Interactive 2D TopOpt App

iOS: Direct AppStore link, Android: Google Play link, Windows(**): download, Mac OSX: download, Linux: download

A UserGuide with app description and tutorials can be downloaded from here.

The TopOpt App is an interactive topology optimization tool that solves the minimum compliance problem in 2D. The App allows the user to change loads, supports and the volume fraction on the fly, and watch the design evolve to a new optimum in real-time.

New features in version 2.4 (released March 25, 2014):

  • Performance improvement (iOS only)

Features introduced in the previous releases:

  • Export functionality - allows for easy 3D printing of the optimized structures.
  • Multiple load cases
  • Gravity loads
  • Passive elements (Prescribed solid or void regions)
  • Custom grid size
  • Scale loads
  • Pause/Resume Optimization
  • More streamlined user-interface
  • Decreased minimum stiffness resulting in better designs

The App is available for iOS and Android devices and can be downloaded from the Apple App store or Google Play. A web-version (PC and Mac) can be found here, and a Linux stand-alone version can be downloaded from here.

Details of the implementation can be found in [1] for which an uncorrected version can be downloaded from here.

The App is developed using the multiplatform game engine Unity3D for interactive features and graphics. Unity3D supports the C# language and the TopOpt kernel is therefore written solely in C#. The TopOpt kernel uses the density approach [2], or the SIMP method, for design interpolation, and solves the minimization problem by an optimality criterion as given in [2,5,6]. To obtain a fine design representation, the multiresolution (MTOP) approach presented in [3] is used. This means that each physical element contains four design variables. Finally, the design is projected onto a two times finer mesh, where a heaviside projection is applied to render the material boundaries more sharply black and white. The elasticity problem is solved using 4-node finite elements [4] and the linear system is solved by a direct solver.

The TopOpt App has been developed as part of the NextTop project funded by the Villum Foundation.


[1] N. Aage, M.N. Jørgensen, C.S. Andreasen and O. Sigmund. Interactive topology optimization on hand-held devices, Struct Multidisc Optim, Vol. 47, No. 1, 2013, p. 1-6.

[2] M.P. Bendsøe and O. Sigmund. Topology Optimization; Theory, Methods and Applications. Springer Verlag Berlin Heidelberg New York, 2nd edition, 2004.

[3] T. H. Nguyen, G. H. Paulino, J. Song, and C. H. Le. A computational paradigm for multiresolution topology optimization (mtop). Struct Multidisc Optim, 41:525–539, 2010.
[4] O. C. Zienkiewicz and R. L. Taylor. Finite Element Method: (parts 1-3). Butterworth-Heinemann, fifth edition, 2000.

[5] O. Sigmund. A 99 line topology optimization code written in MATLAB, Struct Multidisc Optim, 21(2):120-127, 2001.

[6] E. Andreassen, A. Clausen, M. Schevenels, B. S. Lazarov and O. Sigmund. Efficient topology optimization in MATLAB using 88 lines of code, Struct Multidisc Optim,43:1-16, 2010. 

(**) Windows requires you to have the newest Visual C++ Redistributables installed. So please download and install the 64-bit versions of the VC++R2012 and VC++R2013 from Microsofts website.

Updated for windows users: If the app starts but no design is shown, this might be a problem with the ACML library and your windows. Download an alternative build from here.
17 JANUARY 2019