Workshop on Engineering Optimization 2019

9.00-9.10

Opening

9.10-9.50

150 years history of topology optimization

Abstract: It is widely known in topology optimization that the first publication is the paper of Michell in 1904. The reality is that he generalized Maxwell's work published in 1870. Also there are significant papers on the optimality criteria method what are fundamental starting point of this research field. Wasiutyński [1] formulated first in 1939 the minimum-potential criterion what plays primary importance in this field. The optimization community has almost no knowledge about the publications in topology optimization at the 50s of the past century. At this time at the Cambridge University a group of researcher (Foulkes, Cox, Hemp) published significant results what are generally not known. The design was elaborated in elastic or plastic ways and the optimized structures were trusses at the early period although this object was called frame structure. The classical solutions of the different type of plate or shell problems can be followed by the works of Mróz, Prager, Shield.
This state of art presentation will overview in detailed these "hidden" results after Hemp [2]. The following parts will be presented:
A: the minimum-potential criterion of Wasiutyński,
B: basic elements of topology optimization:
1. one can see what kind of results of Maxwell were published and generalized;
2.what types of developments were elaborated in 2D. Lines of principal strains. Conditions of Equilibrium. Special solutions.
3.Michell type theorem for plates and developments. Constant stress solutions. Alternative approaches.
C: The period of 1970-2000 is also covered by the use of the selected works of Prager, Rozvany, Taylor, Kikuchi, Bendsoe, Olhoff.
This lecture will overview these almost forgotten results and put an end to have no information about the developments in topology optimization.

References
[1] Z. Wasiutyński, Strength design. Part I: Methods of strength design. Part II: Design for minimum potential. Part III: On the design of I-beams, Akademia Nauk Technicznych, Warsaw, 1939.
[2] W. S. Hemp, Theory of Structural Design, NATO Studies, Report No. 214, Paris, 1958.n

9.50-10.10

On optimal topology design of thermomechanical actuators

Abstract: The actuator action is aimed to maximize displacement in a prescribed direction on its boundary due to thermal excitation inducing initial strain and related stress fields. The mechanical stress and strain fields satisfy the linear elasticity relations, equilibrium and geometric compatibility conditions. The steady state temperature field satisfies the heat conduction equations and boundary conditions. The thermal field is not coupled with the mechanical field, but the stress and strain fields are dependent on the thermal strain induced by boundary or distributed heat sources.
Two cases are considered, namely
1. The control point on the actuator boundary is free of mechanical loading.
2. The actuator interacts with an adjacent structure with the contact force proportional to normal displacement component.
In the first case the optimal structure exhibits maximal rotation of its elements connected by hinges to a continuum structure. In the second case the microstructure evolution depends on the stiffness ratio of the interacting body and the actuator, tending to a Michell type structure for high stiffness ratio. The illustrative numerical examples for two cases are presented.

References
[1] S.M. Giusti, Z. Mróz, A. A. Novotny, J. Sokolowski, Topology design of thermomechanical actuators, Structural and Multidisciplinary Optimization, 55, 1575-1587, 2017.
[2] S.M. Giusti, Z. Mróz, A. A. Novotny, J. Sokolowski, Topology design of thermomechanical actuators combined with heat source optimization, Journal of Functional Analysis and Applications, 2019 (in print).

10.10-10.30

Applications of Michell's Theory in Design of High-rise Buildings, Large-scale Roofs and Long-span bridges

Abstract: The theory of Michell's structures reveals how to optimally transmit the given external load to a given support and how to optimally transmit the given system of self-equilibrated loads. In Michell's structures bending is totally eliminated, while single members are fully stressed by tensile and compressive forces. As a result, the structure is perfectly suited to applied external loading and has minimal possible weight. Since this remarkable idea has been proposed by A.G.M. Michell in 1904 [1] many specific analytical and numerical solutions corresponding to various loads and boundary conditions have been derived [2]. These solutions did not remain only the theoretical concepts but also have inspired civil and mechanical engineers and have influenced selected contemporary designs of high-rise building, large-scale roofs and long-span bridges.
The objective of this contribution is to present and critically analyze practical applications of Michell's theory in civil engineering. The first part of the talk will present the concepts of Michell-inspired "wingy" and "bulbous" skyscrapers proposed by Polish architects Wacław Zalewski and Wojciech Zabłocki as well as selected buildings constructed by international architectural office Skidmore, Owings and Merill. Further, constructions of the large-scale coverings of two famous Polish commercial buildings, Supersam in Warsaw and Spodek in Katowice, will be analyzed in order to reveal applied by their designers combination of tensegrity principle and Michell's theory resulting in ingenious interplay of compressive and tensile forces. In the last part of the presentation, the theoretical layouts of Michell's structures created over multiple spans [3] and recent numerical solutions of topology optimization problems related to bridge design [4] will be compared against selected existing constructions of long-span cable-stayed bridges, suspension bridges and arch bridges.

