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Multi-Objective Genetic Topological Optimization for Design of composite wall barriers under blast loading
- 1. Multi-Objective Genetic Topological Optimization for Design of composite wall barriers under blast loading Prepared by: Sardasht Sardar Weli Structural Optimization Prof. Dr Logo Janos 2019
- 2. General Overview o The aim of this presentation is to show the utilization of Topology Optimization to optimize a wall barrier thickness and its resistance under the extreme environment which is blast loading. o Composite material has been chosen to enhance the wall barrier capacity. o Multi-objective Genetic Optimization is suggested to optimize the objective functions. Source: https://www.javelin-tech.com
- 3. • “Barriers are generally used to prevent propagation of explosions.” [1] o What are Barriers? • They can also reduce blast pressures in the near range. X < 10 . H o What are the missions of barriers in the extreme environment? X H R Introduction – Blast Analysis
- 4. Introduction – Blast Analysis • Explosions generate a high rate pressure wave. o Blast Loading Environment Computational Fluid Dynamics (CDF) Source: UFC Source: [7]
- 5. • High Strength to Weigh Ratio • Flexibility in Obtaining desired property o Composite Wall Weak faces would be allowed to fail, strong face control the stress, the overall structure remain safe. AND……? Improve Blast Resistance Adjusting the stiffness of the composite layers FURTHERMORE……? Multi-Objective Topological Optimization using the Microstructural Homogenization Method Introduction – Blast Analysis
- 6. Introduction - Topology Optimization • Enables deriving macro field equations from micro field equations. I. It is used to calculate the average constitutive parameters of a composite material, II. since for inhomogeneous material, the elasticity tensor Eijkl is varying at the microscopic scale. o Homogenization Technique • It is able to address the trade of between multiple objective functions. • There is also no need to specify weight on the various specific objection function value. o Multi-objective Genetic Optimization OBJECTIVE FUNCTIONS f1 • Objective Function f2 • Objective Function
- 7. Methodology - Homogenization o This method can be applied on the composites which has a periodic unit cells. o It is assumed that the microstructure is much more smaller than a part or the structure which is used in the application [2]. 𝑇ℎ𝑒 𝑚𝑖𝑐𝑟𝑜𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑠 𝑎𝑟𝑒 𝒀 𝟏, 𝒀 𝟐, 𝒀 𝟑 𝑓𝑜𝑟 3𝐷 𝑎𝑛𝑑 𝒀 𝟏, 𝒀 𝟐 𝑓𝑜𝑟 2𝐷 𝑌 = 0, 𝑌1 , 0, 𝑌2 , 0, 𝑌3 3D 𝑌 = 0, 𝑌1 , 0, 𝑌2 2D 𝒘𝒉𝒆𝒓𝒆 𝒖 𝒊𝒔 𝒕𝒉𝒆 𝒎𝒊𝒔𝒓𝒐𝒔𝒄𝒐𝒑𝒊𝒄 𝒅𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕, 𝒂𝒏𝒅 𝜼 𝒊𝒔 𝒄𝒆𝒍𝒍 𝒔𝒊𝒛𝒆 Y Macrostructure X Microstructure 𝑌 = 𝑋 𝜂
- 8. Methodology - Homogenization o A unit cell of the composite material is used to determine the property of each layer. 9 Elements Material 1 Material 2 either After the displacement is applied, the FEA is used to calculate the unknown stresses at all 16 nodes. 𝑆11 𝑆12 0 𝑆12 𝑆22 0 0 0 66 𝜀1 𝜀2 𝛾12 = 𝜎1 𝜎1 𝜏12 Then find 𝑬 𝟏, 𝑬 𝟐 and 𝒗 𝑬 𝟏, 𝑬 𝟐 and 𝒗 are the homogenized properties of the unit cell [2].𝑺 𝟏𝟏 = 𝟏 𝑬 𝟏 𝑺 𝟏𝟐 = −𝒗 𝟏𝟐 𝑬 𝟏 𝑺 𝟐𝟐 = 𝟏 𝑬 𝟐 𝑺 𝟔𝟔 = 𝟏 𝑮 𝟏𝟐
- 9. Methodology - Homogenization o Considering the first order form of microscopic displacement, then the strain field would be: 𝜀𝑖𝑗 0 𝑆𝑡𝑟𝑎𝑖𝑛 𝑑𝑢𝑒 𝑡𝑜 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡. 𝜀𝑖𝑗 ∗ 𝑆𝑡𝑟𝑎𝑖𝑛 𝑑𝑢𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑜𝑟𝑑𝑒𝑟 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑟 𝑖𝑛ℎ𝑜𝑚𝑜𝑔𝑒𝑛𝑒𝑜𝑢𝑠 𝑛𝑎𝑡𝑢𝑟𝑒 𝑜𝑓 𝑐𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙 𝑐𝑎𝑙𝑙𝑒𝑑 𝑓𝑙𝑢𝑐𝑡𝑢𝑎𝑡𝑖𝑜𝑛 𝑠𝑡𝑟𝑎𝑖𝑛 [3] 𝜀𝑖𝑗 0 𝜀𝑖𝑗 0 𝜀𝑖𝑗 0 𝜀𝑖𝑗 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 2D 𝜀𝑖𝑗 0 𝜀𝑖𝑗 0 𝜀𝑖𝑗 0 𝜀𝑖𝑗 0 𝜀𝑖𝑗 0 𝜀𝑖𝑗 0 𝜀𝑖𝑗 0 𝜀𝑖𝑗 0 𝜀𝑖𝑗 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 3D The homogenized stiffness tensor may be written as: 𝜼 𝟎
