1 / 50

Evolutionary Optimization Method for Thermal Protection System Design

CDOC. Evolutionary Optimization Method for Thermal Protection System Design. Department of Mechanical and Materials Engineering Wright State University, Dayton, OH, 45435. Air Vehicles Directorate WPAFB, OH, 45433. Thermal Protection System (TPS).

jered
Download Presentation

Evolutionary Optimization Method for Thermal Protection System Design

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CDOC Evolutionary Optimization Methodfor Thermal Protection System Design Department of Mechanical and Materials Engineering Wright State University, Dayton, OH, 45435 Air Vehicles Directorate WPAFB, OH, 45433

  2. Thermal Protection System (TPS) • Responsible for protecting the spacecraft’s components from melting due to high re-entry temperatures. • Key technology that enables a spacecraft to belightweight, fully reusable, and easily maintained. • Consists of different types of materials that are distributed all over the spacecraft, such as felt blankets, ceramic tiles, carbon-carbon leading edge, and metallic TPS.

  3. Metallic TPS • The metallic TPS makes maintenance and replacement easier • Its inherent ductility and design flexibility offers the potential for a more robust system with lower maintenance costs than competing TPS systems < ARMOR TPS model > < X-33 metallic TPS panel >

  4. Metallic TPS PLATE (Unremovable region) FRAME z x, y SUPPORT CHALLENGES IN DESIGN • Weight is a key disadvantage in its use • Thermal and acoustic loading conditions tend to be at odds with one another It is difficult to develop an optimum TPS model

  5. This research incorporates the multi-objective optimization problem into the Evolutionary Structural Optimization (ESO) algorithm using the weighted objectives technique Metallic TPS REMEDIES • The support height is increased to reduce the heat transfer to the fuselage by inserting more insulators. • A frame for thin plate is attached to prevent flutter due to acoustic loading.

  6. Structural Optimization Method Topology design is for determining the distribution pattern of material and void. This 0-1 discrete problem is transferred into a continuous one • Homogenization method (Bendsoe and Kikuchi, 1988) : The design region is assumed consisting of the porous microstructure and material density distribution is optimized by taking size and direction of the hole of the micro-structure as design variables. • Density-based method (Yang and Chuang, 1999) : This method heuristically designs the material properties such as Young’s modulus and density for each finite element directly to find optimal material distributions. • Cellular automation generation method (Inou, 1994) : Evolution of the organism is considered cell automaton based on the local field rule and it is the evolution makes the structure form that adapted to the dynamics environment.

  7. Continuous approaches to topology optimization : Hard to derive sensitivity functions (Mathematically difficult!!) : Make Final design to be different by a penalty rule for gray regions : Hard to apply a sensitivity for stress (Usually, strain energy is used) The evolutionary structural optimization (ESO) method or The bidirectional evolutionary structural optimization (BESO) method : Discontinuous approach, which deals with only 0-1 distribution (No penalty function) : very simple concept !! : Stress, as well as strain energy can be easily utilized

  8. Evolutionary Structural Optimization (ESO) Methodfor Thermal Protection System Design

  9. Short Cantilever Beam Michell Structure with Fixed Supports Evolutionary Structural Optimization (ESO) Method • Based on a simple concept that the residual structure evolves toward an optimum by gradually removing inefficient material. STATIC OPTIMIZATION PROBLEM low stress values low strain energy values A number of elements with are removed from structure

  10. CONVENTIONAL ESO FOR EIGENVALUE PROBLEM (1-1) • General eigenvalue problem (1-2) • Rayleigh quotient • Change of the i th frequency (1-3) (1-4) (1-5)

  11. Challenges of Dynamic Control Parameter • No direct consideration of the modal stiffness • The control parameter characteristic changes due to mode-switching, which is prevalent in three-dimensional structures • Mode-switching adversely influences the material removal for the desired frequency CONVENTIONAL ESO FOR EIGENVALUE PROBLEM Using a dynamic control parameter based on the Rayleigh quotient, (1-6) A number of elements with high positive values are eliminated to increase the natural frequency of interest.

  12. To resolve these problems, • Static control parameter using von Mises stress is applied to consider the modal stiffness • The static control parameter is expanded to include the neighboring natural modes, as well as the natural mode of interest Eliminating a large number of elements from a structure through many iterative steps … Results in very weak modal stiffness ! Drastic alteration in the natural frequency of interest !

