Axel Schumacher

Bubble method for topology and shape optimization of structures

This paper addresses a novel method of topology and shape optimization. The basic idea is the iterative positioning of new holes (so-called “bubbles”) into the present structure of the component. This concept is therefore called the “bubble method”. The iterative positioning of new bubbles is carried out by means of different methods, among others by solving a variational problem. The insertion of a new bubble leads to a change of the class of topology. For these different classes of topology, hierarchically structured shape optimizations that determine the optimal shape of the current bubble, as well as the other variable boundaries, are carried out.

Topology and Shape Optimization Procedures Using Hole Positioning Criteria

The topology of any constructions, i.e., the position and arrangement of structural elements in a given design space, has strong influence on its structural behaviour. Currently, the topology is still chosen intuitively or by referring to existing constructions (“Current Design World State”), or it is selected from a number of different variants. The topology optimization aims at the use of mathematical-mechanical strategies in a design process.

An Automated Optimization Process for a CAE Driven Product Development

Within the product development the need for generating design variants is given in many situations, for example to optimize an existing initial design with respect to new or modified requirements. For an efficient process it is essential that these variations can be done very easily within a small timeframe. In the virtual product development the physical characteristic of a component is determined by numerical simulation. Commercial software products exist for nearly each physical phenomenon. Often these methods are covered under CAE. A fundamental issue for building and analyzing variants easily and fast is a seamless interaction between the CAD and CAE software tools. This paper presents a powerful CAD/CAE sequence to the engineers community, where in contrast to other approaches results of the CAE analysis directly interact with CAD data. This strategy is supported by describing the products geometry by parameters. The CAD/CAE sequence is integrated in an optimization loop. The presented application example is an automotive part.

Decision Makings for Initial Designs Made of Advanced Materials

The “Bubble Method” is one of the methods of topology optimization techniques. Its basic idea is to iteratively position new holes (bubbles) in a structure by means of a definite function and a hierachically secondary shape optimization. The expression of the definite function depends on the special optimization functionals and the material behaviour. In this paper the difference of optimal shapes of a cantilever disc made of ductile and brittle materials is presented and, furthermore, the Bubble Method is used for finding a best possible initial design of a cantilever disc made of ductile materials.

MULTIDISCIPLINARY OPTIMIZATION STRATEGY - TOOL FOR AN EFFICIENT DESIGN PROCESS OF LARGE-SCALE AIRCRAFT

Multidisciplinary Design Optimization (MDO) strategies will play an increasingly important role for the future improvement and acceleration of the single phases of a design process. This development is of particular importance for all high-tech branches like air- and spacecraft industries. The highly complex behavior of advanced large-scale airplanes strictly requires reliable layout strategies. The highly multidisciplinary character of the evolving design problems requires the use of strategies that facilitate the interaction between different analysis methods and the respective disciplines. The MDO-strategies have to comply with the processing of design tasks within special teams (e.g., aircraft performance, aircraft design, structural mechanics, structural design loads, flight dynamics and control, adaptive aircraft structures).

An Element Deactivation and Reactivation Scheme for the Topology Optimization Based on the Density Method

Topology optimization results based on the homogenization or density method highly depend on the discretization of the design space. The smallest possible dimension of the optimized structure is one element edge length. If the mesh can be refined, smaller design features can be represented and thereby the performance of the optimized structures can be improved. But the mesh refinement is limited by the computational cost of the Finite Element Analysis (FEA).

Automatic Definition of Density-Driven Topology Optimization with Graph-Based Design Languages

Today, the product development process is characterized by increasing diversity. A trend towards customer-tailored products can be observed. This trend demands new processes for product development and manufacturing. Increasing product individuality up to lot size one can be faced with methods, which automate the design process and avoid redundant manual work. As the number of tools involved in the product development process is ever-increasing, one goal is to eliminate the distribution of knowledge into several software tools and begin with one central and consistent data model from where all the software tools used can be triggered automatically. This goal can be addressed by using graph-based design languages [1], which themselves are based on the Unified Modeling Language (UML). On the manufacturing side, one technology can be seen in the additive manufacturing process. For finding a good structure, a combination of additive manufacturing and topology optimization can be advantageous because of the ability of additive manufacturing to create almost arbitrary geometry. Using the example of a lightweight quadrocopter, we propose a graph-based design language which integrates topology optimization and can cover different aspects of the multi-disciplinary product development process: requirements, abstract product functions, design constraints (i.e. equations) and costs among others. The topology optimization triggered by the design language can take into account different product configurations (i.e. packaging configurations) and accordingly makes design proposals (i.e. structural proposals for the frame of the quadrocopter). The executable nature of the graph-based design language reduces the design time significantly.

A Topology Optimization Scheme for Crash Loaded Structures Using Topological Derivatives

This paper deals with a topology optimization scheme for crash loaded structures. The presented approach combines the numerical calculation of Topological Derivatives with a level-set method. In a microscale investigation on a planar shell with a hole under perpendicular stresses a meta-model for the Topological Derivatives is derived. This meta-model provides the sensitivities for the optimization of the macroscale mechanical problem. The iterative volume reduction with a level-set method, a linear mapping scheme and filtering allows the crash simulation with smooth boundaries. An academic example illustrates the applicability of the optimization scheme.

Automatic Generation, Validation and Correlation of the Submodels for the Use in the Optimization of Crashworthy Structures

The structural optimization of large crashworthy systems like a vehicle body in a crash loaded case is a time consuming and costly process. The computation time can be reduced by dividing the large system (main model) into small systems called submodels. These submodels can be effectively used in the optimization to shorten the response time of the simulation. The generation of submodels by hand is challenging and requires a lot of effort and knowledge to create and validate them. This paper presents a workflow to automatically generate and validate the submodels using various mathematical functions.

Considering Linear Buckling for 3D Density Based Topology Optimization

Stability is an important issue in topology optimization, since results of the optimization are often framework structures. If some trusses of these structures are subjected to compression, they maybe buckle and the structure fails.