Structural optimization of flexible components within a multibody dynamics approach

Structural optimization techniques rely on mathematical foundations in order to reach an optimized design in a rational manner. Nowadays, these techniques are commonly used for industrial applications with impressive results but are mostly limited to (quasi-) static or frequency domain loadings. The objective of this thesis is to extend structural optimization techniques to account for dynamic load cases encountered in multibody applications. The thesis relies on a nonlinear finite element formalism for the multibody system simulation, which needs to be coupled with structural optimization techniques to perform the optimization of flexible components in an integrated way. To tackle this challenging optimization problem, two methods, namely the fully and the weakly coupled methods, are investigated. The fully coupled method incorporates the time response coming directly from the MBS in the optimization. The formulation of the time-dependent constraints are carefully investigated as it turns out that it drastically affects the convergence of the optimization process. Also, since gradient-based algorithms are employed, a semi-analytical method for sensitivity analysis is proposed. The weakly coupled method mimics the dynamic loading by a series of equivalent static loads (ESL) whereupon all the standard techniques of static response optimization can be employed. The ESL evaluation strongly depends on the formalism adopted to describe the MBS dynamics. In this thesis, the ESL evaluation is proposed for two nonlinear finite element formalisms: a classical formalism and a Lie group formalism. An original combination of a level set description of the component geometry with a particular mapping is adopted to parameterize the optimization problem. The approach combines the advantages of both shape and topology optimizations, leading to a generalized shape optimization problem. The adopted system-based optimization framework supersedes the classical component-based approach as the interactions between the component and the system can be consistently accounted for

Poster: Dynamic response optimization of structural components within a multibody system approach

LIGHTCAR (Contract RW-6500

Weakly and fully coupled methods for structural optimization of flexible mechanisms

peer reviewedThe 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. First, a rigid or flexible MBS simulation is performed, and second, each component is optimized independently using a quasi-static 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 constraints at the price of a more complex optimization process

Structural optimization of multibody system components described using level set techniques

The structural optimization of the components in multibody systems is performed using a fully coupled optimization method. The design’s predicted response is obtained from a flexible multibody system simulation under various service conditions. In this way, the resulting optimization process enhances most existing studies which are limited to weakly coupled (quasi-) static or frequency domain loading conditions. A level set description of the component geometry is used to formulate a generalized shape optimization problem which is solved via efficient gradient-based optimization methods. Gradients of cost and constraint functions are obtained from a sensitivity analysis which is revisited in order to facilitate its implementation and retain its computational efficiency. The optimizations of a slider-crank mechanism and a 2-dof robot are provided to exemplify the procedure

Optimal design of flexible mechanisms using the Equivalent Static Load method and a Lie group formalism

Historically, the optimization of mechanisms started with the selection of several configurations where-upon structural optimization was perform based on representative loading conditions coming from the designer experience for each posture [8]. This approach is doubtful since a few configurations can hardly represent the overall motion and the optimal design entirely depends on the designer’s choices. With the evolution of multibody system (MBS) analysis, Bruns and Tortorelli [4] proposed an approach combining rigid MBS analysis and optimization techniques to design optimal components. The opti-mization procedure was performed with load cases evaluated during the MBS analysis. They illustrated their method on the design of a slider-crank mechanism loaded with the maximum tensile force calculated during the simulation. Considering the time-dependent loading conditions coming from the MBS analysis, the optimization problem is rather complex and a lot of research has been conducted to remove this time dependency. For instance, Oral and Kemal Ider [7] investigated the representation of the constraints either by the most critical constraint or summarized with a Kresselmeier-Steinhauser function. An important breakthrough has been made by Kang, Park and Arora [6] who proposed a method to define Equivalent Static Loa

Structural optimization of flexible components under dynamic loading within a multibody system approach: a comparative evaluation of optimization methods based on a 2-dof robot application.

This paper is dedicated to a comparative evaluation between two methods of optimization to realize the structural optimization of flexible components in mechanical systems modeled as multibody systems. A nonlinear finite element method based formalism is considered for the dynamic simulation of the flexible multibody system. The first method is the Equivalent Static Load method which enables to transform a dynamic response optimization problem into a set of static response optimization problems. The second method treats directly the dynamic optimization problem in an integrated manner where the optimization process is carried out directly based on the time response coming from the multibody system approach. However, the first method proposed by Kang, Park and Arora was developed under the assumption that the multibody system is described using a floating frame of reference. Therefore, in order to carry on the comparison using a unique multibody system approach, a method is first proposed to derive the equivalent static loads when using a nonlinear finite element method based formalism. The comparative evaluation is then carried out on the simple academic example of the mass minimization of a two-arm robot subject to tracking deviation constraints. Conclusions are finally drawn for future work and stringent comparison.Environnement d’Ingénierie Assistée par Ordinateur pour l’Analyse et l’Optimisation de la Liaison-Sol, des Transmissions et de l’Acoustique de Véhicules Automobiles à des fins d’Allégement et de Réduction de Consommation d’Energi

Modelling of joints with clearance and friction in multibody dynamic simulation of automotive differentials

Defects in kinematic joints can sometimes highly influence the simulation response of the whole multibody system within which these joints are included. For instance, the clearance, the friction, the lubrication and the flexibility affect the transient behaviour, reduce the component life and produce noise and vibration for classical joints such as prismatic, cylindric or universal joint. In this work, a new 3D cylindrical joint model which accounts for the clearance, the misalignment and the friction is presented. This formulation has been used to represent the link between the planet gears and the planet carrier in an automotive differential model

Investigations on a Level Set based approach for the optimization of flexible components in multibody systems with a fixed mesh grid

This paper considers the optimization of flexible components in mechanical systems thanks to a "fully integrated" optimization method which includes a flexible multibody system simulation based on nonlinear finite elements. This approach permits to better capture the effects of dynamic loading under service conditions. This process is challenging because most state-of-the-art studies in structural optimization have been conducted under (quasi-)static loading conditions or vibration design criteria and also because this ``fully integrated" optimization method is not a simple extension of static optimization techniques. The present paper proposes an approach based on a Level Set description of the geometry. This method leads to an intermediate level between shape and topology optimizations. Gradient-based optimization methods are adopted for their convergence speed. Numerical applications are conducted on the optimization of a connecting rod of a reciprocating engine with cyclic dynamic loading to show the feasibility and the promising results of this approach