WO2020211012A1 - Quick collaborative optimization method for hybrid fiber composite plate-shell structure - Google Patents
Quick collaborative optimization method for hybrid fiber composite plate-shell structure Download PDFInfo
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- the invention belongs to the technical field of composite material structure optimization design, and relates to a rapid collaborative optimization method for a hybrid fiber composite material plate and shell structure.
- Fiber-reinforced composite materials are composite materials formed by reinforcing fiber materials, such as glass fiber, carbon fiber, aramid fiber, etc., and matrix materials through forming processes such as winding, molding or pultrusion. Because fiber reinforced composite materials have the following characteristics: (1) high specific strength and large specific modulus; (2) material performance can be designed; (3) corrosion resistance and durability; (4) thermal expansion coefficient and concrete similar. These characteristics enable fiber-reinforced composite materials to meet the needs of modern structures for large-span, towering, heavy-load, light-weight and high-strength, and work under harsh conditions. At the same time, it can also meet the requirements of the industrial development of modern building construction. It is widely used in various civil buildings, bridges, highways, oceans, hydraulic structures and underground structures.
- Hybrid fiber composite materials There are many types of fiber-reinforced composite materials. Each type of fiber-reinforced composite material has its own advantages and disadvantages. For example, carbon fiber composite materials have high specific strength and high specific stiffness, but they are expensive and have low elongation. Therefore, they appeared in the 1970s. Hybrid fiber composite materials. Hybrid fiber composite material is a strong and tough structural material formed by two or more fibers through different hybrid methods. It not only retains the respective characteristics of the fiber and is compatible with different properties, but also shows some unique advantages. Currently, hybrid fiber composite materials are widely used in aviation, aerospace, automobiles, ships, medical and other fields. The design freedom of hybrid composite materials is greater than that of single fiber composite materials.
- hybrid composite component technology is more than that of single fiber composite material, which further expands the design freedom of components. If the rigidity of the wingtip of the glass fiber composite aircraft wing is not enough, carbon fiber can be appropriately used in the wingtip to make a hybrid composite member to increase the rigidity. Moreover, the design of this hybrid composite material component is not difficult to achieve in the process.
- Hybrid fiber composite materials can be designed according to the structural performance requirements, through different types of fibers, the relative content of different fibers, and different hybrid methods to meet the requirements for both composite structure and function. Where performance permits, replacing some high-priced fibers with low-priced fibers to make hybrid composite components can reduce material costs.
- hybrid fiber composite materials expands the freedom of structural design and the scope of application of materials, can reduce structural quality, reduce material costs, and improve economic benefits. Therefore, the invention of an efficient optimization design method suitable for the structure of hybrid fiber composite materials is becoming more and more important. This is also an effective way to give full play to the potential advantages of hybrid fiber composite materials and a necessary means to promote the wide application of hybrid fiber composite materials.
- the invention mainly solves the problem that the hybrid fiber composite material structure is difficult to carry out cross-scale design variable collaborative optimization, and solves the problem of low efficiency of large-scale structural calculation and optimization in engineering, and proposes a rapid collaborative optimization method for hybrid fiber composite material plate and shell structure.
- Use discrete material optimization methods to achieve collaborative optimization of hybrid fiber composite structures to solve different structural functional requirements Integrated design of composite materials.
- geometric partition and model reduction technology to improve the efficiency of numerical analysis and optimization, to solve the problem of low efficiency in large-scale structural optimization.
- This method fully considers the influence of the coupling relationship between variables of different scales on the macro response of the structure.
- a macro-variable stiffness innovative design is obtained, which expands the design space and can fully tap the potential of the hybrid fiber composite material to meet the design requirements And reduce the material cost of the innovative design configuration, thereby improving economic efficiency.
- a rapid collaborative optimization method for hybrid fiber composite plate and shell structure which specifically includes the following steps:
- the first step is to establish a library of candidate materials.
- the analytical method is a mixed formula method, and the numerical method includes a homogenization method, a representative voxel method, and the like.
- the second step is to establish a three-dimensional finite element numerical model and perform geometric partitioning.
