JP2022521907A - High-speed coordinated optimization method for plate-wound shell structure of hybrid fiber composite material - Google Patents
High-speed coordinated optimization method for plate-wound shell structure of hybrid fiber composite material Download PDFInfo
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Abstract
ハイブリッド繊維複合材料の板巻きシェル構造に対する高速協調最適化方法であって、複合材料構造最適化設計の技術分野に属し、１）代替材料ライブラリを確立するステップと、２）３次元有限要素数値モデルを確立し、幾何学的分割を行うステップと、３）モデル次数低減法を用いて次数低減数値解析モデルを確立するステップと、４）最適化行列式を確立し、離散材料最適化設計を行うステップと、を含む。連続補間関数を用いて離散代替材料ライブラリにおける離散材料を特徴付け、モデルの幾何学的分割及び最適化目標並びに制約に従って設計変数を割り当て、次数低減モデルを用いて数値計算を行って目標と制約応答を得て、離散材料最適化設計を行い、マルチ変数の協調最適化を達成し、最適化設計構成を得る。本発明は、ハイブリッド繊維複合材料構造の一体化設計を達成し、構造トポロジー、繊維含有量、繊維角度、積層順序などの複数積層変数の協調最適化設計を達成し、構造機能的要件を満たすとともに、構造重量を軽減し、材料コストを低減することができる。A high-speed coordinated optimization method for plate-wound shell structures of hybrid fiber composites, which belongs to the technical field of composite material structure optimization design, 1) steps to establish an alternative material library, and 2) three-dimensional finite element numerical model. Steps to establish and perform geometric division, 3) Steps to establish order reduction numerical analysis model using model order reduction method, and 4) Establish optimization determinant and perform discrete material optimization design. Including steps. Characterize discrete materials in a discrete alternative material library using continuous interpolation functions, assign design variables according to model geometric division and optimization goals and constraints, and perform numerical calculations using order reduction models to perform goals and constraint responses. The discrete material optimization design is performed, multi-variable co-optimization is achieved, and the optimized design configuration is obtained. The present invention achieves an integrated design of a hybrid fiber composite material structure, achieves a coordinated optimization design of multiple stacking variables such as structural topology, fiber content, fiber angle, stacking order, and meets structural and functional requirements. , The structural weight can be reduced and the material cost can be reduced.
Description
本発明は、複合材料構造最適化設計の技術分野に属し、ハイブリッド繊維複合材料の板巻きシェル構造に対する高速協調最適化方法に関する。 The present invention belongs to the technical field of composite material structure optimization design and relates to a high-speed cooperative optimization method for a plate-wound shell structure of a hybrid fiber composite material.
繊維強化複合材料は、ガラス繊維、炭素繊維、アラミド繊維などの強化繊維材料と母材が、巻き付け、圧印、又は引き抜きなどの成形プロセスにより形成された複合材料である。繊維強化複合材料は、（１）比強度が高く、比弾性率が大きい、（２）材料特性が意匠性を有する、（３）耐食性及び耐久性が高い、（４）熱膨張係数がコンクリートに近い、という特徴を有する。これらの特徴により、繊維強化複合材料は、近年の構造物の大スパン化、嵩高化、高負荷化、軽量化かつ高強度、過酷な条件での動作開発の要件を満たすとともに、近年の建築施工の工業化開発の要件を満たすことができるため、各種の民生用建築物、橋梁、道路、海洋、水上構造物及び地下構造物などの分野に幅広く利用されている。繊維強化複合材料は、多種多様であり、炭素繊維複合材料は、比強度が大きく、比剛性が高いが、高価であり、伸びが低いなど、強化繊維複合材料のそれぞれに特有の利点及び欠点があるため、１９７０年代にハイブリッド繊維複合材料が出現している。ハイブリッド繊維複合材料は、２種類以上の繊維が異なるハイブリッド方式により形成された強靭な構造材料である。これは、繊維のそれぞれの特徴を保持し、異なる属性を並立させるだけでなく、いくつかの固有の優勢を示す。現在、ハイブリッド繊維複合材料は、航空、宇宙、自動車、船舶、医療などの分野で幅広く利用されている。ハイブリッド複合材料部材は、単一繊維複合材料よりも設計の自由度が大きい。ハイブリッド複合材料部材プロセスは、単一繊維複合材料よりも実現可能性が高く、それに応じて部材の設計の自由度をさらに拡大する。ガラス繊維複合材料の航空機翼の翼端部の剛性が不十分である場合、剛性を高めるために、炭素繊維を翼端部に適切に使用してハイブリッド複合材料部材を製造することができる。また、そのようなハイブリッド複合材料部材の設計は、プロセス上困難ではない。ハイブリッド繊維複合材料は、構造的使用性能要件に応じて、異なるタイプの繊維、異なる繊維の相対的含有量、異なるハイブリッド方式により、複合材料構造と機能の並立に対する要件を満たすように設計することができる。また、性能が許す限り、高価な繊維の一部を安価な繊維で置換してハイブリッド複合材料部材を製造することにより、材料コストを低減することができる。一方、ハイブリッド複合材料部材を、適当に高価ではあるが高性能な繊維を使用して製造することにより、材料の高性能／価格比が得られ、同様に大きな経済効果が得られる。ハイブリッド繊維複合材料の使用は、構造設計の自由度と材料の適用範囲を拡大し、構造重量を軽減し、材料コストを低減し、経済効果を高めることができる。したがって、ハイブリッド繊維複合材料の構造に適用するための効率的な最適化設計方法を発明することは、ますます重要であり、これは、ハイブリッド繊維複合材料の潜在的な優勢を十分に発揮するための有効なアプローチでもあり、ハイブリッド繊維複合材料の幅広い適用を推進するために必要な手段である。 The fiber-reinforced composite material is a composite material in which a reinforcing fiber material such as glass fiber, carbon fiber, and aramid fiber and a base material are formed by a molding process such as winding, stamping, or drawing. Fiber-reinforced composite materials have (1) high specific strength and high specific elastic modulus, (2) material properties with design properties, (3) high corrosion resistance and durability, and (4) thermal expansion coefficient for concrete. It has the characteristic of being close. Due to these characteristics, the fiber-reinforced composite material meets the requirements for large span, bulkiness, high load, light weight and high strength of structures in recent years, and operation development under harsh conditions, as well as recent construction work. It is widely used in various fields such as civilian