- 10. Methodology – Blast Load Simulation • It is used to model the real pressure wave generated from the explosion. • Since (1) burial of explosive material, (2) height from surface or explosive material, (3) radial distance from explosive charge (4) the TNT equivalent or weight in kilograms of explosive can be used as input parameter. o Computational Fluid Dynamic (CFD) Lagrangian Frame of Reference Eularian Frame of Reference Solid Fluid Dynamic
- 11. • Based on the material properties in each layer FEA is used to discretize the layers. • ANSYS-AUTODYN was used to simulate the pressure wave generated by the high explosive material (TNT). o Finite Element Simulation Methodology – Blast Load Simulation Dynamic Model is required Jones- Wilkins-Lee Equation of State [4] • FEA is conducted by ANSYS. CFD
- 12. Explosion Pressure Distribution at time t. • At each load step in the FEA, a specific load profile output from the CFD simulation is applied to the left side layer of the composite wall. o Finite Element Simulation Methodology – Blast Load Simulation • For each time step, the stress distribution in both layers of the composite wall is saved for post processing.
- 13. Methodology – Multi-objective Genetic Optimization (MOGO) Classical • To address the trade of between the objective functions when more than one objective function is necessary, MOGA is employed. o Multi Objective Genetic Algorithm (MOGA) Lie the Objective Function in the Pareto Front Category 1 • Use Single Objective Optimization and address MOGO to consider the preference Category 2 • Establishes an optimization method that is multi- objective in nature Weighted Sum Method, ϵ Constrain Method and etc… MOGA
- 14. Methodology – Multi-objective Genetic Optimization (MOGO) Classical o Steps required to conduct MOGA I. A population size n is selected and generated without duplication. II. Design Variables are selected. III. All non-dominated designs are assigned to 0 and 1. IV.Higher is better fitness conversion is applied. V. The Algorithm is prevented from converging to a single solution. Two objective functions representing the maximum stress-to-strength ratio (𝒇 𝟏) and the weight (𝒇 𝟐)of the composite are defined. 𝑓1 = 𝑚𝑎𝑥1 ≤ 𝑚 ≤ 𝑛{ max 𝜎 𝑚 𝑇 𝜎 𝑚 𝑈𝑇 , max(𝜎 𝑚 𝐶 ) 𝜎 𝑚 𝑈𝐶 } and 𝑓2 = 𝑚=1 𝑁 𝐴. 𝑇 𝑚. 𝜌 𝑚
- 15. • The optimization problem is formulated as a multi-objective nonlinear optimization that targets to the maximum stress-to- strength ratio and to minimize weight of the composite while meeting the bounds for layer thicknesses as follows Methodology – Multi-objective Genetic Optimization (MOGO) Classical o Steps required to conduct MOGA 𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑓1, 𝑓2 𝑆𝑢𝑏𝑗𝑒𝑐𝑡𝑒𝑑 𝑡𝑜 𝑇 𝑚 𝑚𝑖𝑛 ≤ 𝑇 𝑚 ≤ 𝑇 𝑚 𝑚𝑎𝑥 1 ≤ 𝑚 ≤ 𝑁 • 𝑇 𝑚 is the thickness of each layer, the design variables are 𝑇 𝑚 𝑚𝑖𝑛 , 𝑇 𝑚 𝑚𝑎𝑥 and 18 other design variables related to elastic properties • The optimization finishes when the stopping criteria is met and the final design variables are then saved.
- 16. Methodology – Overall Procedure Blast CFD Simulation Pressure Profile FE Model Initialize Population Design Variables, 𝑓1 𝑎𝑛𝑑 𝑓2MOGA Return Final Population Evaluate the Population Members Stopping Criteria met? NO YES
- 17. Expected Result o The MOGA method produces a Pareto front Pareto Front Material 1 Material 2 Layer 1 Layer 2 Thickness 1 Thickness 2 stress-to-strength ratio Any composite structures that exhibited stress-to-strength ratios above 1.0 are excluded Why 3x3? Why not 4x4? If yes, how?
