Optimization of Flexible Multibody Dynamic Systems Using the Equivalent Static Load Method

Kang, Bongkoo; Park, Gyung-Jin; Arora, Jasbir S.

doi:10.2514/1.4294

Cited by 82 publications

(70 citation statements)

References 25 publications

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“…3.2 Derivation of the equivalent static loads using a floating frame of reference formalism Initially, the ESL method has been developed for flexible MBS modeled using a floating reference frame formulation [18]. In order to develop the ESL derivation, the equations of motion and the notations corresponding to this formalism are first reminded.…”

Section: Introduction and Definitionmentioning

confidence: 99%

“…Firstly, a rigid or flexible MBS simulation computes the loads applied to each component and secondly, each isolated component is optimized independently using a quasi-static approach in which a series of equivalent static load cases obtained from the MBS simulation are applied to the respective components. An important development has been made by Kang et al [18] who proposed a rational method to define equivalent static loads (ESL) to optimize flexible mechanisms. During the static response optimization process, whereas ESL are implicit functions of the dynamic simulation response, they are not updated.…”

mentioning

confidence: 99%

“…In addition, the standard ESL method was developed for flexible MBS described using a floating reference frame formulation [18]. This formalism facilitates the derivation of the equivalent static loads notably as this formulation deals with body-attached frame.…”

mentioning

confidence: 99%

“…In order to realize a fair comparison between both optimization methods, it is preferable to use a unique MBS formalism. Therefore, another contribution of this paper is to adapt the ESL method to the nonlinear finite element formulation because the ESL method proposed by Kang et al [18] cannot be simply translated and directly applied to the latter formalism.…”

mentioning

confidence: 99%

“…In [18], the authors define an equivalent static load as follows: Definition 1. When a dynamic load is applied to a structure, the equivalent static load is defined as the static load that produces the same displacement field as the one created by the dynamic load at an arbitrary time.…”

Section: Introduction and Definitionmentioning

confidence: 99%

See 4 more Smart Citations

Weakly and fully coupled methods for structural optimization of flexible mechanisms

2015

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The paper concerns a detailed comparison between two optimization methods that are used to perform the structural optimization of flexible components within a multibody system (MBS) simulation. The dynamic analysis of flexible MBS is based on a nonlinear finite element formulation. The first method is a weakly coupled method which reformulates the dynamic response optimization problem in a two-level approach. Firstly, a rigid or flexible MBS simulation is performed and secondly, each component is optimized independently using a quasistatic approach in which a series of equivalent static load (ESL) cases obtained from the MBS simulation are applied to the respective components. The second method, the fully coupled method, performs the dynamic response optimization using the time response obtained directly from the flexible MBS simulation. Here, an original procedure is proposed to evaluate the ESL from a nonlinear finite element simulation, contrasting with the floating reference frame formulation exploited in the standard ESL method. Several numerical examples are provided to support our position. It is shown that the fully coupled method is more general and accommodates all types of constraint at the price of a more complex optimization process.

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Section: Introduction and Definitionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

Section: Introduction and Definitionmentioning

confidence: 99%

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Weakly and fully coupled methods for structural optimization of flexible mechanisms

2015

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Several simultaneous formulations for transient dynamic response optimization: An evaluation

Wang¹,

Arora

2009

Numerical Meth Engineering

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SUMMARYSeveral simultaneous formulations for transient dynamic response optimization are described, analyzed and compared. A key feature of the formulations is that the state variables, in addition to the real design variables, are treated as independent variables in the optimization process. The state variables include different combinations of generalized displacements, velocities and accelerations. Formulations based on different discretization techniques for first-order and second-order differential equations are presented. Finite difference, Newmark's method and methods based on collocation are all discussed. Similar to the simultaneous analysis and design approach used for the optimization of structures subjected to static loads and the direct collocation/transcription method for optimal control, the equations of motion are treated as equality constraints. A major advantage of these formulations is that special design sensitivity analysis methods are no longer needed. However, the formulations have larger numbers of variables and constraints. Therefore, sparsity of the problem functions must be exploited in all the calculations. Advantages and disadvantages of the formulations are discussed. The numerical results for an example problem and performance features of the formulations are compared. All the formulations converge to the optimum solution for the example problem. They are quite efficient for a smaller number of time grid points; however, the computational times increase as the number of grid points is increased.

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Shape optimization of the initial blank in the sheet metal forming process using equivalent static loads

Lee

Park

2010

Numerical Meth Engineering

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SUMMARYIn the sheet metal forming process, forming the final desired shape is difficult to obtain due to wrinkling, tearing, failure of material, etc. Various conditions of the forming process should be controlled for the desired shape. These conditions are the velocity of the punch, the friction factor, the blank holding force, the initial shape of the blank and others. Many researchers have conducted studies to predetermine the initial blank shape. The structural optimization technique is one of them. Non-linear response structural optimization is required because non-linearities are involved in the analysis of the metal forming process. When the conventional method is utilized, the cost is extremely high due to repeated non-linear analysis for function and sensitivity calculation. In this paper, the equivalent static loads (ESLs) method is used to determine the blank shape which leads to the final desired shape and reduced wrinkling. The ESLs method is a structural optimization method where non-linear dynamic loads are transformed into ESLs, and these ESLs are utilized as external loads in linear response optimization. The design is updated in linear response optimization. Non-linear analysis is performed with the updated design and the process proceeds in a cyclic manner. An optimization formulation is defined for the examples, the formulated problems are solved to verify the proposed method and the results are discussed. Non-linear analysis is performed using the commercial software LS-DYNA, NASTRAN is used for calculating the ESLs and linear response optimization, and an interface program for LS-DYNA and NASTRAN is developed.

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Optimization of Flexible Multibody Dynamic Systems Using the Equivalent Static Load Method

Cited by 82 publications

References 25 publications

Weakly and fully coupled methods for structural optimization of flexible mechanisms

Weakly and fully coupled methods for structural optimization of flexible mechanisms

Several simultaneous formulations for transient dynamic response optimization: An evaluation

Shape optimization of the initial blank in the sheet metal forming process using equivalent static loads

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