Weakly and fully coupled methods for structural optimization of flexible mechanisms

Abstract

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.

Topology optimization of a flexible multibody system with variable-length bodies described by ALE–ANCF

“…Compared with the integrated optimization method [32], the ESL method has many merits, such as high efficiency in computation and convenience in implementation [15,32]. In this study, the ESL method is modified to deal with the topology optimization problem for the dynamic response of an FMBS with variable-length bodies.…”

“…Consequently, the topology optimization can be performed using the method of the equivalent static loads (ESL) or directly from the dynamic simulation of an FMBS. The former is named the ESL method [15,18,[27][28][29][30][31], while the latter is called the integrated optimization method [16,32]. For an FMBS with variable-length bodies, the design domain varies over time.…”

Simultaneous topology and size optimization of a 3D variable-length structure described by the ALE–ANCF

“…The detailed derivation of the ESL sets and a brief optimization computation flow are also given. For the fully coupled optimization formulation, the readers can refer to references [3,[16][17][18].…”

“…Compared with the fully coupled optimization method, the ESL method turns out to be more efficient in computation for the cases in [18,19], and it has been successfully applied to many dynamic response optimization problems [3, 15, 17-20, 23, 24, 49, 50]. The ESL method is therefore employed in this study and reevaluated in subsection 3.2 to deal with the variable-length characteristics.…”

“…The optimization of a 3D variable-length structure can be performed either directly from the aforementioned dynamic analysis of FMBS or from a series of equivalent static analyses [15,16]. The former is called the fully coupled method or the integrated optimization method [16][17][18], while the latter is called the weakly coupled method or the equivalent static loads (ESL) method [16,[19][20][21][22][23][24][25]. Compared with the fully coupled method, the weakly coupled method has two significant merits.…”