- 18. Expected Result Solution # T1 (mm) T2 (mm) Stress/Strength (S/S#) Weight (W) #(kg) Micro 1 Micro 2 1 T1-#1 T2-#1 S/S#1 W#1 2 T1-#2 T2-#2 S/S#2 W#2 3 T1-#3 T2-#3 S/S#3 W#3 n T1-#n T2-#n S/S#n W#n T1 T2 S/S W
- 19. Results from [2] It is very obvious that by increasing the stress to strength ratio, the weight is decreasing. This resulted in decreasing the thickness of layer one and the thickness of layer two.
- 20. Summary o The blast load is applied and the pressure profile is generated by CFD. o The Homogenization is applied to consider the inhomogeneity of microstructure materials. o The MOGA is employed to optimize the thickness of the composite wall. o The stress and strength ratio was optimized to its higher allowable ratio. o The stress and strength ratio greater than 1 is discarded from the solution
- 21. References [1] Unified Facility Criteria (UFC) [2] Multi-objective Genetic Topological Optimization for Design of Blast Resistant Composites [3] Design of Material Structures using Topology Optimization [4] DSD/WBL-CONSISTENT JWL EQUATIONS OF STATE FOR EDC35 [5] Prof. Dr. Logo Janos, Lecture notes “Structural Optimization”. [6] Dr. Matteo Bruggi, Short Course on Topology Optimization of Structures. [7] Calculation of Blast Loads for Application to Structural Components: Administrative Arrangement No JRC 32253-2011 with DG-HOME Activity A5 - Blast Simulation Technology Development Q&A Thank you,
Editor's Notes
- There may other reasons like small thickness and architectural reasons
- Then the stresses are summed for each direction and divided by the number of total nodes. This new stress value represents the average stress for the homogenized unit cell.
- Please read the paper 3 to understand a periodic material in two dimensions where the microstructure consists of a matrix material with circular inclusions of another material and a three dimensional material (right) consisting of fibres embedded in a matrix material.
- Lagrangian is when the mesh is deforms as the material deforms and vice verse. And also each element represents the amount of material. Eularian is when the nodes are fix nor the mesh size when it is subjected to a load. Instead the material is pushing to the support. Lagrangian can be used when there is no much deformation such as solid Eularian can be used when there is big deformation such as fluids. Eularian is much more expensive computationaly since the material transferring and also tracking in each cell how much material exist. Each cell can contain more than one material
- The properties used by the FEA model are the modulus of elasticity in the radial direction, the modulus of elasticity in the y direction, Poisson’s ratio and the shear modulus. The density of the layers is calculated using the rule of mixtures method. The thickness of each layer of the composite plate is a design variable.
- MOGA directly identifies non-dominated design points that lie on the Pareto front. The advantage of the MOGA method over the conventional weighted-sum method, is that MOGA finds multiple points along the entire Pareto front whereas the weighted-sum method produces only a single point on the Pareto front. Moreover, MOGA is more capable of finding points on the Pareto front when the Pareto front is non-convex. Srinivas and Deb [27] proposed non-dominated sorting genetic algorithms (NSGA). NSGA basically finds the non-dominated set of points (which constitute the first front) and gives them a large fitness value. This process continues until the entire population is classified into several domination fronts by giving smaller fitness values for the new fronts. Multiple techniques have been suggested to reduce computational time by considering rules to preserve diversity and keep the elite [28, 29]. MOGA has been successfully applied to many problems including topology optimization [30,
- It may also be observed from Fig. 6 that the amount of Titanium used in the composite is greatly reduced when moving from low stress-to-strength ratios to high ones approaching 1.0 with a relatively low weight. This is important because Titanium is a much heavier metal and more expensive to process than Aluminum. Why 3x3? A unit cell of 3×3 for each layer was chosen for the simulation environment because discretizing the solution space increases the number of required calculations exponentially. Using MOGA, 1,000 evaluations resulted in 67 solutions. 16 of these solutions were infeasible because they yielded a stress-to-strength ratio greater than 1.0. For the 3×3 case 1,000 evaluations is only about 0.38% of the total solution space. In order to cover 0.38% of the 4×4 case would require 16,384,000 evaluations. Currently, the run time is 43.7 h, while increasing the unit cell to 4×4 would require 7.16 e5 hours
- A major limitation ofthe above work is its use ofimplicit method to model the transfer of the blast wave to the composite plate. Future work will include an explicit blast model that is used to simulate the blast process every time the material properties of the layers are changed. This will increase the accuracy of the optimization results while yielding a more realistic blast simulation problem. Explicit blast modeling is necessary because when a blast wave encounters a solid object the pressure is transferred to the object surface and causes the object to deform based on the stiffness of the material. This means that the stiffness of the plate affects the magnitude and shape ofthe pressure transfer. Currently, the pressure transfer is assumed to be the same for all microstructures. As the pressure transfer changes, the stress distribution will simultaneously change requiring a different optimal microstructure than when assuming the same pressure wave. The blast model may also be modified to account for different soil properties, which might alter the blast pressure. Finally, composite plate optimization can be extended to incorporate probabilistic definition ofsafety using reliability theory [30]