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Optimization procedures in structural design

2003; American Society of Mechanical Engineers; Volume: 56; Issue: 4 Linguagem: Inglês

10.1115/1.1576807

2379-0407

H. Eschenauer,

Structural Analysis and Optimization

Hans A EschenauerHans A Eschenauer was born in 1930. After finishing high school, he was first trained as machine fitter and then decided to study Theoretical Mechanical Engineering at the Technical University of Berlin. After graduating as Dipl-Ing (MSc) in 1957, he worked in different development departments of industrial companies. In 1963 he became scientific assistant at the Technical University of Darmstadt, where he received his Doctor of Engineering (Dr-Ing) degree in the field of Mechanics in 1968. After further industrial employment with Krupp Industries as Head of the Antenna Structures and Advanced Technologies Department in Duisburg, he was appointed Full Professor for Mechanics at the University of Siegen in 1975, where he gave courses on Mechanics and Applied Mechanics with special emphasis on fundamentals, plates, shells, and structural optimization. His main research activities were in the fields of Multiobjective, Multilevel, Topology, and Multidisciplinary Structural and System Optimization. In addition, he held various positions in the Department of Mechanical Engineering and in the autonomous university administration (eg, Senate, research committees). In 1984 he established the Research Laboratory for Applied Structural Optimization, and in 1992 he became founder and Head of the Board of the Research Center for Multidisciplinary Analyses and Applied Structural Optimization FOMAAS, a central university institute. After his retirement in 1995 he remained Head of the FOMAAS Board until 1999. He is still a Member of the Board and responsible for some research projects in cooperation with industry. During his industrial employment and university service times, Hans Eschenauer received several awards, including the European Steel Design Award 1974, in Delft/The Netherlands, the 1995 ASME Design Automation Award, in Boston, MA, USA, the 1996 ASME Machine Design Award, in Irvine, CA, USA and the URP Award of the Ford Motor Company 2000, in Detroit, MI, among others. He is a member of several national and international professional societies and executive and award committees, and acts as referee for national professional societies and executive and award committees, and as referee for different research councils and scientific journals. He is the author, coauthor, and editor of various monographs and textbooks, and has contributed more than 230 papers/lectures in scientific journals and conferences. He chaired and cochaired sessions at numerous international conferences and seminars. Hans Eschenauer has been married to his wife Gerda for more than 50 years and has a son and daughter, as well as two grandchildren.After graduating from the Technical University of Berlin, I at first worked in the development and calculation departments of turbine and centrifugal pumps companies, focusing on the field of strength and dynamics. This provided a unique opportunity to put to practice the knowledge acquired during my studies where I specialized in Theoretical Mechanical Engineering. In doing so, I particularly dealt with the calculation-based layout of casings and turbine propellers subjected to pressure, thermal, and dynamic loads. In the scope of my work I developed a special transfer matrix procedure which was able to calculate maximum pressures in spiral casing pumps. Based on my industrial experience, I then accepted an offer made by my later mentor and supervisor, Professor Walter Schnell, to become his scientific assistant at the Institute of Mechanics of the Faculty of Mathematics and Physics at the Technical University of Darmstadt. In addition to teaching, which was an integral and compulsory part of that position, I engaged in scientific research mainly into the problem of deformations and stresses occurring in load-supporting structures (disks, plates, shells) subjected to thermal loads. Particularly in the 1960s, this problem field was highly important in air- and spacecraft technology, in power and turbine construction, in reactor and process design, as well as in telescope design. Hence, I devoted my doctoral dissertation to the topic of Thermoelastic plate equations—Buckling of a cantilever plate. The work was completed in 1968 at which time I graduated as a Doctor of Engineering (Dr-Ing) under the supervision of Professors W Schnell and K Marguerre (both Technical University of Darmstadt). Following the tenure at Darmstadt Technical University, I returned to industry as Head of the Department of Antenna Structures and Advanced Technologies at Krupp Industrial and Steel Engineering, Duisburg-Rheinhausen. This proved to be a real challenge, as my studies never provided me with an opportunity to deal with the aspects of telescope design. Still, my thorough education in theoretical engineering had provided me with a sound and reliable foundation to successfully address the new challenge. One of the first tasks in the scope of my new professional engagement was the establishing of model equations to evaluate the dynamic behavior of parabolic antennas and telescopes. The observation and tracking of satellites and other space units require terrestrial systems with adjustable parabolic antennas as an integral part. Here, the driving control governs the tracking in such a way that signals can be sent and received