- a three-dimensional finite element numerical model of composite plate and shell structure is established, and the finite element numerical model is geometrically partitioned according to the geometric shape and functional requirements of the structure.
- the geometric partition can not only accelerate the optimization process, but also make the optimization results meet the manufacturing process, and obtain a novel structural design form that is easy to process and manufacture.
- the partition optimization design of the plate and shell structure can expand the design space of the structure, and subsequent optimization of discrete materials can obtain a variable stiffness plate and shell structure with different candidate materials for each adjacent area.
- the third step is to use the model reduction method to establish a reduced-order numerical analysis model.
- model reduction methods to reduce the dimensions of the finite element numerical model and reduce the value Analyze the computational cost to achieve rapid collaborative optimization design of hybrid composite materials.
- the model reduction methods include: feature orthovalent intrinsic orthogonal decomposition (Proper Orthogonal Decomposition, POD) method, and dynamic mode decomposition (Dynamic Mode Decomposition, DMD) method.
- the steps to establish a reduced-order model mainly include: First, use sampling methods such as Latin hypercube and orthogonal sampling to extract a certain number of sample points in the discrete design space, and perform fine finite element numerical analysis on the selected sample points, based on the above-mentioned fine analysis As a result, an initial reduction base is established. Secondly, the key components of the structure are extracted from the initial reduced basis through mathematical methods such as principal component analysis, and the reduced basis vector is constructed. Finally, based on the reduced basis vector, the degree of freedom of the fine finite element numerical model is reduced, and a reduced-order model is constructed, so that the reduced-order model can calculate the response to the accuracy while reducing the analysis time.
- the fourth step is to establish an optimized column formula and perform an optimized design of discrete materials.
- the objectives and constraints are based on the specific requirements at the initial stage of the design, which generally include mechanical responses such as stiffness, frequency, and buckling.
- the general form of the optimized column is as follows:
- x is the design variable
- x i is the i-th component of the design variable
- L is the number of design variables
- u is the mechanical control equation
- F is the objective function
- G is the constraint function.
- the discrete materials in the candidate material library obtained in the first step are used as design variables, and a continuous interpolation function is used to characterize the discrete materials in the candidate material library.
- the partitioned three-dimensional finite element numerical model obtained in the second step is used as the geometric model of the design, and the design variables are allocated according to the geometric partition of the model and the optimization objectives and constraints.
- Use the reduced-order model obtained in the third step as the numerical analysis model used in the optimization process use the reduced-order model to perform numerical calculations to obtain the target and constraint response, and perform the discrete material optimization design to realize the fiber body fraction, fiber angle, and layer sequence
- the collaborative optimization design of other multi-scale variables obtains the optimal design configuration that meets the functional requirements.
- the specific steps include:
- C e is the element constitutive matrix
- w i is the weight coefficient of the candidate material
- C i is the equivalent shell stiffness matrix of the candidate material
- material units e j corresponding to the design variable i is an alternative numbers
- n e is the number of the finite element model unit
- p is the penalty value.
- the calculation methods of sensitivity information include direct method, adjoint method and difference method.
- the optimization methods include Newton's method, quasi-Newton's method, moving asymptote method and so on.
- the beneficial effects of the present invention are: in view of the cross-scale and multi-level design variables of the hybrid fiber composite material structure, the present invention unifies the design variables of different scales to the same level by establishing a candidate material library, and develops discrete material optimization design to obtain Novel structural material layout configuration, so as to realize the collaborative optimization design of hybrid fiber composite materials. And through geometric partition and model reduction methods, the optimization process is accelerated, and rapid optimization design is realized.
- the method proposed in the present invention can realize the integrated design of the hybrid fiber composite material structure, realize the cross-scale and multivariable collaborative optimization design of structure topology, fiber content, fiber angle, layup sequence, etc., and meet the needs of structural functions while reducing the structure Quality, reduce material costs and improve economic efficiency.
- FIG. 1 is an implementation flow chart of a method for rapid collaborative optimization of hybrid fiber composite material plate and shell structure provided by an embodiment of the present invention
- Figure 2 is a conceptual diagram of optimization results provided by an example of the rectangular thin plate of the present invention.
