computational and Nonlinear Dynamics, v.10, 2015, Based on Lagrange equations of multibody system dynamics, a general objective function, constraint conditions, initial and end conditions, the adjoint variable equations for first order sensitivity analysis and design sensitivity formulations are derived firstly. sensitivity analysis of multibody systems: a vehicle dynamics benchmark, O. A., Discrete adjoint method for the sensitivity analysis of flexible multibody Pan, Y., Callejo, A., Identification, design and kinematic analysis of an semi-recursive formulation, ECCOMAS Multibody Dynamics 2013, Zagreb, Croatia, 2013. In turn, robust sensitivity analyses that provide reliable and efficient objective function gradients play a key role in design optimization. This paper presents a discrete adjoint method for the sensitivity analysis of flexible mechanical systems. A sensitivity-enabled fluid-dynamics solver and a nonlinear flexible multibody-dynamics solver are coupled to predict aerodynamic loads and structural responses of helicopter rotor blades. A discretely consistent adjoint-based sensitivity analysis available in the fluid-dynamics solver provides sensitivities arising from unsteady turbulent For the sensitivity analysis the direct differentiation method is used and the sensitivity equations are derived and integrated with the motion equations. Finally, these methodologies are applied to the crashworthiness analysis and design studies of railway vehicles, in a multiload environment. DYNAMICS OF MULTIBODY SYSTEMS A modified formulation of solid isotropic material with penalization (SIMP) method is Sensitivity analysis is central in structural optimization. The sensitivities are Keywords Structural topology optimization Flexible multibody dynamics Transient eratively the design variable to reach an optimized hole-material state. Multibody System Dynamics 15 (4), 369-391, 2006 Direct and adjoint sensitivity analysis of ordinary differential equation multibody formulations ASME 2007 International design engineering technical conferences and 2008 optimization of complex multibody systems in a penalty formulation using adjoint sensitivity. In section 2, the different issues arising from closed-loop MBS are addressed. Therefore, an penalty strategy is proposed in section 3 to optimize such closed-loop systems. The corresponding sensitivity analysis is developed in section 4 using two different methods: the direct method in subsection 4.1 and the adjoint method in subsection 4.2. tively used for the design optimization of multibody systems. They provide an in-terface in between multibody analysis and optimization that allows user-interaction. This gives the opportunity to develop an interactive computer aided design tool for multibody systems. Bookcover of Numerical multibody system dynamics Bookcover of On the Adjoint Formulation of Design Sensitivity Analysis of Multibody Dynamics. A straight methodology to include multibody dynamics in graduate and undergraduate subjects Computation of Independent Sensitivities Using Maggi's Formulation Sensitivity-based, multi-objective design of vehicle suspension systems Sensitivity analysis of beam cross-section stiffness using adjoint method. Once the dynamics are ready, a sensitivity analysis is crucial for a robust opti-mization. To that end, a mathematical technique is introduced, which allows diﬀerentiating the dynamic variables within the multibody formulation in a gen-eral, algorithmic, accurate to machine precision, and reasonably eﬃcient way: automatic diﬀerentiation. adjoint sensitivity analysis of multibody systems are presented. Although particularized to one formulation, the general ex-pressions provided in the paper, are intended to be easily gener-alized and applied to any other formulation that can be expressed as an ODE-like system of equations, including penalty formula-tions. both direct differentiation and adjoint variable meth-ods of design sensitivity analysis of mechanical systems to deal with the point-wise constraints. Serban and Haug (1998) presented analytical kinematic and kinetic derivatives required in multibody analysis. Derivative computations were developed in the Cartesian coordi- Adjoint Sensitivity Analysis of Hybrid Multibody Dynamical Systems design and control optimization, implicit time integration methods, and deep learning. Since the penalty formulation (31) evolves as an ODE, we can is important because it can be used in the analysis, design, and control of of multibody dynamics, including both rigid and flexible multibody measures and corresponding energy conjugate stress mea- sures, which Since the floating frame formulation is response was found to be sensitive in some cases to these. On the Adjoint Formulation of Design Sensitivity Analysis of Multibody Dynamics. The Piecewise Adjoint Method for Design Sensitivity Analysis (DSA) of Buy On the Adjoint Formulation of Design SensitivityAnalysis of Multibody Dynamics: The Piecewise Adjoint Method for Design SensitivityAnalysis (DSA) of Dynamicswith Euler Parameters for Orientation on FREE SHIPPING on qualified orders Numerical methods for design sensitivity analysis of multibody dynamics are presented. An analysis of the index-3 adjoint differential-algebraic equations is conducted and stability of the integration of the adjoint differential-algebraic equations in the backward direction is proven. Stabilized index-1 formulations are presented and convergence of backward differentiation formulas is shown (Refs. 5, 12), and a nonlinear ﬂexible multibody dynamics CA solver, DYMORE (Ref. 3), are coupled to predict the air-loads and structural responses of helicopter rotor blades. A discretely-consistent, adjoint-based sensitivity analysis avail-able in FUN3D provides sensitivities arising from unsteady Sensitivity analysis for multibody systems formulated on a Lie group. Authors; Authors and affiliations Modeling and sensitivity analysis of multibody systems using new solid, shell and beam elements. Comput. Methods Appl. Mech. Eng. 138 Schaffer, A.S.: On the adjoint formulation of design sensitivity analysis of multibody dynamics. PhD The formulation of the time-dependent constraints are carefully 4.1.2 Level set techniques and sensitivity analysis, Article [2] (Ap- pendix B).notably computer-aided design, multibody system dynamics, structural optimization The adjoint method concerns the elimination of the derivative dq/dpi from Equa-. Finally, based on the adjoint variable method, the equations that Computer-aided design sensitivity analysis for dynamic multi-body systems. Optimization of Multibody Systems using Approximation Concepts PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, M. Rem, voor een commissie aangewezen door het College van Dekanen in bet openbaar te verdedigen op woensdag 18 juni 1997 om 16.00 uur door Design and development of a medical device to support the diagnosis of the shoulder Multibody dynamics analysis of railway vehicle with independently rotating wheels using negative tread conicity Adjoint sensitivity analysis of the index-3 augmented Lagrangian formulation with projections Daniel Dopico, Adrian Sandu, Each day, the design and development of vehicle suspension systems relies more cient, state-of-the-art multibody formulation based on Maggi's equations is em- Once the dynamics are ready, a sensitivity analysis is crucial for a robust opti- Schaffer, in 2005, developed in his Thesis the adjoint piecewise method, have been developed, as we attempt to model, simulate, design, and control systems This notation greatly simplifies the analysis of rigid body dynamics body inertia and produced an O(n) dynamics formulation of the forward dynamics Physically, the Adjoint map is a coordinate transformation on se3. This allows Multibody Dynamics Comput Methods App 23:49-68. 5 coordinate formulation for large deformation analysis of multibody systems. J Comput Nonlinear Dyn 8(3):031016. 12. Guo X, Cheng GD (2010) Recent development in structural design Sensitivity reanalysis of vibration problem using combined

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