intermittently. The antenna structure, including drive unit and transmission, is the control path within the drive control loop. Owing to the fact that the radio astronomers intended to measure radiation in the millimeter and even sub-millimeter range, the demands pertaining to the accuracy of the antennas' tracking control had to be permanently increased. Hence, when developing high performance antennas we had to establish simulation models as realistically as possible to simulate, in the project phase already, the given demands for different states of loading by varying the system parameters. This task required a close cooperation of mechanics, control and drive engineering, and radio astronomy in order to produce sufficiently precise results—in other words, we had to solve a multidisciplinary or, as it is termed today, a mechatronic task. Figure 1 shows a schematic sketch of a track-and-wheel type radio telescope with an azimuth-elevation support, consisting of the azimuth unit A (pylon, pyramid, base frame) and the B-B supported elevation unit E (supporting structure for elevation and reflector). Realized antenna structures of this type are the 100-m-Radio Telescope in Effelsberg, Germany of the Max Planck Institute for Radio Astronomy (MPIfR), Bonn, Germany, and the 30-m-Helios Control Station of the Central German Earth Station, Weilheim, Germany as a part of the American-German solar probe project HELIOS. The formulation of the system equations had to take into account a number of nonlinear effects like loose connections and Coulomb friction, as well as excitations caused by wind forces and tooth errors. In addition, the behavior of the telescope structure was to be investigated for different initial conditions when assuming deterministic disturbance signals (step and ramp functions) of the momentums of the drive and brace engine. The thus achieved simulation results were then compared with the values gained from measurements at the 30-m control station; this showed good convergence 1. In addition to the development and construction of the HELIOS control station in the scope of the solar probe project, I succeeded in acquiring a new project: the development, calculation, design, and construction of a Magnetic Field Simulator. The system serves the qualification and acceptance tests of the solar probe which requires measurements of the static and time-variant eigenfields of the probe, and the calibration of the magnetic measurement systems. The simulator has to fulfill the highest demands of measurement accuracy, and at the same time must simulate the environmental conditions as precisely as possible. The simulator's core component is a triple-axis system according to Braunbek with a total of four coils per axis. The field homogeneity of a coil system largely depends on the accurate positioning of the coils and their deformation behavior. This project required extensive structural analytical simulation calculations 2. Essential impetus toward structural optimization was gained by the conception, development, calculation, design, and construction of a 30-m-Millimeter Wave Radio Telescope (MRT) jointly commissioned by the Max Planck Institute for Radio Astronomy, Bonn, Germany and the German-French Institute for Radio Astronomy in the mm-Range (IRAM), Grenoble, France. The telescope has been erected on the 3000 m high Pico Veleta, Spain (Fig. 2). Developing a telescope with such dimensions (30 m diameter of the parabola aperture) with maximum precision (shape and adjustment accuracy) and, at the same time, low cost was a challenge per se. In addition, it was demanded that the telescope not only showed a stable control behavior in all positions with a lowest eigenfrequency of >2.5Hz, but owing to the erection site, it also had to withstand extreme wind velocities, temperature gradients, and layers of ice. This was nothing less than a multicriteria optimization task. Also, the solution of this problem again proved that the modeling, simulation, and optimization of structures and/or systems cannot be achieved without an interdisciplinary cooperation. This can best be shown at the example of developing a radio telescope, where—in analogy with Collar's aeroelastic triangle—the three disciplines Antenna Technology, Structural Mechanics, and Control Engineering are linked to each other in a triangle, arranged around the central discipline Multidisciplinary Structural Optimization (Fig. 3). We call this an MDA (MultiDisciplinary Analysis) Triangle. Of course, this presentation can be suitably adapted to other problem fields. In 1975, I was offered an appointment for the position of Full Professor to the Chair of Mechanics at the University of Siegen, which I accepted for the Winter Semester 1975–76. Based on my previous experience gained in the design and construction of highly precise radio telescopes, I immediately concentrated my research activities on the field of structural optimization. After the establishment of a structural mechanics working group at the Institute of Mechanics and Control Engineering/Mechatronics, we continued working on the development of the 30-m-MRT, together with a further partner from industry, MAN Gustavsburg. This was made possible by way of an agreement with and through funding by Krupp Industrial and Steel Engineering, Duisburg-Rheinhausen, Germany. Based on the previous Trial-and-Error results obtained in the optimal layout of radio telescope components, I first started fundamental research into the fields of Vector or Multicriteria Optimization3, Multilevel