References
[1] A.G.M. Michell, 1904, The limits of economy of material in frame structures, Philosophical Magazine, Vol. 8, No. 47, pp. 589-597.
[2] T. Lewiński, T. Sokół, C. Graczykowski, Michell Structures, Springer, 2019, ISBN 978-3-319-95179-9.
[3] A.V. Pichugin, A. Tyas, M. Gilbert, L. He, 2005, Optimum structure for a uniform load over multiple spans, Structural and Multidisciplinary Optimization, Vol. 52, pp. 1041-1050
[4] H.E. Fairclough, M. Gilbert, A.V. Pichugin, A. Tyas, I. Firth, 2018, Theoretically optimal forms for very long-span bridges under gravity loading, Proceedings of the Royal Society: Part A, Vol. 474: 20170726.

10.30-10.40

Coffee break

10:40-11:20

Interior Point Methods for Large Scale Optimization

Abstract: In this talk I will discuss an impact made by interior point methods (IPMs) for optimization. IPMs deliver efficient and reliable solution techniques for linear, quadratic, nonlinear, second-order cone and semidefinite programming problems and excel when dimensions of problems are large [1,2]. They also provide an inspiration for a design of more general schemes for solving other classes of optimization problems by using an inexact Newton method embedded into a continuation scheme.
IPMs have been aplied to solve a plethora of engineering applications. In this talk I will briefly mention two of them:
(i) Sparse approximations arising when solving inverse problems in signal/image processing [3,4]; and
(ii) Truss layout optimization problems arising in structural optimization [5], including cases when a global stability of the truss structure is taken into account [6].

References:
[1] J. Gondzio, Interior point methods 25 years later, European Journal of Operational Research 218 (2012) pp. 587--601. DOI: 10.1016/j.ejor.2011.09.017
[2] J. Gondzio, Convergence analysis of an inexact feasible interior point method for convex quadratic programming, SIAM Journal on Optimization 23 (2013) No 3, pp. 1510--1527. DOI: 10.1137/120886017
[3] I. Dassios, K. Fountoulakis and J. Gondzio, A preconditioner for a primal-dual Newton conjugate gradients method for compressed sensing problems, SIAM Journal on Scientific Computing 37 (2015) pp. A2783-A2812. DOI: 10.1137/141002062
[4] K. Fountoulakis and J. Gondzio, A second-order method for strongly convex L1-regularization problems, Mathematical Programming 156 (2016), pp. 189--219. DOI: 10.1007/s10107-015-0875-4
[5] A.G. Weldeyesus and J. Gondzio, A specialized primal-dual interior point method for the plastic truss layout optimization, Computational Optimization and Applications 71 (2018) pp. 613--640. https://doi.org/10.1007/s10589-018-0028-9
[6] A. G. Weldeyesus, J. Gondzio, L. He, M. Gilbert, P. Shepherd and A. Tyas, Using member adding technique to solve truss layout optimization problems with constraints on global stability, Structural Modelling and Optimization (online 15 June 2019). https://doi.org/10.1007/s00158-019-02312-9

11.20-11.40

Selected applications of computational intelligence methods to optimization in architecture

Abstract: Architecture is: Form and Function. This presentation shows several original optimization methods applied to these inseparable aspects of architecture:
The concept of Extremely Modular Systems (EMSs) [1] for creating free-form architectural objects with as few types of modules as possible is outlined and illustrated with several examples. There are four basic advantages of EMSs: i. Economical - as they are suitable for mass fabrication, thus lowering the cost so they can be broadly applied; ii. Functional - as they allow for reconfiguration, expansion, reduction, rapid deployment; iii. Robustness - since every module which failed can be easily replaced with an identical but functional one; iv. Scientific - as they are suitable for intelligent mathematical modeling. Such systems, however, have one major disadvantage - unintuitiveness. In other words, direct (manual) assembly is infeasible. The EMS optimization objectives are presented. Due to the modularity of the system the optimization is discrete and highly non-linear. Graph-theoretic and meta-heuristic methods for EMS optimization are presented.
A novel approach of multi-objective optimization of the architectural functional layout (FL) [2] of a single story family house considering position and orientation on site is presented.
FL is optimized for the following objectives: functionality (defined by users), insolation (calculated according to geographical conditions), outside view attractiveness (assessed on-site) and external noise (measured on-site) is presented. A case study on an existing site is presented. The output of this optimization is a set of room configurations with their locations and orientations on the site returned to the user for final selection.

