Our publications

2019: Weider, K.; Schumacher, A.
Adjoint method for Topological Derivatives for optimization tasks with material and geometrical nonlinearities
In Rodrigues, H. C. and Herskovits, J. and Mota Soares, C. M. and Araújo, A. L. and Guedes, J. M. and Folgado, J. O. and Moleiro, F. and Madeira, J. F. A., Editor, EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization
Page 867--878
Publisher: Springer International Publishing, Cham
2019
867--878
DOI: 10.1007/978-3-319-97773-7_75
ISBN: 978-3-319-97772-0; Dienemann, R.; Schumacher, A.; Fiebig, S.
Considering linear buckling for 3D density based topology optimization
In Rodrigues, H. C. and Herskovits, J. and Mota Soares, C. M. and Araújo, A. L. and Guedes, J. M. and Folgado, J. O. and Moleiro, F. and Madeira, J. F. A., Editor, EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization
Page 394--406
Publisher: Springer International Publishing, Cham
2019
394--406
DOI: 10.1007/978-3-319-97773-7_36
ISBN: 978-3-319-97772-0
2018: Weider, K.; Schumacher, A.
A topology optimization scheme for crash loaded structures using Topological Derivatives
In Schumacher, A. and Vietor, T. and Fiebig, S. and Bletzinger, K.-U. and Maute, K., Editor, Advances in Structural and Multidisciplinary Optimization from Springer eBook Collection Engineering
Page 1601--1614
Publisher: Springer, Cham
2018
1601--1614
DOI: 10.1007/978-3-319-67988-4_120
ISBN: 978-3-319-67988-4; Schneider, D.; Schumacher, A.
Finding Optimized Layouts for Ribs on Surfaces Using the Graph and Heuristic Based Topology Optimization
In Schumacher, A. and Vietor, T. and Fiebig, S. and Bletzinger, K.-U. and Maute, K., Editor, Advances in Structural and Multidisciplinary Optimization from Springer eBook Collection Engineering
Page 1615--1628
Publisher: Springer, Cham
2018
1615--1628
DOI: 10.1007/978-3-319-67988-4_121
ISBN: 978-3-319-67988-4; Walser, A.F.; Schumacher, A.; Singh, H.; Schöne, C.; Benito-Cia, L.
Verschachtelte Optimierung des Crashverhaltens von Fahrzeugen mit automatisch erzeugten und bewerteten Submodellen
19. VDI-Kongress SIMVEC
2018
DOI: 10.51202/9783181023334-47; Schumacher, A.
Robust Design through Numerical Analysis - Research State of the Art
Automotive CAE Grand Challenge 2018
2018; Klinke, N.; Schumacher, A.
Parameterization setup for metamodel based optimizations of Tailor Rolled Blanks
In Schumacher, A. and Vietor, T. and Fiebig, S. and Bletzinger, K.-U. and Maute, K., Editor, Advances in Structural and Multidisciplinary Optimization from Springer eBook Collection Engineering
Page 1833--1850
Publisher: Springer, Cham
2018
1833--1850
DOI: 10.1007/978-3-319-67988-4_137
ISBN: 978-3-319-67988-4; Schumacher, A.
On the current need of Expert Rules for the Topology Optimization of Structures with Non-Linear Behaviors
Proceeding of the 13th World Congress on Computational Mechanics (WCCM XIII) and 2nd Pan American Congress on Computational Mechanics (PANACM II)
2018; Schneider, D.; Link, S.; Schumacher, A.; Ortmann, C.
Graph and Heuristic Based Topology Optimization of Crashworthiness Composite Profile Structures Manufactured by Vacuum Infusion and Gluing
Proceeding of the 13th World Congress on Computational Mechanics (WCCM XIII) and 2nd Pan American Congress on Computational Mechanics (PANACM II)
2018; Schumacher, A.
Einsatz der Strukturoptimierung zum Finden neuer Leichtbaustrukturen
Leichtbaugipfel 2018