Optimization4, and into Mathematical Programming (MP) Methods. These activities were funded, in particular, by the German Research Council (DFG) in the scope of several projects. In structural optimization it is essential to note that the application of optimization theories in a design process depends on the theoretical aspects of the technical problem. Between 1975 and 1985 the treatment of this problem environment led to a number of doctoral theses conceived under my supervision; these works provided the fundamental elements toward the emergence of SAPOP (Structural Analysis Program and Optimization Procedure) 5 which follows the so-called Three-Columns-Concept (Fig. 4). Here, Column 1 contains the problem definition, modeling, and structural analysis; Column 2 provides numerous MP-algorithms and special methods; Column 3 finally formulates the optimization model including optimization strategies (eg, multicriteria optimization). The three columns can be presented in the form of an optimization loop (analogous to a control loop) which allows one to determine optimum designs (Fig. 5). Subsequent to the aforementioned research, we conducted fundamental investigations into shape optimization 6, the use of advanced materials (composite materials, ceramics), and the consideration of manufacturing processes (casting and forming, tape-laying for fiber composites) in the conception phase 78910. In 1983 I spent a sabbatical leave as a visiting professor at the Universities of Alberta, Edmonton and Calgary, Canada. At the last named university, Prof Peter Vermeulen developed a special type of concentrated solar energy system, the so-called Rear Focus Collector. According to A Spyridonos, it consists of several frustrum-type reflector shells linked together by two intersecting ribs. The focus of the rays and, accordingly, the absorber are located behind the collector in contrast to the usual parabolic reflector. In many discussions, Peter Vermeulen and I contemplated the question of how an optimal design could be determined (eg, by varying the single frustrum shells). For this purpose, we set up a problem definition and performed a modeling. The actual optimization calculations were then conducted in Siegen in the form of a vector optimization problem using a weighted distance function. As essential objective functions, the system efficiency (depending on the concentrating factor and intercepting factor) and the weight of the single collector shells were selected. The thus achieved numerical results proved to be rather promising; the concentrating factor, for instance, could be increased substantially by variation of the collector shells 11. The rather encouraging advances achieved to that point were appreciated and hence funded by further research institutions and industrial companies. In 1985 this resulted in the establishment of the Research Laboratory for Applied Structural Optimization at the Institute for Mechanics and Control Engineering of the Mechanical Engineering Department. Between 1980 and 1985 the Research Laboratory cooperated with the Max Planck Institute for Radio Astronomy (MPIfR), Bonn, the Steward Observatory (University of Arizona, Tucson) and Krupp Industrial and Steel Engineering, Duisburg-Rheinhausen, Germany, in the conception, development, and construction phases of a highly precise 10-m Radio Telescope for the Submillimeter Wave Range (SMT). This again was a great challenge for the entire field of radio telescope design, as the extreme specifications required for the structure could only be met by applying advanced materials like the use of Carbon Fiber Reinforced Plastics for the paraboloidal reflector. This problem was solved after investigations into the optimal layout of carbon fiber reinforced materials; a respective, rather voluminous research project which was accredited and funded by the Federal German Ministry of Research and Technology (BMFT), Bonn under the title Fiber Composite Design—Calculation, Optimization, Tests12. The 10-m-SMT has been erected on the 3300 m high Mt Graham near Safford, AZ, USA and commissioned in the meantime. The acceptance measurements displayed a good convergence with the conducted calculations. In a subsequent project, we dealt with the shape optimization of satellite tanks with the aim of achieving a weight minimization at the prescribed volume and at the same time fulfilling given constraints regarding stresses and buckling. This project was accomplished by our working group in cooperation with MBB ERNO Space Technologies and the Institute of Lightweight Design at the Technical University RWTH of Aachen, Germany (Prof H O¨ry). Furthermore, we addressed the shape optimization of an automotive wheel design with the objectives: weight minimization and obeying stress constraints. In this project, multilevel optimization was used by dividing the entire structure under investigation into subcomponents. Another long-term cooperation emerged with MBB/DASA, Ottobrunn (near Munich) that concerned the treatment of large scale systems. In this project, which went on until the mid-1990s, we supported MBB in the development of the optimization software LAGRANGE in parallel with our in-house SAPOP procedure. These different research projects had made it quite clear to me that there existed substantial shortfalls in the exchange between the single special disciplines, resulting in problems when it came to treating complex tasks and establishing realistic models. In 1991, I therefore filed an application to the University's Senate for the foundation