buildings, bridges, roads, oceans, water structures and underground structures because it can meet the requirements for industrial development. There are a wide variety of fiber-reinforced composites, and carbon fiber composites have the advantages and disadvantages of each of the reinforced composites, such as high specific strength, high specific rigidity, but high cost and low elongation. For this reason, hybrid fiber composite materials have emerged in the 1970s. The hybrid fiber composite material is a tough structural material formed by a hybrid method in which two or more kinds of fibers are different. It retains the characteristics of each of the fibers and not only parallels the different attributes, but also shows some inherent dominance. Currently, hybrid fiber composite materials are widely used in fields such as aerospace, automobiles, ships, and medical treatment. Hybrid composite members have greater design freedom than single fiber composites. The hybrid composite material process is more feasible than a single fiber composite material, thereby further increasing the degree of freedom in designing the material. If the wing tips of the glass fiber composite are not sufficiently rigid, carbon fibers can be appropriately used for the wing tips to produce hybrid composite members in order to increase the rigidity. Also, the design of such hybrid composite members is not difficult in the process. Hybrid fiber composites can be designed to meet the requirements for composite structure and functional juxtaposition with different types of fibers, relative content of different fibers, and different hybrid methods, depending on structural performance requirements. can. Further, as long as the performance allows, the material cost can be reduced by substituting a part of the expensive fiber with the inexpensive fiber to manufacture the hybrid composite material member. On the other hand, by manufacturing the hybrid composite material member by using appropriately expensive but high-performance fibers, a high-performance / price ratio of the material can be obtained, and a similarly large economic effect can be obtained. The use of hybrid fiber composites can increase the degree of freedom in structural design and the scope of the material, reduce the structural weight, reduce the material cost and increase the economic effect. Therefore, it is increasingly important to invent efficient optimized design methods for application to the structure of hybrid fiber composites, in order to fully realize the potential advantages of hybrid fiber composites. It is also an effective approach and a necessary means to promote the widespread application of hybrid fiber composites.
有限要素などの数値解析方法の高速な発展に伴い、数値モデルに基づく構造最適化方法が複合材料構造最適化設計の重要なアプローチの１つとなっている。従来の複合材料構造設計では、一般に、トポロジー、形状、寸法の最適化の順序に従って、複合材料の繊維角度、繊維含有量、積層順序を設計変数として、異なるスケールの設計変数をレベルに応じて段階的にデカップリング最適化する。変数のグループ化かつデカップリングの方式は最適化効率を向上させるが、構造応答に対する変数間カップリング関係の影響を無視し、設計空間を制限し、ハイブリッド繊維複合材料の優勢を十分に発揮できない。文献の検討によれば、現在、有効なハイブリッド繊維の板巻きシェル構造の効率的な最適化設計方法はない。したがって、ハイブリッド繊維複合材料の板巻きシェル構造に対する高速協調最適化方法を発明するとともに、ハイブリッド複合材料の構造トポロジー、繊維含有量、繊維角度、積層順序などのクロススケール変数を達成する効率的な協調最適化設計を発明し、構造機能的要件を満たすとともに、構造重量を軽減し、材料コストを低減し、経済効果を高めることが強く望まれている。 With the rapid development of numerical analysis methods for finite elements, structural optimization methods based on numerical models have become one of the important approaches for composite material structural optimization design. In traditional composite structural design, generally, according to the order of optimization of topology, shape, and dimensions, the fiber angle, fiber content, and stacking order of the composite are used as design variables, and design variables of different scales are stepped according to the level. Decoupling optimization. Although the variable grouping and decoupling method improves the optimization efficiency, it ignores the influence of the intervariable coupling relationship on the structural response, limits the design space, and cannot fully demonstrate the superiority of the hybrid fiber composite material. According to the review of the literature, there is currently no effective optimized design method for the plate-wound shell structure of hybrid fibers. Therefore, while inventing a fast coordinated optimization method for plate-wound shell structures of hybrid composites, efficient coordination to achieve cross-scale variables such as structural topology, fiber content, fiber angle, stacking order of hybrid composites. It is strongly desired to invent an optimized design, meet structural and functional requirements, reduce structural weight, reduce material costs and enhance economic effectiveness.
