Optimization of Multibody Dynamics Using Pointwise Constraints and Arbitrary Functions

Volume 2A: 24th Biennial Mechanisms Conference ◽

10.1115/96-detc/mech-1569 ◽

1996 ◽

Author(s):

Javier Urruzola ◽

Alejo Avello ◽

Juan T. Celigüeta

Keyword(s):

Objective Function ◽

Multibody Dynamics ◽

Symbolic Computation ◽

Optimization Problems ◽

Variable Method ◽

Adjoint Variable Method ◽

Adjoint Variable ◽

Design Variables ◽

Complex Optimization ◽

Pointwise Constraints

Abstract Multibody dynamics optimization requires the computation of sensitivities of the objective function and the constraints. This calculation can be done by two methods, direct differentiation and adjoint variable method, that are reviewed in this paper. In either cases, the complexity of the terms that appear in the formulation makes almost a need the use of symbolic computation for the derivation of sensitivities. An existing symbolic manipulator designed for multibody optimization has been enhanced with new and more powerful capabilities. The use of arbitrary functions as design variables and pointwise constraints permits the solution of more complex optimization problems. Some illustrative examples prove the capacity of the method to handle complex optimization problems.

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Optimal Shape Design of Pressure-Driven Microchannels Using Adjoint Variable Method

ASME 5th International Conference on Nanochannels, Microchannels, and Minichannels ◽

10.1115/icnmm2007-30109 ◽

2007 ◽

Author(s):

Osamu Tonomura ◽

Tatsuya Takase ◽

Manabu Kano ◽

Shinji Hasebe

Keyword(s):

Pressure Drop ◽

Incompressible Flows ◽

Optimal Shape ◽

Variable Method ◽

Shape Design ◽

Optimal Shape Design ◽

Adjoint Variable Method ◽

Adjoint Variable ◽

Initial Shape ◽

Design Variables

The shape of microchannels is an important design variable to achieve the desired performance. Since most microchannels are, at present, designed by trial and error, a systematic optimal shape design method needs to be established. Computational fluid dynamics (CFD) is often used to rigorously examine the influence of the shape of microchannels on heat and mass transport phenomena in the flow field. However, the rash combination of CFD and the optimization technique based on evaluating gradients of the cost function requires enormous computation time when the number of design variables is large. Recently, the adjoint variable method has attracted the attention as an efficient sensitivity analysis method, particularly for aeronautical shape design, since it allows one to successfully obtain the shape gradient functions independently of the number of design variables. In this research, an automatic shape optimization system based on the adjoint variable method is developed using C language on a Windows platform. To validate the effectiveness of the developed system, pressure drop minimization problems of a 180° curved microchannel and a branched microchannel in incompressible flows under constant volume conditions are solved. These design examples illustrate that the pressure drop of the optimally designed microchannels is decreased by about 20% ∼ 40% as compared with that of the initial shape.

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Second-Order Design Sensitivity Analysis of Mechanical System Dynamics by a Mixed Direct Differentiation Adjoint Variable Method

Volume 2: 24th Design Automation Conference ◽

10.1115/detc98/dac-5575 ◽

1998 ◽

Author(s):

Javier Urruzola ◽

José Manuel Jiménez

Keyword(s):

Sensitivity Analysis ◽

Design Sensitivity ◽

Second Order ◽

Variable Method ◽

Adjoint Variable Method ◽

Adjoint Variable ◽

Direct Differentiation ◽

Design Variables ◽

Adjoint Variables ◽

Derivatives Of

Abstract This paper presents a new approach to second order sensitivity analysis of multibody dynamics. Adjoint variables together with direct differentiation are used to derive first- and second-order derivatives of measures of dynamic response with respect to design variables. It is shown that the proposed method can be compared advantageously to the fully adjoint variable method proposed by Haug in terms of simplicity and numerical cost. In order to validate the algorithm, a simple oscillator example proposed by Haug is solved analytically and by the mixed method, with identical results.

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