2018; Beyer, F.; Schumacher, A.; Baumgart, C.
Einsatz der Graphen- und Heuristikbasierten Topologieoptimierung für den Entwurf einer pulvermetallurgisch herstellbaren, doppelsymmetrischen Crashzelle
9. Freiberger Crashworkshops
2018; Weider, K.; Schumacher, A.
Efficient analysis of topological sensitivities for crash problems using LS-Dyna implicit
15. LS-DYNA-Forum
2018; Diez, C.; Kunze, P.; Toewe, D.; Wieser, C.; Harzheim, L.
Big-Data based rule-finding for analysis of crash simulations
In Schumacher, A. and Vietor, T. and Fiebig, S. and Bletzinger, K.-U. and Maute, K., Editor, Advances in Structural and Multidisciplinary Optimization from Springer eBook Collection Engineering
Page 396--410
Publisher: Springer, Cham
2018
396--410
DOI: 10.1007/978-3-319-67988-4_31
ISBN: 978-3-319-67988-4; Falconi, C.; Walser, A.F.; Singh, H.; Schumacher, A.
Automatic generation, validation and correlation of the submodels for the use in the Optimization of crashworthy structures
In Schumacher, A. and Vietor, T. and Fiebig, S. and Bletzinger, K.-U. and Maute, K., Editor, Advances in Structural and Multidisciplinary Optimization from Springer eBook Collection Engineering
Page 1558--1571
Publisher: Springer, Cham
2018
1558--1571
DOI: 10.1007/978-3-319-67988-4_117
ISBN: 978-3-319-67988-4; Ramsaier, M.; Stetter, R.; Till, M.; Rudolph, S.
Automatic Definition of density-driven Topology Optimization with graph-based Design Languages
In Schumacher, A. and Vietor, T. and Fiebig, S. and Bletzinger, K.-U. and Maute, K., Editor, Advances in Structural and Multidisciplinary Optimization from Springer eBook Collection Engineering
Page 1168--1184
Publisher: Springer, Cham
2018
1168--1184
DOI: 10.1007/978-3-319-67988-4_88
ISBN: 978-3-319-67988-4; Dienemann, R.; Schumacher, A.; Fiebig, S.
An Element Deactivation and Reactivation Scheme for the Topology Optimization based on the Density Method
In Schumacher, A. and Vietor, T. and Fiebig, S. and Bletzinger, K.-U. and Maute, K., Editor, Advances in Structural and Multidisciplinary Optimization from Springer eBook Collection Engineering
Page 1127--1142
Publisher: Springer, Cham
2018
1127--1142
DOI: 10.1007/978-3-319-67988-4_85
ISBN: 978-3-319-67988-4; Advances in Structural and Multidisciplinary Optimization: Proceedings of the 12th World Congress of Structural and Multidisciplinary Optimization (WCSMO12)
In Schumacher, A. and Vietor, T. and Fiebig, S. and Bletzinger, K.-U. and Maute, K., Editor from Springer eBook Collection Engineering
Publisher: Springer, Cham
2018
DOI: 10.1007/978-3-319-67988-4
ISBN: 978-3-319-67988-4
2017: Dienemann, R.; Schumacher, A.; Fiebig, S.
Topology optimization for finding shell structures manufactured by deep drawing
Structural and Multidisciplinary Optimization, 56 (2) :473--485
2017
ISSN: 1615-147X
DOI: 10.1007/s00158-017-1661-0; Srinivasan, M.; Maettig, P.; Glitza, K. W.; Sanny, B.; Schumacher, A.; Duhovic, M.
Validation of Numerical Modeling for the Prediction of Elastic and Failure Behavior of Diamond Powder Filled Woven Composites
Open Journal of Composite Materials, 07 (02) :63--84
2017
DOI: 10.4236/ojcm.2017.72004; Weider, K.; Marschner, A.; Schumacher, A.
A Systematic Study on Topology Optimization of Crash Loaded Structures using LS-TaSC
11th European LS-DYNA Conference
2017; Singh, H.; Schumacher, A.; Falconi, C.; Walser, A.F.; Trentmann, S.; Benito-Cia, L.; Foussette, C.; Krause, P.