  13. * Note that Derivation of New Dynamic Control Parameter The response of the equation of motion (1) is described in modal coordinates as (1) (2) where , , The displacement of each nodal point is computed by implementing the concept of virtual static displacement for each mode shape. By assuming =0, (3)

  14. The displacement of each nodal point is computed by implementing the concept of virtual static displacementfor each mode shape. By assuming ω=0, (3) modal displacement (generalized displacement) generated by external force { F }. The natural mode can be treated as a response (displacement) by applying the external force whose modal displacement is 1 for the rth mode and 0 for the other modes. When {Fr} is the external force satisfying this condition, (4)

  15. : mode of interest : mode of interest : neighboring mode : neighboring mode • Force magnitude for each natural mode is different from others • A higher natural mode requires a larger external force due to thecomplexity of the mode shape The magnitude of {Fr} is scaled to be that of the external force of the interested natural mode. (5) The scaled external force vector can estimate the displacement of the r th natural mode by the force magnitude of the interested natural mode (6)

  16. If , only is selected because has very small value for r th natural mode. Dynamic Control Parameter by von Mises Stress (7) Eq. (7) considers not only the ith natural frequency, but also its neighboring natural frequencies by choosing maximum stress of rth natural mode If , , as well as are selected because approaches to that of the natural mode of interest. A number of elements with the smallest stresses, that is, the most inefficient elements, are removed from the structure.

  17. Cantilever Structure • Fixed Region • Removable region • 2% of the total number are eliminated in each iteration. • Unremovable region Weighting Factor Change Evolutionary History of Frequencies

  18. 66% REMOVAL Using Proposed Control Parameter 930 Hz Using Conventional Control Parameter 712 Hz Comparison between conventional ESO and new ESO

  19. TPS Design with Heat Transfer Problem • Minimize TPS weight : subject to • Using weighting objectives method: (8) • Transient heat analysis: Four corners are simply supported Initial Metallic TPSModel

  20. Optimization Challenge for TPS Model with a Thin Plate Plate (Unremovable) • A local mode can be observed at the plate region due to its thinness Frame Z Support X To avoid the local mode, Fixed region Modified - Dense-meshed structure - Few elements removal in one iteration Too much computational cost !

  21. TPS Design Process Design optimization of the support and frame regions are conducted separately TPS initial model with dense mesh TPS support design by topology optimization Modified TPS initial model based on the topology result TPS support design by shape optimization TPS frame design Optimum TPS model

  22. The support region is designed by shape optimization from the modified initial structure • The frame region is designed separately using shape optimization Research Approach Research Approach • The support region is designed by topology optimization using ESO algorithm Initial structure modified from topology result

  23. TPS Support Design • The initial TPS model is set up as a full-meshed structure. • Plate and frame region are set as unremovable. • Topology optimization is applied to the conventional ESO and the new ESO with the proposed control parameter. Unremovable

  24. Change of the Fundamental Natural Frequency • Fundamental natural frequency is improved up to certain percentage of material removal. • As the removed volume percentage increases, the conventional method decreases the fundamental natural frequency very quickly because there are no direct considerations of mode-switching phenomenon and modal stiffness. • The proposed method keeps the fundamental natural frequency higher.

  25. Change inMaximum Thermal Stress • In the conventional method, the maximum thermal stress increases at an early stage because the control parameterdoesn’t consider thermal stress. • As the removed volume percentage increases, the maximum thermal stress decreases because the heat transfer to the bottom side is decreased by eliminating elements. • ( Elements that connect between the plate and the support region ) • The proposed method restrains the increase in maximum thermal stress from increasing at an early stage, as well as at increased volume reduction.

  26. 933.6 Hz 906.8 Hz 1stNatural Frequency 1stNatural Frequency Maximum Stress Maximum Stress 0.523 GPa 0.330 GPa 740 (346 lb) 568 (263 lb) Number of Elements Number of Elements Stress constraint is violated in both the cases Resultant Models with the Fundamental Frequency at 900 Hz Conventional Method Proposed Method

  27. TPS Support Redesign by Shape Optimization • The initial TPS model with hollow cube is chosen from the previous result. • Shape optimization (Called ‘Nibbling ESO’) is applied. • Plate and frame region are set as unremovable. • For the fixed region, - In dynamic analysis, additional stiffness [ kX, kY, kZ ]=[ 0, 0, 108] (N/m) are set up at four edges of the plate. The local mode will have a higher natural frequency when compared with the fundamental natural frequency of the support’s first bending mode.

