Construction of Stable and Lightweight Technical Structures Inspired - PowerPoint PPT Presentation

Construction of Stable and Lightweight Technical Structures Inspired by Ossification of Bones using Osteogenetic P Systems ALEXANDER MELCHER ILIJA VUKOREP THOMAS HINZE

Bone formation and its use for technical structures

Ossification of Bones Osteoblasts Bone tissue Osteoclasts

Ossification of Bones

Idea and Approach of Articial Ossification 1 – Initial Structure 3 – Osteoblasts/-clasts 5 – Loop Start 7 - Elimination 9 – Static Calculation 11.1 – Filament 12 – Loop End Modification 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search 11.2 – Filament Output Analysis & Motion Out Out 11.1 11.1 3 9 11.2 12 1 5 6 7 8 10 2 4 11.2

Utilized Software HoopSnake - Yconst Grasshopper - Robert McNeel & Associates Rhinoceros 3D - Robert McNeel & Associates Karamba - Clemens Preisinger

Program Structure Out 11.1 11.2 12 9 3 1 5 6 7 8 10 11.2 2 4 11.1 Out 11.2 3 9 12 1 5 6 7 8 2 10 4 11.2

Program Structure - Detail

1 Initial Structure Generation 1 – Initial Structure 3 – Osteoblasts/-clasts 5 – Loop Start 7 - Elimination 9 – Static Calculation 11.1 – Filament 12 – Loop End Modification 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search 11.2 – Filament Output Analysis & Motion Out Out 11.1 11.1 3 9 11.2 12 1 5 6 7 8 10 2 4 11.2

1 Initial Structure Generation The technique of natural neighbour interpolation (Lloyd's algorithm) based on Voronoi diagrams is employed to create the initial filament structure.

1 Initial Structure Generation

2 Static Analysis 1 – Initial Structure 3 – Osteoblasts/-clasts 5 – Loop Start 7 - Elimination 9 – Static Calculation 11.1 – Filament 12 – Loop End Modification 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search 11.2 – Filament Output Analysis & Motion Out Out 11.1 11.1 3 9 11.2 12 1 5 6 7 8 10 2 4 11.2

2 Static Analysis At this point the forces affecting the structure are taken into consideration. In this case, all the upper nodes are affected by a vertical force and all lower nodes act as bearings.

3 Distribution of Osteoblasts and Osteoclasts 1 – Initial Structure 3 – Osteoblasts/-clasts 5 – Loop Start 7 - Elimination 9 – Static Calculation 11.1 – Filament 12 – Loop End Modification 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search 11.2 – Filament Output Analysis & Motion Out Out 11.1 11.1 3 9 11.2 12 1 5 6 7 8 10 2 4 11.2

3 Distribution of Osteoblasts and Osteoclasts Osteoblasts and Osteoclasts are being disturbed randomly throughout the initial bounding box of the structural element.

4 Filament Bounds 1 – Initial Structure 3 – Osteoblasts/-clasts 5 – Loop Start 7 - Elimination 9 – Static Calculation 11.1 – Filament 12 – Loop End Modification 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search 11.2 – Filament Output Analysis & Motion Out 11.1 3 9 11.2 12 1 5 6 7 8 10 2 4 11.2

4 Filament Bounds Defining the bounds of every filament is important for the following static calculations and the calculation of the motion direction for the Osteoblasts and Osteoclasts.

5 Start of the artificial Ossification 1 – Initial Structure 3 – Osteoblasts/-clasts 5 – Loop Start 7 - Elimination 9 – Static Calculation 11.1 – Filament 12 – Loop End Modification 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search 11.2 – Filament 11.2 – Filament Output Analysis & Motion Analysis Out Out 11.1 11.1 3 9 11.2 12 1 5 6 7 8 10 2 4 11.2

5 Start of the artificial Ossification All information generated during the step 1 to 4 are being used to initiate the artificial ossification. At this point indicators for the termination of the process can be taken into consideration.

