Dynamics analysis of linear elastic planar mechanisms

Liu, Jin-Fan; Yang, James; Abdel‐Malek, Karim

doi:10.1007/s11044-006-9031-5

Cited by 3 publications

(4 citation statements)

References 46 publications

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“…For a more detailed discussion on the selection of the modes used the interested reader is referred to Refs. [15][16][17][18][19][20]46]. …”

Section: Flexible Multibody Equations Of Motionmentioning

confidence: 99%

“…The stiffness optimization can be associated with the maximum value of the elastic deformation energy, which is formulated as the min-max optimization described by (19). The extra design variable β∈ ]0, 1] introduced serves as a moving limit for the elastic deformation energy, being its initial value set to 0.8.…”

Section: Maximum Deformation Energy Optimizationmentioning

confidence: 99%

“…Different formulations for the description of flexible multibody systems have been proposed in the literature presenting relative advantages, and also drawbacks, with respect to the formulation used here [9][10][11][12][13]. However, the flexible multibody descriptions based on generalized elastic coordinates relative to body fixed frame not only use the standard linear finite element mass and stiffness matrices directly but also allow for the reduction of the number of elastic degrees of freedom, either by applying substructuring techniques [14], the Craig-Bampton method [3,15], the mode superposition technique [8,[16][17][18][19][20] or other reduction techniques [21], leading to simpler and computationally efficient models.…”

Section: Introductionmentioning

confidence: 99%

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Optimization of a complex flexible multibody systems with composite materials

2007

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The paper presents a general optimization methodology for flexible multibody systems which is demonstrated to find optimal layouts of fiber composite structures components. The goal of the optimization process is to minimize the structural deformation and, simultaneously, to fulfill a set of multidisciplinary constraints, by finding the optimal values for the fiber orientation of composite structures. In this work, a general formulation for the computation of the first order analytical sensitivities based on the use of automatic differentiation tools is applied. A critical overview on the use of the sensitivities obtained by automatic differentiation against analytical sensitivities derived and implemented by hand is made with the purpose of identifying shortcomings and proposing solutions. The equations of motion and sensitivities of the flexible multibody system are solved simultaneously being the accelerations and velocities of the system and the sensitivities of the accelerations and of the velocities integrated in time using a multi-step multi-order integration algorithm. Then, the optimal design of the flexible multibody system is formulated to minimize the deformation energy of the system subjected to a set of technological and functional constraints. The methodologies proposed are first discussed for a simple demonstrative example and applied after to the optimization of a complex flexible multibody system, represented by a satellite antenna that is unfolded from its launching configuration to its functional state.

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“…For a more detailed discussion on the selection of the modes used the interested reader is referred to Refs. [15][16][17][18][19][20]46]. …”

Section: Flexible Multibody Equations Of Motionmentioning

confidence: 99%

Section: Maximum Deformation Energy Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimization of a complex flexible multibody systems with composite materials

2007

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“…The system equation matrix shows a large number of null elements and submatrix blocks of fixed size. The Markowitz sparse matrix solver is employed here to solve the system of equations defined by Equation (4) [Duff et al 1986;Ambrósio 2003;Liu et al 2007]. …”

Section: Introductionmentioning

confidence: 99%

Optimization of a satellite with composite materials

Ambrósio

Neto

Leal

2007

JOMMS

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The design of complex flexible multibody systems for industrial applications requires not only the use of powerful methodologies for the system analysis, but also the ability to analyze potential designs and to decide on the merits of each one of them. This paper presents a methodology using optimization procedures to find the optimal layouts of fiber composite structure components in multibody systems. The goal of the optimization process is to minimize structural deformation and to fulfill a set of multidisciplinary constraints. These methodologies rely on the efficient and accurate calculation of the system sensitivities to support the optimization algorithms. In this work a general formulation for the computation of the first order analytic sensitivities based on the direct differentiation method is used. The direct method for sensitivity calculation is obtained by direct differentiation of the equations defining the response of the structure with respect to the design variables. The equations of motion and the sensitivities of the flexible multibody system are solved simultaneously and, therefore, the accelerations and velocities of the system, and the sensitivities of the accelerations and velocities, are integrated in time using a multistep multiorder integration algorithm. Different models for the flexible components of the system, using beam and plate elements, are also considered. Finally, the methodology proposed here is applied to the optimization of the unfolding of a complex satellite made of composite plates and beams. The ply orientations of lamination are the continuous design variables. The potential difficulties in the optimization of composite flexible multibody systems are highlighted in the discussion of the results obtained.

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