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

Construction of Stable and Lightweight Technical Structures Inspired by Ossification

• f Bones using Osteogenetic P Systems

ALEXANDER MELCHER ILIJA VUKOREP THOMAS HINZE

Bone formation and its use for technical structures

Ossification of Bones

Osteoblasts Osteoclasts Bone tissue

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 Modification 12 – Loop End 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search 11.2 – Filament Analysis & Motion Output

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

Utilized Software

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

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

Program Structure

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

Program Structure - Detail

1 Initial Structure Generation

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

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

11.2 – Filament Analysis & Motion

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 Modification 12 – Loop End 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search Output

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

11.2 – Filament Analysis & Motion

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 Modification 12 – Loop End 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search Output

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

11.2 – Filament Analysis & Motion

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 Modification 12 – Loop End 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search Output

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

11.2 – Filament Analysis & Motion

4 Filament Bounds

Defining the bounds

• f 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 Modification 12 – Loop End 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search 11.2 – Filament Analysis Output

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

11.2 – Filament Analysis & Motion

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 Modification 12 – Loop End 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search Output

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

11.2 – Filament Analysis & Motion

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 Modification 12 – Loop End 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search Output

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

11.2 – Filament Analysis & Motion

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 Modification 12 – Loop End 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search Output

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

11.2 – Filament Analysis & Motion

8 Simplification of connected filaments

2D reduction multiple filaments 3D reduction three 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

• f force.

In order to „smooth“ the corners the adjacent filaments are joined into one single 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 Modification 12 – Loop End 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search Output

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

11.2 – Filament Analysis & Motion

Mechanical force – side view

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.

10 Osteoblasts/-clasts search for closest filament

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

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

11.2 – Filament Analysis & Motion

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

• ptimize 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 Modification 12 – Loop End 2 – Static Analysis 4 – Filament Bounds 6 – Structure Analysis 8 - Simplification 10 – Filament Search Output

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

11.2 – Filament Analysis & Motion

11.1 Modification of the Filaments

D B C A

Depending on whether an Osteoblast or an Osteoclast is close enough to a filament, the 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.

11.2 Filaments Analysis & Osteoblast/-clast motion

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

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

11.2 – Filament Analysis & Motion

11.2 Filaments Analysis & Osteoblast/-clast motion

Amount of forces The element‘s cross-sections

The direction of movement for the osteoblasts and osteoclasts depend on the level of mechanical stress found in the filaments. The mechanical stress σ present in an element is defined as the amount of force F affecting element's cross-sectional area A by σ = F / A .

Direction of movement

12 End of a cycle of the artificial Ossification

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

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

11.2 – Filament Analysis & Motion

12 End of a cycle of the artificial Ossification

All information generated during the

• ne cycle of artificial

Ossification is being used to initiate the next cycle. The step count increments with each cycle until the indicator for termination is reached.

11.2 Filaments Analysis & Osteoblast/-clast motion

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

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

11.2 – Filament Analysis & Motion

Output

At any point of the artificial ossification an

• utput of the current

structure can be produced.

Intial properties:

• 300 Osteoblasts
• 300 Osteoclasts
• 3128 filaments
• Downward vertical

external forces on all top nodes

• Bearings on all

buttom nodes

Case Study - Cube

0 cycles 300 cycles 600 cycles 900 cycles 1200 cycles 1500 cycles

Intial properties:

• 300 Osteoblasts
• 300 Osteoclasts
• 3128 filaments
• Downward vertical

external forces on all top nodes

• Bearings on all

buttom nodes

Case Study - Cube

0 cycles 300 cycles 600 cycles 900 cycles 1200 cycles 1500 cycles

Overlaying all sections Visible main force lines Intial properties:

• 300 Osteoblasts
• 300 Osteoclasts
• 3128 filaments
• Downward vertical

external forces on all top nodes

• Bearings on all

buttom nodes

Case Study - Cube

Case Study - Bridge

Bearing version A Bearing version B

Intial properties:

• 200 Osteoblasts
• 200 Osteoclasts
• 1559 filaments
• Downward vertical

external forces on all top nodes

400 cycles 500 cycles 200 cycles 300 cycles 0 cycles 100 cycles

Case Study - Bridge

Intial properties:

• 200 Osteoblasts
• 200 Osteoclasts
• 1559 filaments
• Downward vertical

external forces on all top nodes

500 cycles 0 cycles

Case Study - Bridge

Intial properties:

• 200 Osteoblasts
• 200 Osteoclasts
• 1559 filaments
• Downward vertical

external forces on all top nodes

Main force lines - silhouette Main force lines - model

Case Study - Bridge

Intial properties:

• 200 Osteoblasts
• 200 Osteoclasts
• 1559 filaments
• Downward vertical

external forces on all top nodes