本発明は、ハイブリッド繊維複合材料構造のクロススケール設計変数の協調最適化が難しい問題を主に解決し、工学における大規模構造の計算最適化効率が低い問題を解決するために、ハイブリッド繊維複合材料の板巻きシェル構造に対する高速協調最適化方法を提供する。繊維含有量、繊維角度、トポロジー変数などのクロススケール、複数階層の設計変数を同じマクロスケールに統合し、代替材料ライブラリを確立し、離散材料最適化方法を用いてハイブリッド繊維複合材料構造の協調最適化を達成し、異なる構造機能的要件における複合材料一体化設計を解決する。かつ、幾何学的分割とモデル次数低減技術を組み合わせて数値解析と最適化効率を向上させ、大規模構造の最適化効率が低い問題を解決する。この方法は、構造のマクロ応答に対する異なるスケールの変数カップリング関係の影響を十分に考慮し、材料分割レイアウト最適化によりマクロ変剛性の革新的設計をもたらし、設計空間を拡大し、ハイブリッド繊維複合材料の潜在力を十分にマイニングし、設計要件を満たし、材料コストを低減する革新的設計構成を提供することで、経済効果を高めることができる。 The present invention mainly solves the problem that it is difficult to coordinately optimize the cross-scale design variables of the hybrid fiber composite material structure, and solves the problem that the computational optimization efficiency of the large-scale structure in engineering is low. Provides a high-speed co-optimization method for the plate-wound shell structure of. Coordinated optimization of hybrid fiber composite structures using discrete material optimization methods, establishing alternative material libraries by integrating cross-scales such as fiber content, fiber angles, topology variables, and multi-tier design variables into the same macroscale. Achieve the solution of composite material integrated design with different structural and functional requirements. At the same time, by combining geometric division and model order reduction technology, numerical analysis and optimization efficiency are improved, and the problem of low optimization efficiency of large-scale structures is solved. This method takes into account the effects of variable coupling relationships of different scales on the macro response of the structure, resulting in an innovative design of macrovariability by optimizing the material split layout, expanding the design space and expanding the hybrid fiber composite material. By providing innovative design configurations that fully mine the potential of, meet design requirements, and reduce material costs, economic effectiveness can be enhanced.
上記の目標を達成するために、本発明の技術的解決手段は、以下のとおりである。 In order to achieve the above object, the technical solution of the present invention is as follows.
ハイブリッド繊維複合材料の板巻きシェル構造に対する高速協調最適化方法であって、具体的に以下のステップを含む。 It is a high-speed cooperative optimization method for a plate-wound shell structure of a hybrid fiber composite material, and specifically includes the following steps.
第１のステップでは、代替材料ライブラリを確立する。 The first step is to establish an alternative material library.
試験方法、解析方法、数値計算方法を用いて、異なる繊維体積分率、異なるミクロ繊維分布を有する複合材料の材料属性を求め、古典的な積層板理論を用いて、異なる繊維角度及び積層順序積層板の一般的なシェル剛性係数を計算した。異なる組合積層板のシェル剛性係数を、後続の離散材料最適化の準備としてハイブリッド繊維複合材料の代替材料ライブラリを確立する代替材料（離散材料最適化における設計変数）として使用される。代替材料ライブラリを確立し、異なるレベルの強さを有する材料を代替材料ライブラリに入れることは、本特許のマクロスケール協調最適化を達成するための重要な技術であり、異なるスケールの設計変数を同じ階層に統合し、異なるスケール変数間のカップリング関係を十分に考慮することで、ハイブリッド繊維複合材料構造のマクロスケール、複数階層の変数協調最適化設計を達成することができる。 Using test methods, analysis methods, and numerical calculation methods, the material attributes of composite materials with different fiber volume fractions and different microfiber distributions were determined, and using classical laminate theory, different fiber angles and stacking order stacking were performed. The general shell stiffness modulus of the plate was calculated. The shell stiffness coefficients of the different union laminates are used as an alternative material (design variable in discrete material optimization) to establish an alternative material library for hybrid fiber composites in preparation for subsequent discrete material optimization. Establishing an alternative material library and putting materials with different levels of strength into the alternative material library is an important technique for achieving the macroscale co-optimization of this patent, with the same design variables at different scales. By integrating into layers and fully considering the coupling relationships between different scale variables, macroscale of hybrid fiber composite structure and variable co-optimization design of multiple layers can be achieved.
前記解析方法は、混合式法であり、数値方法は、均一化方法、代表体積要素法などを含む。 The analysis method is a mixed method, and the numerical method includes a homogenization method, a representative volume element method, and the like.
第２のステップでは、３次元有限要素数値モデルを確立し、幾何学的分割を行う。 In the second step, a three-dimensional finite element numerical model is established and geometric division is performed.