References
[1] Zawidzki M., Discrete Optimization in Architecture - Extremely Modular Systems, SpringerBriefs in Architectural Design and Technology, Springer Singapore, 2017.
[2] Zawidzki M., Discrete Optimization in Architecture - Architectural & Urban Layout, SpringerBriefs in Architectural Design and Technology, Springer Singapore, 2016.

11.40-12.00

Size and shape design optimization of truss structures using the Jaya algorithm

12.00-13.00

Lunch break

13:00-13:40

Least Weight Trusses And Least Compliant Bodies. Optimal Layout Problems, Recovery Of Underlying Microstructure And First Steps Towards 3D Printing

Abstract: The problem of minimum compliance of trusses of given weight as well as the problem of minimum weight of trusses of a bounded stress are both unsolvable; to make them well posed one should admit infinite number of bars, see [1]. To have a better insight into the continuum solutions we should have at our disposal highly accurate numerical methods for truss optimization. The ground structure method is one of them. Its exposition is one of the aim of the paper.
The contemporary methods of 3D printing make it possible to produce structural elements of shapes and microstructural characteristics ideally suited for the predicted applications. The most essential criterion is to adjust the compliance to the predicted loading. The problem of minimization of the compliance of linear elastic structures may be solved by using the stress-based formulation which makes it possible to perform explicitly minimization over the design parameters (stiffnesses or elastic moduli) and reduce the problem to an auxiliary problem of mathematical structure of optimum transshipping. The latter problem involves a statically admissible stress field; the unknown stress field minimizes the given functional with the integrand expressed by a certain norm (or a gauge). Due to the linear growth of the functional of the auxiliary problem its minimizer vanishes on a sub-domain of the given design domain thus determining the place where the material (or the structural members) is not necessary. The optimal structure is formed in the effective domain of the minimizer. The above scheme applies both to the classical Michell problem (see Ch. 3-5 in Ref.[1]) as well as to the material optimization problems corresponding to designing: a) anisotropy(AMD), cubic symmetry (CMD), c) isotropy(IMD) with two independent moduli, d) Young's modulus design (YMD), see Ch. 7.2 in Ref.[1]. Extensions towards multi-load cases are possible, see Ref.[2]. The stress field being the mentioned minimizer determines the optimal moduli of anisotropy of the optimal structure, yet does not deliver any information on the underlying microstructure. The lecture will discuss the available methods of recovery of optimal isotropic and cubic microstructures with a special emphasis put on the auxetic microstructures, see Ref.[3].
The second part of the lecture concerns optimum design of roofs composed of arches subjected to transmissible vertical loads. The variational setting of the theory of Prager-Rozvany archgrids has been recently put forward in Ch.6 of Ref.[1]. The roofs are formed of arches going in two orthogonal directions. This setting will be extended and illustrated by new designs of optimal roofs spanned over non-convex and multi-connected domains. The designs will be compared with 3D Michell structures corresponding to transmissible loads, obtained with using new adaptive versions of the ground structure method.

References
[1] T. Lewiński, T. Sokół, C.Graczykowski. Michell Structures, Springer, Cham, 2019.
[2] S.Czarnecki and T.Lewiński. Pareto optimal design of non-homogeneous isotropic material properties for the multiple loading conditions, Physica Status Solidi B: Basic Solids State Physics. 254: 1600821, 2017.
[3] S. Czarnecki, T. Łukasiak, T. Lewiński. The isotropic and cubic material designs. Recovery of the underlying microstructures appearing in the least compliant continuum bodies, Materials, 10(10): 1137, 2017.

13.40-14.00

Exact analytical solution of Michell cantilever on circular support for unequal permissible stresses in tension and compression

Abstract: In his pioneering work, Michell (1904) derived optimality criteria of least-volume trusses and showed that the optimal truss is immersed in an appropriate field of virtual displacements. Michell started his investigation from Maxwell theorem (1870) and deduced that the layout of the optimal truss can be determined by solving the simplified problem with equal permissible stresses in tension and compression (σ_T=σ_C). This conclusion, however, is valid only for Maxwell class of problems, when all external loads together with reaction forces, if any, are known. Rozvany (1996) indicated that Michell's solution of his very first example, involving a point load and a circular support seems to be incorrect for σ_T≠σ_C and would need to be revised. The aim of the present study is to provide an exact analytical solution to this particular problem, which was possible to obtain using the adaptive ground structure method (Gilbert et al 2001, Sokół 2018).

