Enforcing a force-displacement curve of a nonlinear structure using topology optimization with slope constraints

Lee, Jongsuh; Detroux, Thibaut; Kerschen, Gaëtan

doi:10.3390/APP10082676

Request a copy

Article (Scientific journals)

Enforcing a force-displacement curve of a nonlinear structure using topology optimization with slope constraints

Lee, Jongsuh; Detroux, Thibaut; Kerschen, Gaëtan

2020 • In Applied Sciences, 10 (8), p. 2676

Peer Reviewed verified by ORBi

Permalink
https://hdl.handle.net/2268/323303

DOI
10.3390/APP10082676

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

111_appsc_2020.pdf

Author postprint (6.16 MB)

Request a copy

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

Force-displacement curve; Hardening and softening nonlinearities

Abstract :

[en] The objective of this study is to develop an optimization methodology to find a layout that traces a prescribed force-displacement curve through a topology optimization approach. To this end, we propose an objective function to minimize the difference between a prescribed force-displacement curve and the curve calculated at each iteration of the optimization process. Slope constraints are introduced to solve issues encountered when using a small number of target points. In addition, a projection filter is employed to suppress the gray region observed between the solid and void regions, which generally occurs when using a density-based filter. A recently proposed energy interpolation scheme is implemented to stabilize the instability in the nonlinear analysis, which generally results from excessive distortion in the void region when the structure is modeled on a fixed mesh in the topology optimization process. To validate the outlined methodology, several case studies with different types of nonlinearity and structural features of the obtained layouts are investigated.

Disciplines :

Mechanical engineering

Author, co-author :

Lee, Jongsuh ; Department of Mechanical Engineering, Dong-A University, Busan, South Korea

Detroux, Thibaut ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Kerschen, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Language :

English

Title :

Enforcing a force-displacement curve of a nonlinear structure using topology optimization with slope constraints

Publication date :

April 2020

Journal title :

Applied Sciences

eISSN :

2076-3417

Publisher :

MDPI AG

Volume :

Issue :

Pages :

2676

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://www.mdpi.com/2076-3417/10/8/2676/pdf

Funding text :

This research received no external funding. This work was supported by the Dong-A University research fund.

Available on ORBi :

since 11 October 2024

Statistics

Number of views

6 (0 by ULiège)