複合材料の板巻きシェル構造の３次元有限要素数値モデルを確立し、有限要素数値モデルを構造の幾何学的形状、機能的要件に応じて幾何学的分割処理する。幾何学的分割は、最適化の進行を加速するだけでなく、最適化結果が加工製造プロセスを満たすことを可能にし、加工製造を容易にする新規な構造設計形をもたらす。板巻きシェル構造に対する分割最適化設計は、構造の設計空間を拡大することができ、続いて、離散材料最適化により、各隣接する領域がいずれも異なる代替材料である可変剛性の板巻きシェル構造を得ることができる。 A three-dimensional finite element numerical model of the plate-wound shell structure of the composite material is established, and the finite element numerical model is geometrically divided according to the geometric shape and functional requirements of the structure. Geometric divisions not only accelerate the progress of optimization, but also allow optimization results to meet the machining manufacturing process, resulting in new structural design forms that facilitate machining manufacturing. Split-optimized design for sheet-wound shell structures can expand the design space of the structure, followed by discrete material optimization, which is a variable-rigidity plate-wound shell structure in which each adjacent region is a different alternative material. Can be obtained.
第３のステップでは、モデル次数低減法を用いて次数低減数値解析モデルを確立する。 In the third step, a model order reduction method is used to establish a degree reduction numerical analysis model.
複雑な構造詳細を有するハイブリッド繊維板巻きシェル構造について、精密モデルに基づく有限要素解析の展開は、多くの計算リソース及び計算時間を必要とし、最適化の進行を加速するために、本発明は、モデル次数低減法を用いて有限要素数値モデルの次元を低減し、数値解析の計算コストを低減することで、ハイブリッド複合材料の高速協調最適化設計を可能にする。前記モデル次数低減法は、特徴正値固有直交分解法（ＰｒｏｐｅｒＯｒｔｈｏｇｏｎａｌＤｅｃｏｍｐｏｓｉｔｉｏｎ、ＰＯＤ）、動力学モード分解法（ＤｙｎａｍｉｃＭｏｄｅＤｅｃｏｍｐｏｓｉｔｉｏｎ、ＤＭＤ）を含む。 For hybrid fiber plate-wound shell structures with complex structural details, the development of finite element analysis based on precision models requires a lot of computational resources and computational time, and the present invention accelerates the progress of optimization. By reducing the dimensions of the finite element numerical model using the model order reduction method and reducing the computational cost of numerical analysis, it enables high-speed cooperative optimization design of hybrid composite materials. The model order reduction method includes a feature positive value eigen-orthogonal decomposition method (ProperOrthogonal Decomposition, POD) and a dynamic mode decomposition method (DMD).
次数低減モデルを確立するステップは、主に、まずラテン超方格サンプリング、直交サンプリングなどのサンプリング法を用いて離散設計空間において所定数の標本点を抽出し、選択された標本点に対して精密有限要素数値解析を行い、上記の精密解析の結果に基づいて初期縮約基を確立するステップと、次に、主成分解析などの数学的方法により初期短縮基から構造の主な成分を抽出し、短縮基ベクトルを構築するステップと、最後に、短縮基ベクトルに基づいて、精密有限要素数値モデルに対して自由度短縮を行い、次数低減モデルを構築し、精度応答を満たせる次数低減モデルを計算できるようにするとともに、解析時間を減少するステップと、を含む。 The steps to establish a degree reduction model are mainly to first extract a predetermined number of sample points in a discrete design space using sampling methods such as Latin supersquare sampling and orthogonal sampling, and then precisely for the selected sample points. A step of performing finite element numerical analysis and establishing an initial contraction group based on the result of the above precision analysis, and then extracting the main components of the structure from the initial shortening group by a mathematical method such as principal component analysis. , The step of constructing the shortening group vector, and finally, based on the shortening group vector, the degree of freedom is shortened for the precision finite element numerical model, the order reduction model is constructed, and the order reduction model that can satisfy the accuracy response is calculated. Includes steps to enable and reduce analysis time.
第４のステップでは、最適化行列式を確立し、離散材料最適化設計を行う。 In the fourth step, the optimization determinant is established and the discrete material optimization design is performed.
最適化行列式及び離散材料最適化モデルを設計要求に従って確立し、目標及び制約は、一般に、剛性、周波数、屈曲などの力学的応答を含む設計初期の具体的な要求に従うものとする。最適化行列式の一般式は、以下のとおりであり、
第１のステップで得られた代替材料ライブラリにおける離散材料を設計変数として、連続補間関数を用いて代替材料ライブラリにおける離散材料を特徴付ける。第２のステップで得られた分割３次元有限要素数値モデルを設計の幾何学的モデルとして、モデルの幾何学的分割及び最適化目標並びに制約に従って設計変数を割り当てる。第３のステップで得られた次数低減モデルを最適化過程で用いる数値解析モデルとして、次数低減モデルを用いて数値計算を行って目標と制約応答を得て、離散材料最適化設計を行い、繊維体積分率、繊維角度、積層順序などのマルチスケール変数の協調最適化設計を達成し、機能的要件を満たす最適化設計モデルを得る。具体的なステップは、以下を含む。 Using the discrete material in the alternative material library obtained in the first step as a design variable, the discrete material in the alternative material library is characterized by using a continuous interpolation function. The divided 3D finite element numerical model obtained in the second step is used as a geometric model for design, and design variables are assigned according to the geometric division and optimization goals and constraints of the model. As a numerical analysis model that uses the order reduction model obtained in the third step in the optimization process, numerical calculations are performed using the order reduction model to obtain targets and constraint responses, and discrete material optimization design is performed. Achieve co-optimized design of multi-scale variables such as volume fraction, fiber angle, stacking order, and obtain an optimized design model that meets functional requirements. Specific steps include:
(1) 連続補間式を用いて離散材料を連続的に特徴付け、材料補間フォーマットが式（２）に示される。
（２）有限要素次数低減モデルに基づいて、目標関数及び制約を計算し、感度情報を計算する。ここで、感度情報の計算方法には、直接法、付随法、差分法が含まれる。 (2) Based on the finite element order reduction model, the target function and constraints are calculated, and the sensitivity information is calculated. Here, the calculation method of the sensitivity information includes a direct method, an incidental method, and a difference method.