of a Central University Institution, which, after the application had been granted, was to become the Research Center for Multidisciplinary Analysis and Applied Structural Optimization (FOMAAS). This research establishment intended to combine both Fundamental Research and Applied Research by an interdisciplinary, project-related symbiosis of the engineering sciences with applied mathematics and computer sciences, being open to contributions from natural sciences and the humanities. This was based on the following considerations: After completing its foundation phase, our FOMAAS Research Center received a number of research projects funded by the German Research Council DFG. These mainly concerned the further development of structural/system optimization in the fields of Multidisciplinary Modeling, Sensitivity Analysis, and Optimization of Composite Structures (the latter being the title of a DFG package application made together with the Ruhr-University of Bochum and the Universities of Essen and Karlsruhe), Topology Optimization of Component Structures using Hole Positioning Criteria—Bubble Method, and Stochastic Optimization Strategies. The secondly named project, Topology Optimization, is of particular importance for the structural layout in the conceptual phase of a design process 13. The so-called Bubble Method, which emerged in the scope of the work, belongs to the class of Geometrical or Macro-Approaches. In this class, the topology of a solid body can be changed by inserting holes. The conceptual process consists of an iterative positioning of new holes (bubbles) at specific points in the topology domain by means of so-called characteristic equations. These holes and the existing variable boundaries of the continuous body are simultaneously subjected to a shape optimization procedure using approach functions. This means that the boundaries of the body are taken as parameters, and that the shape optimization of the new holes and of the other variable boundaries of the body is carried out as a parameter optimization problem. Thus, a variety of possible topologies is created from which a suitable variant can be chosen according to the manufacturing requirements. A numerical realization of the Bubble Method was achieved via SAPOP which was augmented by a corresponding positioning model (Fig. 6). The method was verified at a number of real-life examples, among others, at the panel supporting structure of the 30-m-MRT (Fig. 2). In doing so we could prove that the Bubble Method was able to determine an optimal structure with sufficient accuracy within a fraction of the time otherwise required by a cumbersome and expensive trial-and-error procedure. For further details, see 14. In 1990, we received a major grant by the German Research Council for a project entitled Stochastic Optimization Strategies with Special Emphasis on the Layout of Components made of Advanced Materials. This field still has an undiminished topicality even today: Owing to the increased importance of considering material parameters in the design process, we are forced to augment the classical layout procedures by including reliability constraints. In this project the particular challenge was to modify the occurring objective functions with suitable decision criteria in the sense of a Pareto optimization. The introduction of the stochastic variables increased the high complexity of the classical structural optimization even further. The required failure probabilities were calculated and implemented into the SAPOP procedure in the form of failure constraints. For his paper, An Augmented Optimization Procedure for Stochastic Optimization and its Application to Design with Advanced Materials, which was conceived in the scope of this project, my coworker Thomas Vietor received the Heinz-Maier-Leibnitz-Award in 1992 for contributions made by young scientists in the field of ceramic materials 15. The award was granted by the Federal Minister of Education and Science, following a suggestion by an award committee. Starting in 1995, my FOMAAS working group took part in an extensive compound project funded by the Ministry of Education and Research (BMBF), Bonn, and entitled Multidisciplinary Structural Optimization in Aircraft Development DYNAFLEX. The principal project management was with the Institute of Aeroelasticity (Prof H Ho¨nlinger) of the German Aerospace Center (DLR), coordinating a cooperation of the Institute for Aircraft and Lightweight Construction (Profs Kossira, P Horst) at the Technical University of Braunschweig, the Institute of Flight Control and Air Traffic (Prof Wilhelm) of the Technical University of Berlin, the Institute of Fluid Mechanics (Prof Laschka) at the Technical University of Munich, the Institute of Flight Mechanics and Flight Control (Prof Well) of the University of Stuttgart, as well as DASA/Airbus Hamburg. The aim of this project was to investigate the interactions between the single substructures of the Airbus A380 large scale aircraft and to test the use of multidisciplinary optimization strategies 16. Applying computer networks in the scope of the optimization of complex systems on the basis of simulation calculations is a logical and consequent augmentation to the optimization strategies developed at FOMAAS. The simulation of a large number of a system model's different variants with respect to the parameters and the topology is the cornerstone of parallelization (coarse-granular parallelism). Consequently, this type of parallel processing does not require the use of high-performance