References
Gilbert M, Tyas A (2003) Layout optimization of large-scale pin-jointed frames. Eng Comput 20:1044-1064
Maxwell C (1870) On Reciprocal Figures, Frames, and Diagrams of Forces. Edinb Roy Soc Proc 7:160
Michell AGM (1904) The limits of economy of material in frame-structures. Philos Mag 8:589-597
Rozvany GIN (1996) Some shortcomings in Michell's truss theory. Struct Optim 12:244-250
Sokół T (2018) On the numerical approximation of Michell trusses and the improved ground structure method. In: Schumacher A, Vietor T, Fiebig S, Bletzinger KU, Maute K (eds) Advances in Structural and Multidisciplinary Optimization. WCSMO 2017. Springer, pp:1411-1417.

14.00-14.20

Stress based methods in topology optimization: Isotropic Material Design and Young Modulus Design

14.20-14.30

Coffee break

14.30-15.10

Discrete Optimization of Grid Shield for Overhead Line Magnetic Field Mitigation

Volodymyr Grinchenko
Department of Physics and Technology of Magnetic Phenomena, State Institution "Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine", Kharkiv, Ukraine

Abstract: The residential epidemiological studies - carried out by the World Health Organization within the framework "The International EMF Project" - have identified a high risk of a power frequency magnetic field for human health [1]. This leads to modern world trends on stricter sanitary standards for the power frequency magnetic field. For example, the energy industry of Ukraine has received the reference level in 0.5 μT for living space [2]. The most intense power frequency magnetic field is provided by high-voltage overhead lines. As the power frequency magnetic field penetrates inside buildings with almost no attenuation [3], some measures to reduce it are to be taken.
Various types of passive loops and active loops are widely used to mitigate the overhead line magnetic field. Such loops are installed near overhead lines and consume relatively much electrical power. The other way of magnetic field mitigation is to use electromagnetic shields installed outside buildings. Traditionally such electromagnetic shields are made of conductive plates [4]. A novel approach to overhead line magnetic field mitigation based on the usage of a grid shield is proposed in [5]. The grid shield consists of a set of aluminium conductors connected in parallel. To increase shielding efficiency on edges of shields, the usage of the U-shaped grid shield is proposed in [6]. It is shown, that efficiencies of overhead line magnetic field reduction by the U-shaped grid shield and by the U-shaped electromagnetic shield are similar, if their quantities of metal are the same. Moreover, the usage the U-shaped grid shield with certain arms allows to reduce the quantity of metal by four times in comparison with the traditional plane electromagnetic shield.
The present work is devoted to the further increasing of the efficiency of U-shaped grid shields. The finite-element model is used for shielding efficiency analyses in [5]-[6]. It is not convenient to use it for shield structure optimization. So the semi-analytical model of the grid shield based on its equivalent circuit is developed in the present work. This allows to calculate currents induced in conductors of the shield and correspondently to calculate the distribution of shielded magnetic field. The magnetic field distributions for several types of grid shield are represented. They are compared with the results of numerical simulation for the verification of the semi-analytical model. In addition, a way of grid shield structure optimization is discussed.


References:
[1] The World Health Organization, The International EMF Project. [Online]. Available: http://www.who.int/peh-emf/project/en/, Accessed on Oct. 18, 2019.
[2] Electrical installation regulations. Kyiv, Ukraine: The Ministry of Energy and Coal Mining of Ukraine, 2017.
[3] V. Rozov and V. Grinchenko, Simulation and analysis of power frequency electromagnetic field in buildings closed to overhead lines, in Proc. 2017 IEEE 1st Ukraine Conf. Electrical and Computer Engineering, pp. 500-503.
[4] D. Bavastro, A. Canova, F. Freschi, L. Giaccone, and M. Manca, Magnetic field mitigation at power frequency: design principles and case studies, IEEE Trans. Ind. Appl., vol. 51, no. 3, pp. 2009-2016, 2015.
[5] V. Grinchenko, Mitigation of overhead line magnetic field by grid electromagnetic shield, in Proc. 2018 IEEE Ukraine Student, Young Professional and Women in Engineering Congr., pp. 74-77.
[6] V. Grinchenko and U. Pyrohova, Mitigation of overhead line magnetic field by U-shaped grid shield, in Proc. 2019 IEEE 2nd Ukraine Conf. Electrical and Computer Engineering, pp. 345-348.