（３）最適化問題が収束するまで、勾配クラス最適化方法を用いて最適化問題を解く。ここで、最適化方法には、ニュートン法、擬似ニュートン法、移動漸近線法などが含まれる。 (3) Solve the optimization problem using the gradient class optimization method until the optimization problem converges. Here, the optimization method includes Newton's method, pseudo-Newton's method, moving asymptote method, and the like.
（４）最適化結果における中間密度を排除し、材料選択の明確な設計結果を得る。 (4) Eliminate the intermediate density in the optimization result and obtain a clear design result of material selection.
本発明の有益な効果は、本発明のハイブリッド繊維複合材料構造に関するクロススケールの複数階層の設計変数問題を、異なるスケールの設計変数を同じ階層に統合する代替材料ライブラリを確立することにより、離散材料最適化設計を展開することにより、新規な構造材料レイアウト構成を得ることで、ハイブリッド繊維複合材料の協調最適化設計を達成する。また、幾何学的分割とモデル次数低減方法により、最適化プロセスを加速し、高速最適化設計を達成する。本発明にて提供される方法は、ハイブリッド繊維複合材料構造の一体化設計を達成し、構造トポロジー、繊維含有量、繊維角度、積層順序などのクロススケール、マルチ変数の協調最適化設計を達成し、構造機能的要件を満たすとともに、構造重量を軽減し、材料コストを低減し、経済効果を高めることができることである。 The beneficial effect of the present invention is to establish an alternative material library that integrates the cross-scale multi-layer design variable problem of the hybrid fiber composite structure of the present invention into the same layer of design variables of different scales. By developing the optimized design, a new structural material layout configuration is obtained, and the coordinated optimized design of the hybrid fiber composite material is achieved. In addition, geometric division and model order reduction methods accelerate the optimization process and achieve high-speed optimization design. The method provided in the present invention achieves an integrated design of a hybrid fiber composite structure, cross-scales such as structural topology, fiber content, fiber angle, stacking order, and multivariate co-optimized design. It is possible to meet the structural and functional requirements, reduce the structural weight, reduce the material cost, and enhance the economic effect.
本発明により解決される方法の問題、採用される方法手段、及び達成される方法の効果をより明確にするために、以下、図面及び実施例を参照して本発明をさらに詳細に説明する。 In order to further clarify the problem of the method solved by the present invention, the method means adopted, and the effect of the method achieved, the present invention will be described in more detail below with reference to the drawings and examples.
図１は、本発明の実施例にて提供されるハイブリッド繊維複合材料の板巻きシェル構造に対する高速協調最適化方法を達成するフローチャートである。図１に示すように、本発明の実施例にて提供されるハイブリッド繊維複合材料の板巻きシェル構造に対する高速協調最適化方法は、１）代替材料ライブラリを確立するステップと、２）３次元有限要素数値モデルを確立し、幾何学的分割を行うステップと、３）モデル次数低減法を用いて次数低減数値解析モデルを確立するステップと、４）最適化行列式を確立し、離散材料最適化設計を行うステップと、を含む。連続補間関数を用いて離散代替材料ライブラリにおける離散材料を特徴付け、モデルの幾何学的分割及び最適化目標並びに制約に従って設計変数を割り当て、次数低減モデルを用いて数値計算を行って目標と制約応答を得て、離散材料最適化設計を行い、繊維体積分率、繊維角度、積層順序などのマルチ変数の協調最適化を達成し、機能的要件を満たす最適化設計構成を得る。具体的なステップは、以下を含む。 FIG. 1 is a flowchart for achieving a high-speed cooperative optimization method for a plate-wound shell structure of a hybrid fiber composite material provided in an embodiment of the present invention. As shown in FIG. 1, the high-speed cooperative optimization method for the plate-wound shell structure of the hybrid fiber composite material provided in the embodiment of the present invention includes 1) a step of establishing an alternative material library and 2) a three-dimensional finite. Steps to establish an element numerical model and perform geometric division, 3) Steps to establish a degree reduction numerical analysis model using the model order reduction method, and 4) Establish an optimization determinant to optimize discrete materials. Includes steps to make the design. Characterize discrete materials in a discrete alternative material library using continuous interpolation functions, assign design variables according to model geometric division and optimization goals and constraints, and perform numerical calculations using order reduction models to perform goals and constraint responses. To obtain an optimized design configuration that meets the functional requirements by performing discrete material optimization design and achieving co-optimization of multi-variables such as fiber integration rate, fiber angle, and stacking order. Specific steps include:
第１のステップでは、代替材料ライブラリを確立する。 The first step is to establish an alternative material library.