Number of downloads

0 (0 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

Bathe, K.J.; Bolourchi, S. A geometric and material nonlinear plate and shell element. Comput. Struct. 1980, 11, 23-48.
Reddy, J.N. An Introduction to Nonlinear Finite Element Analysis; Oxford University Press: New York, NY, USA, 2004.
Reddy, J.N. Theory and Analysis of Elastic Plates and Shells, 2nd ed.; CRC Press: New York, NY, USA, 2007.
Bendsøe, M.P.; Kikuchi, N. Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 1988, 71, 197-224.
Buhl, T.; Pedersen, C.; Sigmund, O. Stiffness design of geometrically nonlinear structures using topology optimization. Struct. Multidiscip. Optim. 2000, 19, 93-104.
Wang, F.; Sigmund, O.; Jensen, J. Design of materials with prescribed nonlinear properties. J. Mech. Phys. Solids 2014, 67, 156-174.
Jansen, M.; Lombaert, G.; Schevenels, M. Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis. Comput. Methods Appl. Mech. Eng. 2015, 285, 452-467.
Luo, Y.; Wang, Y.M.; Kang, Z. Topology optimization of geometrically nonlinear structures based on an additive hyperelasticity technique. Comput. Methods Appl. Mech. Eng. 2015, 286, 422-441.
Sekimoto, T.; Noguchi, H. Homologous topology optimization in large displacement and buckling problems. JSME Int. J. Ser. A Solid Mech. Mater. Eng. 2001, 44, 616-622.
Bruns, T.E.; Sigmund, O.; Tortorelli, D.A. Numerical methods for the topology optimization of structures that exhibit snap-through. Int. J. Numer. Methods Eng. 2001, 55, 1215-1237.
Bruns, T.E.; Sigmund, O. Toward the topology design of mechanisms that exhibit snap-through behavior. Comput. Methods Appl. Mech. Eng. 2004, 193, 3973-4000.
Yoon, G.; Noh, J.; Kim, Y. Topology optimization of geometrically nonlinear structures tracing given load-displacement curves. J. Mech. Mater. Struct. 2011, 6, 605-625.
Mathias, W.; Niklas, I.; Daniel, T. Stiffness optimization of nonlinear elastic structures. Comput. Methods Appl. Mech. Eng. 2018, 330, 292-307.
Gea, H.C.; Luo, J. Topology optimization of structures with geometrical nonlinearities. Comput. Struct. 2001, 79, 1977-1985.
Bruns, T.E.; Tortorelli, D.A. Topology optimization of nonlinear elastic structures and compliant mechanisms. Comput. Methods Appl. Mech. Eng. 2001, 190, 3443-3459.
Bruns, T.E.; Tortorelli, D.A. An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms. Int. J. Numer. Methods Eng. 2003, 57, 1413-1430.
Pedersen, C.B.W.; Buhl, T.; Sigmund, O. Topology synthesis of large-displacement compliant mechanisms. Int. J. Numer. Methods Eng. 2001, 50, 2683-2705.
Yoon, G.; Kim, Y. Element connectivity parameterization for topology optimization of geometrically nonlinear structures. Int. J. Solids Struct. 2005, 42, 1983-2009.
Wang, F.; Lazarov, B.S.; Sigmund, O.; Jensen, J.S. Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems. Comput. Methods Appl. Mech. Eng. 2014, 276, 453-472.
Sigmund, O. On the design of compliant mechanisms using topology optimization. Mech. Struct. Mach. 1997, 25, 493-524.
Jaafer, A.A.; Al-Bazoon, M.; Dawood, A.O. Structural Topology Design Optimization Using the Binary Bat Algorithm. Appl. Sci. 2020, 10, 1481.
Guest, J.K.; Prévost, J.H.; Belytschko, T. Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int. J. Numer. Methods Eng. 2004, 61, 238-254.
Sigmund, O. Manufacturing tolerant topology optimization. Acta Mech. Sin. 2009, 25, 227-239.
Xu, S.; Cai, Y.; Cheng, G. Volume preserving nonlinear density filter based on heaviside functions. Struct. Multidiscip. Optim. 2010, 41, 495-505.
Wang, F.; Lazarov, B.S.; Sigmund, O. On projection methods, convergence and robust formulations in topology optimization. Struct. Multidiscip. Optim. 2011, 43, 767-784.
Andreassen, E.; Clausen, A.; Schevenels, M.; Lazarov, B.S.; Sigmund, O. Effcient topology optimization in MATLAB using 88 lines of code. Struct. Multidiscip. Optim. 2011, 43, 1-16.
Borst, R.D.; Crisfield, M.A.; Remmers, J.J.C.; Verhoosel, C.V. Nonlinear Finite Element Analysis of Solids and Structures, 2nd ed.; A Jonhn Wiley & Sons, Ltd., Publication: Hoboken, NJ, USA, 2012.
Svanberg, K. The method of moving asymptotes-A new method for structural optimization. Int. J. Numer. Methods Eng. 1987, 24, 359-373.
Lazarov, B.S.; Schevenels, M.; Sigmun, O. Robust design of large-displacement comliant mechanisms. Mech. Sci. 2011, 2, 175-182.
Díaz, A.; Sigmund, O. Checkerboard patterns in layout optimization. Struct. Optim. 1995, 10, 40-45.
Sigmund, O.; Petersson, J. Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct. Optim. 1998, 16, 68-75.
Bourdin, B. Filters in topology optimization. Int. J. Numer. Methods Eng. 2001, 50, 2143-2158.
Bendsøe, M.P.; Sigmund, O. Material interpolation schemes in topology optimization. Arch. Appl. Mech. 1999, 69, 635-654.
Ribeiro, P.; Petyt, M. Multi modal geometrical nonlinear free vibration of fully clamped composite laminated plates. J. Sound Vib. 1999, 225, 127-152.
Rivin, E.I. Stiffness and Damping in Mechanical Design; Marcel Dekker, Inc.: New York, NY, USA, 1999.
Boehler, Q.; Vedrines, M.; Abdelaziz, S.; Poignet, P.; Renaud, P. Parallel singularities for the design of softening springs using compliant mechanisms. In Proceedings of the ASME 2015 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Boston, MA, USA, 2-5 August 2015.
Timoshenko, S. Theory of Elastic Stability; International Student Edition; McGraw-Hill: New York, NY, USA, 1936.
Allen, H.G.; Bulson, P.S. Background to Buckling; McGraw-Hill: London, UK, 1980.