15.10-15.50

Optimal Seismic Design of Thin-Walled Steel Tanks

Abstract: An optimization procedure for thin-walled cylindrical steel tanks under seismic loading is investigated in this study. Steel storage tanks are very vulnerable for seismic loading and their behaviour during strong seismic loads is very complex. The seismic response and the buckling of these tanks have been studied by many authors, both experimentally and numerically, but a unified optimum design procedure according to modern seismic codes is still missing. The main purpose of this study is an simple and direct seismic optimum design of steel tanks, avoiding complex methods such as finite or boundary elements. This purpose is attained using home-made software developed by the authors, where the optimal earthquake design satisfies the stability criteria and the provisions of both EC3 and EC8.

15.50-16.00

Coffee break

16.00-16.20

Parametric study on the variable Poisson's ratio

Abstract: The Poisson's ratio (Poisson, 1829) is one of the basic mechanical parameters for geomechanical calculations. When determining the various deformations and the associated tri- and biaxial stresses, the Poisson's ratio plays a very important role. Thus, knowing this material constant is very important for any geomechanical calculation. In rock mechanics, the Poisson's ratio, depending on the rock material, it can be considered constant, although it is not necessarily true. However, the determination of this value is not clear - highly depends on the in situ stress conditions, rock mass quality, stress or strain rate, among the others. Selecting the value of the Poisson's ratio for a rock, from the values-range (Gercek, 2007) set for that rock, is an almost random process, which can significantly affect the result of the calculation. This study presents a parametric study of changes in the value of the Poisson's ratio. It will be analyzed the influence of the confining pressure and the rock mass quality for the Poisson' rate. The Geological Strength Index (GSI) is used for describing the rock mass quality.
Key words: geomechanics, stress-state, Poisson's ratio, rock mass quality

References
[1] S. Poisson (1829), Mémoire sur l'équilibre et le mouvement des corps élastiques. Mem. de l'Acad. Paris, p. 8.
[2] H. Gercek (2007), Poisson's ratio values for rocks, International Journal of Rock Mechanics and Mining Sciences, Volume 44, Issue 1, 2007, Pages 1-13, ISSN 1365-1609, https://doi.org/10.1016/j.ijrmms.2006.04.011.

16.20-16.40

Optimization of sensor placement using continuous approaches

Abstract: The present study provides a comprehensive framework for sensor layout optimization aiming at accurate estimation of the modal coordinates coming from the structural response. The proposed procedure consists of two steps briefly described below. The first step is a selection of vibrational modes taking part in the motion of structures during their normal operation - in this case subjected to traveling load. Among these structures there are various types of bridges especially railway bridges. In the case of present study structural responses are obtained from rigorous finite element (FE) model of the bridge. The FE model is calibrated with measured response of real bridge located in Huta Zawadzka. The calibration process is based on the displacement signals of the bridge under the traveling load.
In the second step modes of interest are selected and a set of candidate sensor locations is proposed. It is a subset of all degrees of freedom (DOFs) of the FE model from which several locations are chosen as best possible locations for the displacement sensors. The above sensor placement problem is a combinatorial task. Many methods for solving such problems have been developed previously, but in the case of large scale structures they require tremendous computational effort. To reduce this effort the so-called convex relaxation is incorporated into optimization process. The technique consists in reformulation of combinatorial problem into continuous convex one [1]. Then, the convex relaxation is achieved by introducing the so-called sensor density function, which assigns a certain metric for individual candidate sensor location [2]. Next, the value of this function is optimized in such a way that it maximize determinant of the Fisher Information Matrix. It has been shown that above algorithm is very effective and is distributing a number of sensors in several iterations only.
Finally, it is worth noting that presented method can be used to distribute sensors for structural health monitoring [3]. Moreover, it can be also applied in modal control strategies in vibration suppression [4].

References
[1] S. P. Chepuri and G. Leus: Sensor Selection for Estimation, Filtering, and Detection. 2014 International Conference on Signal Processing and Communications (SPCOM), 2014.
[2] B. Błachowski, P. Tauzowski, A. Świercz and Ł. Jankowski: Topology optimization approach for dense sensor network distribution over large bridge structures. IX ECCOMAS Thematic Conference on Smart Structures and Materials, Paris, 2019.
[3] T.-H. Yi, H.-N. Li and C.-W. Wang: Multiaxial sensor placement optimization in structural health monitoring using distributed wolf algorithm. Structural Control and Health Monitoring, Vol. 23, No. 4, pp. 719-734, 2016.
[4] A. K. Belyaev, A. V. Fedotov, H. Irschik, M. Nader, V. A. Polyanskiy and N. A. Smirnova: Experimental study of local and modal approaches to active vibration control of elastic systems. Structural Control and Health Monitoring, Vol. 25, No. 2, p. e2105, 2018.

16.40-16.50

Closing discussion