  28. Modified TPS Support Model • Fundamental frequency at 77.7%: 901.5 Hz • Maximum stress at 77.7%: 0.236 GPa • When theadditional stiffness at the plate edge is removed from the structure, the fundamental frequency becomes 871.9 Hz due to the increase in modal mass. Fundamental frequency may be increased by reducing the frame weight.

  29. Plate thickness 0.03 m 0.03 m 0.002m (in PLATE) 0.03 m 0.03 m 0.007m (in FRAME) 0.03 m 0.03 m 0.03m (in SUPPORT) TPS Frame Design • Shape optimization is applied by eliminating elements from the bottom surface of the frame region. • Plate and support regions are set up as unremovable regions. • No thermal stress analysis is used. • TPS model is designed to be lightweight with the fundamental frequency greater than 900 Hz.

  30. Evolutionary Process of the TPS Frame Model • Up to the 41st iteration, fundamental frequency increases. • In the end iterations, the frequency drastically decreases. • Modified TPS model satisfies the frequency constraint at the 45th iteration. • A transient heat transfer analysis is conducted on the TPS model of 45th iteration. View from the Bottom Side of the Frame

  31. Optimized TPS Model • Fundamental natural frequency: 919.8 Hz (>900 Hz) • Maximum thermal stress:0.228GPa (<0.3 GPa) • TPS mass: 76.50 kg(cf. For the full meshed structure, 470 kg) This model reduced its weight until 84% in comparison with the full-meshed structure

  32. It was shown that this control parameter can prevent several problems, which are induced by failing to consider the mode-switching phenomenon and the reduced modal stiffness when a large number of elements are eliminated through many iterative steps. Summary 1. A multi-objective optimization problem for thermal stress and fundamental natural frequency was conducted to make a lightweight TPS model by using Evolutionary Structural Optimization (ESO) algorithm. 2. New control parameter based on static analysis was proposed for the TPS design concerned with dynamic analysis. 3. An efficient way to obtain a metallic TPS model was shown by designing the support and the frame region separately using the ESO method with the proposed control parameter.

  33. Bidirectional ESO Methodfor Thermal Protection System Design

  34. NEW ELEMENT NORMAL ELEMENT ELEMENT TO BE ENFORCED UNNECESSARY ELEMENT Conventional Bidirectional Evolutionary Structural Optimization Method : applies element addition, as well as element removal (e.g. New elements are attached around the elements with overly stress to reduce localized high stress regions in static optimization problem) : starts from a simple structure satisfying boundary conditions, not a full-meshed one : uses control parameters based on Rayleigh quotient for both element addition and removal in eigenvalue optimization problem

  35. Control Parameter Based on Rayleigh Quotient IN THE ADDITION PROCESS (A) This equation expresses the change of the i-th eigenvalue due to attaching the l-th virtual element to the original structure. Some elements whose are most positive among all virtual elements are converted into real elements ! Eq. (A) is also applied to following situation: • The i-th natural frequency increases by adding the l-th element of 　　 ≫0 • The i-th natural frequency decreases by removing the l-th element of 　　 ≪0 There is no drastic change of natural frequency of interest even if “mode-switching” occurs in iterative steps because there is no sudden changes of stiffness of structure.

  36. Control Parameter Based on Rayleigh Quotient IN THE REMOVAL PROCESS (B) This equation expresses the change of the i-th eigenvalue due to removing the l-th element from the original structure. • Only the changes in natural frequencies are evaluated. Nothing is considered about the stiffness of any part of the structure. • The sensitivities of higher-order natural modes are incorrect due to the inaccuracy of the natural frequency calculations. • In the case of mode-tracking, comparison between the current and previous modes is impossible if a new mode appears at the current step, or if a previous mode disappears at the current step. • The change of the natural mode of interest due to the mode-switching phenomenon induces a significant alteration of the structural stiffness in the next evolutionary process. 1 and 2 are the main challenges for the evolutionary method with the fundamental natural frequency optimization.