ハイブリッド繊維複合材料の選択可能な繊維体積分率及び繊維角度を決定し、異なる繊維体積分率の材料属性を、解析法を用いて計算し、異なる繊維角度及び積層順序配列を有する組合積層板の等価シェル剛性係数を、古典的な積層理論に基づいて計算し、全ての設計変数をマクロスケールに統合し、後続の離散材料最適化に使用するための代替材料ライブラリを確立する。図２は、ハイブリッド複合材料構造の協調最適化結果の概念を示す図である。 The selectable fiber volume fractions and fiber angles of the hybrid fiber composite were determined, the material attributes of the different fiber volume fractions were calculated using analytical methods, and the union laminates with different fiber angles and stacking sequence arrangements. Equivalent shell stiffness coefficients are calculated based on classical stacking theory, all design variables are integrated on a macro scale, and an alternative material library for subsequent discrete material optimization is established. FIG. 2 is a diagram showing the concept of the co-optimization result of the hybrid composite material structure.
第２のステップでは、３次元有限要素数値モデルを確立し、幾何学的分割を行う。 In the second step, a three-dimensional finite element numerical model is established and geometric division is performed.
本発明の実施例は、ハイブリッド繊維の矩形状薄板の最適化設計である。ＡＮＡＳＹＳ、ＡＢＡＱＵＳなどの市販有限要素ソフトウェア又は有限要素セルフプログラムから確立された構造の３次元有限要素数値モデルに基づいて、境界条件及び負荷を印加し、経験的及び機能的要件に従って幾何学的分割を行う。本実施例では、５×５の矩形の規則的領域に分割される。図３は、有限要素モデルの境界条件及び幾何学的分割を示す図である。 An embodiment of the present invention is an optimized design of a rectangular thin plate of hybrid fibers. Based on a 3D finite element numerical model of the structure established from commercial finite element software such as ANASYS, ABAQUS or finite element self-programming, boundary conditions and loads are applied and geometric divisions are performed according to empirical and functional requirements. conduct. In this embodiment, it is divided into regular areas of a 5 × 5 rectangle. FIG. 3 is a diagram showing the boundary conditions and geometric division of the finite element model.
第３のステップでは、モデル次数低減法を用いて次数低減数値解析モデルを確立する。 In the third step, a model order reduction method is used to establish a degree reduction numerical analysis model.
まず、離散設計域において最適なラテン超方格サンプリング法を用いて１００個の標本点を抽出し、標本点に基づいて線形屈曲解析を行い、初期ベクトル基を取得する。本実施例では、固有直交分解法（ＰｒｏｐｅｒＯｒｔｈｏｇｏｎａｌＤｅｃｏｍｐｏｓｉｔｉｏｎ、ＰＯＤ）方法を用いて抽出モデルの主成分を解析し、縮約基ベクトルを構築し、次数低減モデルを確立し、高速数値解析を達成する。 First, 100 sample points are extracted using the optimal Latin supersquare sampling method in the discrete design area, and linear bending analysis is performed based on the sample points to obtain an initial vector group. In this embodiment, the principal components of the extraction model are analyzed using the Proper Orthogonal Decomposition (POD) method, a reduction group vector is constructed, a degree reduction model is established, and high-speed numerical analysis is achieved.
第４のステップでは、最適化行列式を確立し、離散材料最適化設計を行う。 In the fourth step, the optimization determinant is established and the discrete material optimization design is performed.
最大屈曲負荷を最適化目標とし、材料コストを制約として最適化行列式を確立し、
第１のステップで得られた代替材料ライブラリにおける離散材料を設計変数として、連続補間関数を用いて代替材料ライブラリにおける離散材料を特徴付け、第２のステップで得られた分割された３次元有限要素数値モデルを設計の幾何学的モデルとして、モデルの幾何学的分割及び最適化目標並びに制約に従って設計変数を割り当て、第３のステップで得られた次数低減モデルを最適化過程で用いる数値解析モデルとして、次数低減モデルを用いて数値計算を行って目標と制約応答を得て、離散材料最適化設計を行い、繊維体積分率、繊維角度、積層順序などのマルチスケール変数の協調最適化設計を達成し、機能的要件を満たす最適化設計モデルを得る。図４は、初期設計構成であり、図５は、最適化された革新的構成設計であり、最適化の具体的なステップは、以下を含む。 Using the discrete material in the alternative material library obtained in the first step as a design variable, the discrete material in the alternative material library is characterized using a continuous interpolation function, and the divided three-dimensional finite element obtained in the second step. The numerical model is used as the geometric model of the design, the design variables are assigned according to the geometric division and optimization goals and constraints of the model, and the order reduction model obtained in the third step is used as the numerical analysis model in the optimization process. , Perform numerical calculation using order reduction model to obtain target and constraint response, perform discrete material optimization design, and achieve co-optimization design of multi-scale variables such as fiber body integral ratio, fiber angle, stacking order, etc. And obtain an optimized design model that meets the functional requirements. FIG. 4 is an initial design configuration, FIG. 5 is an optimized innovative configuration design, and specific steps of optimization include:
（１）連続補間式を用いて離散材料を連続的に特徴付け、材料補間フォーマットが以下に示される。
（２）有限要素次数低減モデルに基づいて、線形屈曲解析を行い、構造物の屈曲負荷を計算し、コンパニオン法を用いて感度情報を計算する。 (2) Based on the finite element order reduction model, linear bending analysis is performed, the bending load of the structure is calculated, and the sensitivity information is calculated using the companion method.