computers, but the rise of powerful computer networks by the middle of the 1990s provided a cost-efficient solution for a distributed, simulation-based optimization. Here, the parallel tool OpTiX, developed in cooperation with the FOMAAS working group of Professor Grauer, played a pioneering role 17. Among others, it was integrated into the aforementioned LAGRANGE system in the scope of a cooperation project with DASA/EADS. Also since the middle of the nineties, commercially available simulation tools have facilitated the modeling and simulation of complex systems to a broad extent. Along with this progress, it became quite obvious that the FOMAAS-developed analysis and optimization methodology for complex structural mechanical systems could also be transferred to other technical and non-technical systems. At the same time, the methods and tools developed by modern computer and information sciences and the new horizons thus opened have gained an increased importance. Since the foundation of FOMAAS in 1992, the number of R&D projects pursued in cooperation with renowned national and international companies has almost doubled. One of the projects addressed the development of a lightweight roller made of carbon fiber reinforced plastics. Here, the aim was to reduce the energy consumption of the drive motor by minimizing the weight of the roller, while given stress constraints had be to obeyed. This project was jointly directed by a local company, Leonard Breitenbach GmbH, and the Ministry of Economics and Technology of North-Rhine Westphalia, Dusseldorf 18. In cooperation with ABB Research Center, Baden-Da¨ttwil, Switzerland, we developed a concept for the optimal shape of spacers in gas-insulated switchgears of transformer plants 19. Finally, FOMAAS received a large scale research assignment by the rail vehicle manufacturer Adtranz (now part of Bombardier Transportation), Siegen/Netphen to develop Computer-based Multidisciplinary Simulation and Optimization Procedures in Rail Vehicle Design. In the first place, this project focused on the optimal layout of bogie frames subjected to stochastic loads with respect to fatigue life and system behavior. It should be mentioned at this point that three doctoral theses were completed under my supervision in the scope of this project 20. The last named activities found a logical continuation in a new project, Nonlinear Fatigue Life Assessment of Structures and their Optimization in Automotive Design, granted in the scope of the FORD University Research Program (URP) Award, funded by Ford Motor Company 21. I received the URP Award for my working group at FOMAAS in the year 2000 21. The results gained from my research activities can be summarized as follows: It is important to mention that all of the above mentioned projects have also found their way into the academic teaching in lectures and seminars in order to acquaint our students with the impact and necessity of the fundamentals. Finally, I would like to mention some collaboration agreements with international institutions: The Institute for Computing Methods and Economization of the Hungarian Academy of Sciences, Budapest, Hungary (1983–88), the Faculte´ Polytechnique de Mons, Belgium (1984–87), the Institute of Fundamental Technological Research of the Polish Academy of Sciences, Warsaw, Poland (1984–85), the Design Productivity Center of the University of Missouri-Columbia, (1984–86), the University of Houston, Texas (1982–86), the Georgia Institute of Technology (GeorgiaTech), Atlanta, (1991–97), the University of Michigan, Ann Arbor, (1988–89), Pennsylvania State University, USA (1993–95), the University of Vancouver, British Columbia, Canada (1990–96), and Waseda University, Tokyo, Japan (1995). Several of my coworkers stayed at these institutions and some of them graduated as MSc. The variety of results obtained in the research projects is also reflected by a large number of events which I have organized together with my colleagues over the years (for a selection see Table 1) and to which I have actively contributed either by opening and/or principal lectures or by organizing individual sessions. In addition, I was involved, as Cochair Europe, in the preparation and organization of numerous ASME Design Automation Conferences (eg, Albuquerque, Minneapolis, Boston, Irvine, Sacramento). At the end of this overview, I would like to mention that, during my professorship at the University of Siegen, about 25 doctoral dissertations devoted to the topic of structural optimization were completed under my supervision. In addition, I was asked to act as external reviewer in the scope of 11 doctoral exams at universities in Germany and abroad. The emerging theses addressed fundamental subjects of structural optimization (deterministic and stochastic vector optimization, multilevel optimization, decomposition strategies, shape and topology optimization, components made of composite materials, of brittle materials, of viscoelastic materials, optimum layout of damping layers for vibration reduction). In most cases, these theses dealt with practice-relevant applications. At this point, I would like to take the opportunity to again express my gratitude to all coworkers for their dedicated work. Finally, it shall not be left unmentioned that several of the dissertations have received renowned awards. Finally, I would like to take the opportunity to express my cordial gratitude to my wife Gerda, who not only gave valuable advice throughout the years, but who also endured the manifold privation with great endurance.