6 Analysing the current Structure 1 – Initial Structure 3 – Osteoblasts/-clasts 5 – Loop Start 7 - Elimination 9 – Static Calculation 11.1 – Filament 12 – Loop End Modification 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search 11.2 – Filament Output Analysis & Motion Out 11.1 3 9 11.2 12 1 5 6 7 8 10 2 4 11.2

6 Analysing the current Structure At this point, the lists of all the Osteoblasts, Osteoclasts and filaments are being reorganized. Depending on if filaments were eliminated within the last cycle, the corresponding element of the static calculation is being deactivated.

7 Elimination of thin and „ dangling “ filaments 1 – Initial Structure 3 – Osteoblasts/-clasts 5 – Loop Start 7 - Elimination 9 – Static Calculation 11.1 – Filament 12 – Loop End Modification 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search 11.2 – Filament Output Analysis & Motion Out Out 11.1 11.1 3 9 11.2 12 1 5 6 7 8 10 2 4 11.2

7 Elimination of thin and „ dangling “ filaments Any filament which has gotten too thin and falls below a minimum threshold will be eliminated. Any “dangling” filaments will also be eliminated as they’re unable to contribute to the transmission of forces.

8 Simplification of connected filaments 1 – Initial Structure 3 – Osteoblasts/-clasts 5 – Loop Start 7 - Elimination 9 – Static Calculation 11.1 – Filament 12 – Loop End Modification 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search 11.2 – Filament Output Analysis & Motion Out 11.1 3 9 11.2 12 1 5 6 7 8 10 2 4 11.2

8 Simplification of connected filaments 2D reduction of two filaments Through elimination may occur a situation in which two or more filaments form corners which would disturb the transmission of forces and generate additional moments of force. In order to „smooth“ the corners the adjacent filaments are joined into one single 2D reduction multiple filaments 3D reduction three filaments filament.

9 Static Calculation of Force at the Filaments 1 – Initial Structure 3 – Osteoblasts/-clasts 5 – Loop Start 7 - Elimination 9 – Static Calculation 11.1 – Filament 12 – Loop End Modification 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search 11.2 – Filament Output Analysis & Motion Out Out 11.1 11.1 3 9 11.2 12 1 5 6 7 8 10 2 4 11.2

9 Static Calculation of Force at the Filaments The given external forces get diverted throughout the filaments and filamentary junctions inside the network towards the ground. Calculation of forces in the inner part of the network requires a strategy of successive determination from the nodes affected by external forces to adjacent filaments and junctions towards the nodes at the bottom. Mechanical force – side view

10 Osteoblasts/-clasts search for closest filament 1 – Initial Structure 3 – Osteoblasts/-clasts 5 – Loop Start 7 - Elimination 9 – Static Calculation 11.1 – Filament 12 – Loop End Modification 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search 11.2 – Filament Output Analysis & Motion Out 11.1 3 9 11.2 12 1 5 6 7 8 10 2 4 11.2

10 Osteoblasts/-clasts search for closest filament Each Osteablast and Osteoclasts searches for the closest filaments in their area of effect. This step is taken in order to optimize the following process of modifying the filaments and movement of the Osteoblasts and Osteoclasts.

11.1 Modification of the Filaments 1 – Initial Structure 3 – Osteoblasts/-clasts 5 – Loop Start 7 - Elimination 9 – Static Calculation 11.1 – Filament 12 – Loop End Modification 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search 11.2 – Filament Output Analysis & Motion Out Out 11.1 11.1 3 9 11.2 12 1 5 6 7 8 10 2 4 11.2

11.1 Modification of the Filaments Depending on whether an Osteoblast or an Osteoclast is close enough to a filament, the A B filament‘s mass is either increased or reduced by increasing or decreasing the radius of the filament within the area of effect of the Osteoblast/-clast. C D

11.2 Filaments Analysis & Osteoblast/-clast motion 1 – Initial Structure 3 – Osteoblasts/-clasts 5 – Loop Start 7 - Elimination 9 – Static Calculation 11.1 – Filament 12 – Loop End Modification 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search 11.2 – Filament Output Analysis & Motion Out 11.1 3 9 11.2 12 1 5 6 7 8 10 2 4 11.2