（３）最適化問題が収束するまで、数学的計画法における移動漸近線（ＭＭＡ）法を用いて最適化問題を解く。 (3) Solve the optimization problem using the moving asymptote (MMA) method in the mathematical programming method until the optimization problem converges.
（４）最適化結果における中間密度を排除し、材料選択の明確な設計結果を得る。図５に示される。 (4) Eliminate the intermediate density in the optimization result and obtain a clear design result of material selection. It is shown in FIG.
本発明は、ハイブリッド繊維複合材料の板巻きシェル構造に対する高速協調最適化方法を提供し、ハイブリッド繊維複合材料構造に関するクロススケールの複数階層の設計変数問題を、異なるスケールの設計変数を同じ階層に統合する代替材料ライブラリを確立することにより、離散材料最適化設計を展開することにより、新規な構造材料レイアウト構成を得ることで、ハイブリッド繊維複合材料の協調最適化設計を達成する。また、幾何学的分割とモデル次数低減方法により、最適化プロセスを加速し、高速最適化設計を達成する。本発明にて提供される方法は、ハイブリッド繊維複合材料構造の一体化設計を達成し、構造トポロジー、繊維含有量、繊維角度、積層順序などのクロススケール、マルチ変数の協調最適化設計を達成し、構造機能的要件を満たすとともに、構造重量を軽減し、材料コストを低減し、経済効果を高めることができる。 The present invention provides a fast coordinated optimization method for plate-wound shell structures in hybrid fiber composites to integrate cross-scale multi-tier design variable problems for hybrid fiber composite structures into the same hierarchy. By developing a discrete material optimization design by establishing an alternative material library to obtain a new structural material layout configuration, a coordinated optimization design of hybrid fiber composite materials will be achieved. In addition, geometric division and model order reduction methods accelerate the optimization process and achieve high-speed optimization design. The method provided in the present invention achieves an integrated design of a hybrid fiber composite structure, cross-scales such as structural topology, fiber content, fiber angle, stacking order, and multivariate co-optimized design. It can meet the structural and functional requirements, reduce the structural weight, reduce the material cost and enhance the economic effect.
最後に説明すべきなのは、上記の各実施例は、本発明の方法手段を説明するためにのみ使用され、それを限定するものではなく、前述の各実施例を参照して本発明を詳細に説明したが、当業者であれば、前述の各実施例に記載の方法手段に対する修正、又はその中の方法特徴の一部又は全部に対する同等の置換は、対応する方法手段の本質を本発明の各実施例の方法手段の範囲から逸脱しないことが理解されるべきである。 Last but not least, each of the above embodiments is used only to illustrate the method and means of the invention and is not intended to limit the invention in detail with reference to each of the above embodiments. As described above, those skilled in the art will find that modifications to the methods described in each of the above embodiments, or equivalent substitutions for some or all of the method features therein, are the essence of the corresponding methods of the invention. It should be understood that the method means of each embodiment do not deviate from the scope of the means.
Claims (5)
第１のステップでは、代替材料ライブラリを確立し、
試験方法、解析方法、数値計算方法を用いて、異なる繊維体積分率、異なるミクロ繊維分布を有する複合材料の材料属性を求め、古典的な積層板理論を用いて、異なる繊維角度及び積層順序積層板の一般的なシェル剛性係数を計算し、異なる組合積層板のシェル剛性係数を、後続の離散材料最適化の準備としてハイブリッド繊維複合材料の代替材料ライブラリを確立する離散材料最適化における設計変数として使用され、
代替材料ライブラリを確立し、異なるレベルの強さを有する材料を代替材料ライブラリに入れ、異なるスケールの設計変数を同じ階層に統合し、ハイブリッド繊維複合材料構造のマクロスケール、複数階層の変数協調最適化設計を達成し、
第２のステップでは、３次元有限要素数値モデルを確立し、幾何学的分割を行い、
複合材料の板巻きシェル構造の３次元有限要素数値モデルを確立し、有限要素数値モデルを構造の幾何学的形状、機能的要件に応じて幾何学的分割処理し、板巻きシェル構造に対する分割最適化設計は、構造の設計空間を拡大することができ、続いて、離散材料最適化により、各隣接する領域がいずれも異なる代替材料である可変剛性の板巻きシェル構造を得ることができ、
第３のステップでは、モデル次数低減法を用いて次数低減数値解析モデルを確立し、
モデル次数低減法を用いて有限要素数値モデルの次元を低減し、数値解析の計算コストを低減することで、ハイブリッド複合材料の高速協調最適化設計を可能にし、
第４のステップでは、最適化行列式を確立し、離散材料最適化設計を行い、
最適化行列式及び離散材料最適化モデルを設計要求に従って確立し、目標及び制約は、剛性、周波数、屈曲などの力学的応答を含む設計初期の具体的な要求に従うものとし、最適化行列式の一般式は、以下のとおりであり、
第１のステップで得られた代替材料ライブラリにおける離散材料を設計変数として、連続補間関数を用いて代替材料ライブラリにおける離散材料を特徴付け、第２のステップで得られた分割３次元有限要素数値モデルを設計の幾何学的モデルとして、モデルの幾何学的分割及び最適化目標並びに制約に従って設計変数を割り当て、第３のステップで得られた次数低減モデルを最適化過程で用いる数値解析モデルとして、次数低減モデルを用いて数値計算を行って目標と制約応答を得て、離散材料最適化設計を行うとともに、繊維体積分率、繊維角度、積層順序などのマルチ変数のクロススケール協調最適化設計を行い、機能的要件を満たす最適化設計構成を得る、
ことを特徴とするハイブリッド繊維複合材料の板巻きシェル構造に対する高速協調最適化方法。 A fast coordinated optimization method for plate-wound shell structures of hybrid fiber composites, including the following steps:
The first step is to establish an alternative material library and
Using test methods, analysis methods, and numerical calculation methods, the material attributes of composite materials with different fiber modulus and different microfiber distributions were determined, and using classical laminate theory, different fiber angles and stacking order were laminated. Calculate the general shell stiffness modulus of the board and use the shell stiffness modulus of different union laminates as a design variable in discrete material optimization to establish an alternative material library for hybrid fiber composites in preparation for subsequent discrete material optimization. Used,
Establish an alternative material library, put materials with different levels of strength into the alternative material library, integrate design variables of different scales into the same hierarchy, macroscale of hybrid fiber composite structure, variable co-optimization of multiple layers Achieved the design,
In the second step, a 3D finite element numerical model is established, geometric division is performed, and the process is performed.