  37. Challenge in Conventional BESO Method ADDITION PROCESS REMOVAL PROCESS (B) (A) No significant decrease in structural stiffness Significant decrease in structural stiffness due to mode-switching Sudden drop of the natural frequency of interest Unstable eigenvalue optimization process • Static control parameter using strain energy or von Mises stress is applied to consider the modal stiffness • The static control parameter is expanded to include the neighboring natural modes, as well as the natural mode of interest

  38. : mode of interest : neighboring mode Static Control Parameter Using Strain Energy Modified natural mode (6) Strain energy Static control parameter in the removal process

  39. A Model Addition Removal Modified model REAL ELEMENT VIRTUAL ELEMENT UNNECESSARY ELEMENT Proposed Bidirectional Evolutionary Structural Optimization Process • Virtual element is newly applied. • In element removal, structural stiffness is only considered to avoid sudden drop of the stiffness. • In element removal, new control parameter is applied to consider mode-switching phenomenon.

  40. Algorithm The objective of this method is : to shift the fundamental natural frequency of a three-dimensional structure to a target frequency as closely as possible. Because of starting from a simply small structure, The number of FE to be added > The number of FE to be removed Stage 1 : the growth stage to grow the structure until raising the fundamental natural frequency to a little bit higher than the target frequency (= upper limit). ( upper limit = target frequency ×α, where α= 1.05~1.50) The number of FE to be removed > The number of FE to be added Stage 2 : the weight reduction stage to control the fundamental natural frequency until it reaches to lower limit(= target freq ×β, where β=1.00~1.02). Stage 3 The number of FE to be removed = The number of FE to be added : the alternation stage to change the positions of the elements

  41. Upper limit Target Frequency (lower limit) STAGE 1 STAGE 2 or 3 Algorithm The evolutionary iterative process is continued until the i th natural frequency (= fundamental natural frequency) converges after the application of the three kinds of stages. The number of finite elements, which are added and removed in an iterative process, is set within 1~2% of the number of elements of the structure .

  42. : Fixed region : Un-removal element Target frequency : 4000 Hz A Bridge Model 1st natural freq. : 2349 Hz Upper limit frequency : 4250 Hz (target frequency ×1.05) 1st mode (2349Hz) 2nd mode (2506Hz) 3rd mode (3658Hz)

  43. Z Y X A Bridge Model “ V shape ” Z X 1st mode (2349Hz) 2nd mode (2506Hz) “ Reverse-V shape ” Z Y 3rd mode (3658Hz)

  44. Availability of Proposed Method << ADDITION >> Control parameter using Rayleigh quotient << REMOVAL >> << REMOVAL >> Control parameter using Rayleigh quotient Control parameter using strain energy METHOD 1 (Conventional method) METHOD 2 (Proposed method) COMPARISON

  45. Total number of element : 352 Total number of element : 316 A Bridge Model In the case of METHOD 1, In the case of METHOD 2,

  46. A Bridge Model 1st mode (2349Hz) 2nd mode (2506Hz) 3rd mode (3658Hz) 1st mode (4028Hz) 2nd mode (4176Hz) 3rd mode (4299Hz) METHOD 2 can select appropriate finite elements to be removed, and can evolve the bridge model to the optimum design stably under the condition that “Mode-switching” happens in.

  47. A Thermal Protection System Model Adaptable, Robust, Metallic, Operable, Reusable (ARMOR) TPS panel X-33's Innovative Metallic Thermal Shield 1st natural freq. 104.8 Hz << Inconel 693 alloy >> E = 196 GPa Density = 7770 kg/m3 Poisson = 0.32 Target freq. 1000 Hz Initial model for designing TPS

  48. A Thermal Protection System Model At the 100th iteration, the fundamental natural frequency is 1011.2 Hz Although "mode-switching" occurs irregularly in the iterative processes between the bending mode in X-axis and the bending mode of Y-axis, which are mutually orthogonal directions, the evolution process is executed very smoothly. Evolutionary history of the first three natural frequencies

  49. A Thermal Protection System Model Initial model Modified model <The fundamental natural mode for the initial model and the modified model >

  50. Summary 1. Two kinds of control parameters are introduced in the bidirectional evolutionary structural optimization. 2. It is shown that the static control parameter can make a natural frequency of interest convergence stable or improved by removing elements with low values. 3. Static control parameter is modified to consider adjacent natural modes, as well as the targeted mode to alleviate the problem of the mode-switching phenomenon. 4. Using the proposed control parameter and new addition process, two representative models are analyzed.

More Related