Developed by Panagiotis Michalatos and Sawako Kaijima

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2 uct topostr Topostruct is a program for structural topology optimization. It s development was influenced by the ideas and methods discussed in the book Topology Optimization, Theory, Methods and Applications writen by M.P. Bendsoe and O. Sigmund. This software is intended primarily towards designers and non engineers that want to familiarize with topology optimization as well as develop thier intuition regrading the structural behaviour of materials. Topostruct supports both two and three dimensional models. The user will input the dimensions and resolution of an orthogonal region in space which will be assigned certain material density. Then the user must place different support conditions and applied loads within this region and finally run the optimizer which will yield a distribution of material that best meets these conditions. Developed by Panagiotis Michalatos and Sawako Kaijima sawapandesign@gmail.com

3 close maximize/restore minimize topostr uct centre view top bottom front back left right toggle perspective for time consuming processes a progress bar will appear. If it takes too long click on the skull icon to terminate the process without killing the programm. User Interface selected object properties main tabs toolbox button check button - unchecked number input main panel hide/show control group Basic Use 1. Select between 2d and 3d system 2. Set Dimensions and resolution of problem domain to desired values and press reset dimensions 3. Add at least one support region and one load region 4. Set target density to the desired fraction of material volume [ usually is good[ 5. Set Number of optimization steps 6. Press Opimize and wait drop down lists scrollbar min scrollbar value [editable] scrollbar max scrollbar toggle visibility button

4 2d system Software information and author details switch between 2d and 3d system Dimensions of problem domain resolution of domain along the x direction. The resolution of the Set dimensions to above numbers other directions will be decided Delete all finite elements whose based on this so that all finite density is less than the value of elements have equal sides. Setting this value too high will the iso contour scroll bar. It will completely remove elemens decreas eperformance signifficantly and may cause the application outside the contour so use only after a few initial optimization to run out of memory. A value of iterations to improve speed of about for 3d and 40 to subsequent steps 100 for 2d should be fine for most cases. Determines the number of iterations for the optimization process. default = 3 This value determines the fraction of material volume that must remain after optimization. default = [ ] The penalization factor determines how fast the optimizer converges to a Black and White solution. default = 3.0 Filtering Determines the number of smoothing steps and the strength of each step for every optimization iteration step. It is there to avoid the checker board effect but also can be used to affect the smoothness of the the final shape. factor that multiplies the self weight of the current system during analysis and optimization Optimize runs the optimizer module for the given parameters Reset all densities to a single value. Do the structural analysis of the current system with no optimization Smooth Current density distribution. Subdivide remaining elements. Pressing this button will double the resolution of the system. IT is intended to be used after a significant number of the initial elelements has been removerd by th Delete below threshold command in order to increase solution detail.

5 2d system Clear all support, load and density regions choose shape of next region to be added Add a support region. All nodes within this region will be fixed. Select the region to adjust fixing type. Add a load region. All nodes within this region will get this applied force. Select the region to adjust force direction and magnitude. Render the grid of finite elements. Useful in conjunction with animation of displacement to see the deformations of individual elements. Animate the model according to calculated displacements. At least one analysis or optimization iteration has to be done before this can show anything. Add a density region. All bricks and quads within this region will have their density fixed to a specific value and not get affected by optimization step. This is usefull for example in order to designate areas in the model that have to remain empty [density 0.0]. The optimized solution will try to by pass them. Scaling of animated deformation Show stress tensor eigenvectors Render stress lines. Integral curves of the stress principal direction vecor fields Choose property to visualize and color scheme Choose density level on which to calculate boundary of current solution. This value is also used for the Delete below threshold function. Apply this kernel to the current density distribution. In this way you can implement custom filters such as smoothing, directional smoothing, sharpening etc..

6 Software information and author details License agreement 3d system switch between 2d and 3d system Dimensions of problem domain Set dimensions to above numbers Delete all finite elements whose density is less than the value of the iso surface level scroll bar. It will completely remove elemens outside the contour so use only after a few initial optimization iterations to improve speed of subsequent steps Determines the number of iterations for the optimization process. default = 3 This value determines the fraction of material volume that must remain after optimization. default = [ ] The penalization factor determines how fast the optimizer converges to a Black and White solution. default = 3.0 Filtering Determines the number of smoothing steps and the strength of each step for every optimization iteration step. It is there to avoid the checker board effect but also can be used to affect the smoothness of the the final shape. factor that multiplies the self weight of the current system during analysis and optimization Optimize runs the optimizer module for the given parameters Reset all densities to a single value. Do the structural analysis of the current system with no optimization Smooth Current density distribution. resolution of domain along the x direction. The resolution of the other directions will be decided based on this so that all finite elements have equal sides. Setting this value too high will decreas eperformance signifficantly and may cause the application to run out of memory. A value of about for 3d and 40 to 100 for 2d should be fine for most cases. Subdivide remaining elements. Pressing this button will double the resolution of the system. IT is intended to be used after a significant number of the initial elelements has been removerd by th Delete below threshold command in order to increase solution detail.

7 3d system Clear all support, load and density regions choose shape of next region to be added Add a support region. All nodes within this region will be fixed. Select the region to adjust fixing type. Add a load region. All nodes within this region will get this applied force. Select the region to adjust force direction and magnitude. Render the grid of finite elements. Useful in conjunction with animation of displacement to see the deformations of individual elements. Animate the model according to calculated displacements. At least one analysis or optimization iteration has to be done before this can show anything. Add a density region. All bricks and quads within this region will have their density fixed to a specific value and not get affected by optimization step. This is usefull for example in order to designate areas in the model that have to remain empty [density 0.0]. The optimized solution will try to by pass them. Scaling of animated deformation Visualize the density field as volumetric fog Render iso surface of current density field at selected iso value. Choose density level on which to calculate boundary of current solution. This value is also used for the Delete below threshold function. controls the type of information visualized by the cross section in the scene. You can manipulate position and orientation of the cross section in the viewport