Established a three-dimensional finite element numerical model of the plate-wound shell structure of composite material, geometrically divided the finite element numerical model according to the geometric shape and functional requirements of the structure, and optimized the division for the plate-wound shell structure. Geometry can expand the design space of the structure, followed by discrete material optimization to obtain variable-rigidity plate-wound shell structures in which each adjacent region is a different alternative material.
In the third step, a degree reduction numerical analysis model is established using the model degree reduction method.
By reducing the dimensions of the finite element numerical model using the model order reduction method and reducing the computational cost of numerical analysis, it enables high-speed cooperative optimization design of hybrid composite materials.
In the fourth step, the optimization determinant is established, the discrete material optimization design is performed, and the design is performed.
Optimized determinants and discrete material optimization models shall be established according to design requirements, and goals and constraints shall follow specific requirements in the early stages of design, including mechanical responses such as stiffness, frequency, bending, etc. The general formula is as follows:
Using the discrete material in the alternative material library obtained in the first step as a design variable, the discrete material in the alternative material library is characterized using a continuous interpolation function, and the divided three-dimensional finite element numerical model obtained in the second step. As a geometric model of the design, design variables are assigned according to the geometric division and optimization goals and constraints of the model, and the order reduction model obtained in the third step is used as a numerical analysis model in the optimization process. Numerical calculation is performed using the reduction model to obtain the target and constraint response, and discrete material optimization design is performed. At the same time, multi-variable cross-scale co-optimization design such as fiber integral ratio, fiber angle, and stacking order is performed. , Get an optimized design configuration that meets the functional requirements,
A high-speed coordinated optimization method for a plate-wound shell structure of a hybrid fiber composite material.
（１）連続補間式を用いて離散材料を連続的に特徴付け、材料補間フォーマットが式（２）に示される。
（３）最適化問題が収束するまで、勾配クラス最適化方法を用いて最適化問題を解き、ここで、最適化方法には、ニュートン法、擬似ニュートン法、移動漸近線法などが含まれ、
（４）最適化結果における中間密度を排除し、材料選択の明確な設計結果を得る、
ことを特徴とする請求項１に記載のハイブリッド繊維複合材料の板巻きシェル構造に対する高速協調最適化方法。 The fourth step specifically includes:
(1) Discrete materials are continuously characterized using a continuous interpolation formula, and the material interpolation format is shown in formula (2).
(3) Until the optimization problem converges, the optimization problem is solved using the gradient class optimization method, and the optimization method includes Newton's method, pseudo-Newton's method, moving asymptote method, and the like.
(4) Eliminate the intermediate density in the optimization result and obtain a clear design result of material selection.
The high-speed cooperative optimization method for a plate-wound shell structure of the hybrid fiber composite material according to claim 1.
ことを特徴とする請求項１又は２に記載のハイブリッド繊維複合材料の板巻きシェル構造に対する高速協調最適化方法。 The analysis method described in the first step is a mixed method, and the numerical method includes a homogenization method, a representative volume element method, and the like.
The high-speed cooperative optimization method for a plate-wound shell structure of the hybrid fiber composite material according to claim 1 or 2.
ことを特徴とする請求項１又は２に記載のハイブリッド繊維複合材料の板巻きシェル構造に対する高速協調最適化方法。 The model order reduction method described in the second step includes a feature positive value eigen-orthogonal decomposition method POD and a kinetic mode decomposition method DMD.
The high-speed cooperative optimization method for a plate-wound shell structure of the hybrid fiber composite material according to claim 1 or 2.
ことを特徴とする請求項３に記載のハイブリッド繊維複合材料の板巻きシェル構造に対する高速協調最適化方法。 The model order reduction method described in the second step includes a feature positive value eigen-orthogonal decomposition method POD and a kinetic mode decomposition method DMD.
The high-speed cooperative optimization method for a plate-wound shell structure of the hybrid fiber composite material according to claim 3.
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