Shape optimization of structural parts in dynamic mechanical systems based on fatigue calculations

Abstract

In this paper a new method for an automated shape optimization of dynamically loaded components in mechanical systems is presented. The optimization is carried out by means of the results of a durability analysis based on finite elements. Load time histories, which are necessary for durability analyses, are derived from a multibody simulation. The whole optimization loop, which is an iterative procedure, incorporates all these gradual analysis steps and is implemented by the authors in a straightforward, batch-oriented manner using wellknown standard software. Since the whole process involves several different analysis types, such as multibody system simulation and durability analysis, the resulting setup is rather complex. Furthermore, the reader may not be familiar with all the terms arising within the context of every single analysis domain. Therefore, some essential aspects of each of the stages involved in the process are explained to provide the reader with the necessary background. In the following, the required software setup as well as the implementation are described. Finally, an academic example is discussed to illustrate and clearly outline the potential of this method.Key words shape optimization, multibody systems, durability analysis, fatigue, lightweight construction, virtual prototyping IntroductionIn the past years the significance of computer aided engineering (CAE) methods in the development processes of various products has increased considerably. The strong demand for shorter development processes induces the need to reduce physical prototyping and testing by replacing it with virtual prototyping by means of CAE methods. Finite element methods (FEM) and multibody system simulation (MBS), for example, play a major role in many fields of industrial production, research and development. Especially in the field of structural mechanics, these techniques are established and used extensively.Although computer-based optimization methods for an application in structural mechanics have been available for several years, they are not very popular. There are several reasons for this:1. Modelling for computer-based optimization is often complex and time-consuming 2. Optimization results and quality strongly depend on boundary conditions and load cases 3. Optimized models are sometimes difficult to interpret and/or produce in realityIn this paper, points one and two, with regard to the special case of dynamically loaded structural components, which are critical in terms of durability, are addressed. Components in dynamic mechanical systems such as parts of a gear are sometimes subject to time-varying loads, which are often stochastic. When lightweight construction is desired, normally questions concerning durability arise. This is especially true for components where failure of these components leads to safety issues. Therefore, the design process of such components always implies durability investigations such as testing, analytical calculations and/or computer-based durability analysis (DA).In ...

Shape optimisation of parts in dynamic mechanical systems with respect to fatigue

“…As already demonstrated (Häußler and Albers 2004), the homogenisation approach to shape optimisation can be extended to integrate fatigue analyses. The local damage D(r ) at location r is determined by the time history of the local stress state as shown in figure 4.…”

“…A coupled approach to the shape optimisation of dynamically loaded parts, based on results of durability analyses, was first presented by the authors in 2000 (Ilzhöfer et al 2000). Further improvements and an integration of multibody system dynamics were presented more recently (Häußler and Albers 2004). The research work presented in this paper is based on the work of Häußler and Albers (2004), and includes new investigations and results, especially for dynamic systems.…”

Gradient Approximation in Flexible Multibody Systems Using a Multigrid Approach

“…Alternatively, the semi-analytic methods such as the direct differentiation method or the adjoint variable method (AVM) can be used, see [1,2] for a detailed explanation. These methods have been successfully implemented to optimize the shape of members of multibody systems using gradient-based optimizers [2][3][4]. For these gradient calculations, in spite of the fact that the equations of motion have to be differentiated with respect to design variables and system states, the computation time is not high, since the number of design variables is small.…”

Metamodel-based optimization of the bolted connection of a wing spar considering fatigue resistance

“…In their study, a fatigue analysis was additionally carried out to verify the durability of the final design. Häußler and Albers 5 presented a new method for an automated shape optimization of dynamically loaded components in the mechanical systems. The optimization was carried out by means of the results of a durability analysis.…”