Hierarchical Multi-Level-Optimization of crashworthy structures using automatic generated submodels
11th European LS-DYNA Conference
2017; Schumacher, A.
Topology Optimization for finding best component layouts - Research State of the Art
Automotive CAE Grand Challenge 2017
2017; Schumacher, A.; Singh, H.; Falconi, C.
Möglichkeiten der Entwicklung von Fahrzeugkomponenten mit optimierten Submodellen
VDI-Konferenz „Cabriolets“
2017; Schumacher, A.
Aktuelle Möglichkeiten und Grenzen der Topologieoptimierung mechanischer Strukturen
27. Ansys User Club (AUC)-Workshop
2017
2016: Dienemann, R.; Schumacher, A.
An efficient optimization method for mechanical shells considering cut--outs
PAMM · Proc. Appl. Math. Mech., 16 (1) :713--714
2016
DOI: 10.1002/pamm.201610345; Diez, C.; Harzheim, L.; Schumacher, A.
Effiziente Wissensgenerierung zur Robustheitsuntersuchung von Fahrzeugstrukturen mittels Modellreduktion und Ähnlichkeitsanalyse
SIMVEC Simulation und Erprobung in der Fahrzeugentwicklung 2016
Publisher: VDI Verlag
2016
DOI: 10.51202/9783181022795-137
ISBN: 9783181022795; Klinke, N.; Schumacher, A.
Finding the best thickness run parameterization for optimization of Tailor Rolled Blanks
14. LS-DYNA Forum
2016; Schumacher, A.
Flexible design models for finding best vehicle concepts
Automotive CAE Grand Challenge 2016
2016; Link, S.; Singh, H.; Schumacher, A.
Influence of submodel size and evaluated functions on the optimization process of crashworthiness structures
14. LS-DYNA Forum
2016; Weider, K.; Schumacher, A.
On the calculation of Topological Derivatives considering an exemplary nonlinear material model
PAMM · Proc. Appl. Math. Mech., 16 (1) :717--718
2016
DOI: 10.1002/pamm.201610347; Srinivasan, M.; Maettig, P.; Glitza, K. W.; Sanny, B.; Schumacher, A.; Duhovic, M.; Schuster, J.
Out of Plane Thermal Conductivity of Carbon Fiber Reinforced Composite Filled with Diamond Powder
Open Journal of Composite Materials, 06 (02) :41--57
2016
DOI: 10.4236/ojcm.2016.62005; Schumacher, A.
Topologieoptimierung von Crashstrukturen mit mathematischen Verfahren, Heuristiken und Submodelltechniken
7. Freiberger Crashworkshop
2016; Dienemann, R.; Schumacher, A.; Fiebig, S.
Topology and shape optimization of sheet metals with integrated deep-drawing-simulation
12th World Congress on Computational Mechanics (WCCM XI)
2016; Hafsa, S.; Schumacher, A.
Topology optimization method for the adaptation of existing structures to new requirements, thru addition of framework structures
12th World Congress on Computational Mechanics (WCCM XI)
2016
2015: Maurer, S.A.; Hager, P.; Schmidt, S.; Schumacher, A.
Verschleißreduktion an Umlenkungen in Leichtmetallgussbauteilen durch numerische Formoptimierung
Gießerei, 102 (102)
2015; Dienemann, R.; Schumacher, A.; Fiebig, S.
Topology optimization considering the requirements of deep-drawn sheet metals
11th World Congress on Structural and Multidisciplinary Optimisation
2015; Schumacher, A.
Leichtbau und Crashsicherheit: Aktuelle Forschungsfelder und Entwicklungsmethoden
Frühjahrseminars der Gesellschaft für Ursachenforschung bei Verkehrsunfällen
2015; Schumacher, A.; Riad, A.; Sauder, C.; Szabo, A.
Leichtbaukonzepte für eine Cabrio-Karosserie - Systematische Strukturuntersuchung ausgehend von eine Limousine
VDI-Konferenz „Cabriolets"
2015; Ortmann, C.; Schumacher, A.
Graphen- und Heuristikbasierte Topologieoptimierung (GHT) von Profilquerschnitten für Crashlastfälle
Zeitschrift für numerische Simulationsmethoden und angrenzende Gebiete (35)
2015; Walser, A.F.; Schumacher, A.
Gemeinsam zur Erfolg
Digital Engineering Magazin (35) :32--34
2015; Fiebig, S.; Sellschopp, J.; Manz, H.; Vietor, T.; Axmann, J.K.; Schumacher, A.
Future tracks for structural optimization for the industrial usage
11th World Congress on Structural and Multidisciplinary Optimisation
2015; Schumacher, A.; Ortmann, C.
Combining state of the art meta-models for predicting the behavior of non-linear crashworthiness structures for shape and sizing optimizations
11th World Congress on Structural and Multidisciplinary Optimisation, Page 477--482
2015; Ortmann, C.; Schumacher, A.
Graph and Heuristic Based Topology Optimization in consideration of the disciplines crash and statics
Proceedings of the NAFEMS Seminar,3 "Optimization and Robust Design"
2015
2014: Schumacher, A.; Hakim, K.
Mathematische Optimierung von Bauteilen mit hochgradig nicht-linearen Eigenschaften
Forschungsreport für den Maschinenbau in Nordrhein-Westfalen
2014; Schumacher, A.
Structural Optimization Background: Chapter 24
In diverse, Editor, Practical Aspects of structural optimization -- A Study Guide
2014; Srinivasan, M.; Maettig, P.; Glitza, K. W.; Sanny, B.; Schumacher, A.
Multiscale calculation for increasing the thermal conductivity of carbon fiber composite with diamond powder
Proceedings of XLI International Summer School-Conference, Page 481--490
2014
DOI: 10.13140/RG.2.1.5035.8169; Ortmann, C.; Schumacher, A.
Meta-models in structural optimization - techniques and strategies
Proceeding of the Automotive CAE Grand Challenge 2014
2014; Ortmann, C.; Schumacher, A.
Mathematical Description and Algorithmization of Expert Knowledge for the Support of the Topology Optimization of Crashworthiness Structures
PAMM · Proc. Appl. Math. Mech., 14 (1) :1023--1026
2014
DOI: 10.1002/pamm.201410488; Schumacher, A.
Integration verfeinerter Materialmodelle in Form- und Topologieoptimierungsverfahren von Bauteilen
Umdruck des DVM-Workshops 2014
2014; Lochner, I.; Schumacher, A.
Homogenization method: Distribution of material densities
In Adriaenssens, S. and Block, P. and Veenendaal, D. and Williams, C., Editor, Shell structures for architecture
Publisher: Routledge/ Taylor & Francis Group, London and New York
2014
DOI: 10.4324/9781315849270
ISBN: 978-0-415-84060-6

Book: Optimization of mechanical structures 3rd edition

3rd edition of the book "Optimization of mechanical structures" published by Springer-Verlag in autumn 2020

The aim of the book is to impart the necessary knowledge for the efficient use of mathematical optimization methods in the design and structural layout of components.

It also provides the essential basics for computer-aided design and calculation.

The author includes the latest developments and areas of application in the field of optimization and discusses the advantages and disadvantages of the various optimization approaches. The concrete applications of optimization presented facilitate familiarization with this mathematically demanding field. With the help of the exercises provided, the reader can consolidate what they have learned on their own computer.

In the current 3rd edition, explanations have been revised and current optimization algorithms and methods have been included.

Link to the book