- (a) is the macroscopic material distribution of the hybrid fiber composite plate;
- (b) is the order of fiber angle layup and the internal fiber body and fiber distribution.
- Fig. 3 is a schematic diagram of the design domain, load boundary and geometric division of the rectangular thin plate of the present invention.
- Figure 4 is the initial design configuration provided by the example of the rectangular thin plate of the present invention; (a) is the angle distribution of the first layer of the laminate; (b) is the angle distribution of the second layer of the laminate;
- Figure 5 is a schematic diagram of an innovative configuration obtained in a method for rapid collaborative optimization of hybrid fiber composite slab and shell structure provided by the example of the rectangular thin plate of the present invention; (a) is the angle distribution diagram of the first layer of the laminate; (b) ) Is the angle distribution diagram of the second layer of laminate;
- Fig. 1 is a flow chart of the implementation of a method for rapid collaborative optimization of hybrid fiber composite material slab and shell structure provided by an embodiment of the present invention.
- a method for rapid collaborative optimization of hybrid fiber composite slab-shell structure provided by an embodiment of the present invention includes: 1) establishing a candidate material library; 2) establishing a three-dimensional finite element numerical model and performing geometric partitioning; 3) Use the model reduction method to establish a reduced-order numerical analysis model; 4) Establish an optimized formula to optimize the design of discrete materials.
- the first step is to establish a library of candidate materials.
- FIG. 1 is a conceptual diagram of the results of collaborative optimization of hybrid composite structures.
- the second step is to establish a three-dimensional finite element numerical model and perform geometric partitioning.
- the example of the present invention is the optimized design of the hybrid fiber rectangular thin plate. Based on commercial finite element software such as ANASYS, ABAQUS or self-compiled finite element program, a three-dimensional finite element numerical model of the structure is established, boundary conditions and loads are applied, and geometrical partitioning is performed according to experience and functional requirements.
- the partition in this example is a 5*5 rectangular regular partition.
- Figure 3 is a schematic diagram of the boundary conditions and geometric partitions of the finite element model.
- the third step is to use the model reduction method to establish a reduced-order numerical analysis model.
- This example uses the Proper Orthogonal Decomposition (POD) method to analyze and extract the main components of the model, construct a reduced base vector, establish a reduced-order model, and achieve rapid numerical analysis.
- POD Proper Orthogonal Decomposition
- the fourth step is to establish an optimized column formula and perform an optimized design of discrete materials.
- P is the buckling load of the structure
- ⁇ j is the j-th eigenvalue obtained from linear buckling analysis
- N ⁇ is the total number of degrees of freedom of the model
- K is the model stiffness matrix
- K ⁇ is the geometric stiffness matrix of the model
- ⁇ j is The eigenvector corresponding to the j-th eigenvalue
- x i is the design variable
- x i is the lower limit of the design variable
- C is the material cost of the structure
- Constraint for the upper limit of material cost is the material cost of the structure.
- C e is the element constitutive matrix
- w i is the weight coefficient of the candidate material
- C i is the equivalent shell stiffness matrix of the candidate material
- material units e j corresponding to the design variable, i is an alternative numbers
- n e is the number of the finite element model unit
- p is the penalty value.
- the present invention provides a rapid collaborative optimization method for hybrid fiber composite material plate and shell structure, aiming at the problem of cross-scale and multi-level design variables of hybrid fiber composite material structure, and unified design variables of different scales to the same by establishing a candidate material library
- a rapid collaborative optimization method for hybrid fiber composite material plate and shell structure aiming at the problem of cross-scale and multi-level design variables of hybrid fiber composite material structure, and unified design variables of different scales to the same by establishing a candidate material library
- the method proposed in the present invention can realize the integrated design of the hybrid fiber composite material structure, realize the cross-scale and multivariable collaborative optimization design of structure topology, fiber content, fiber angle, layup sequence, etc., and meet the needs of structural functions while reducing the structure Quality, reduce material costs and improve economic efficiency.
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Abstract
A quick collaborative optimization method for a hybrid fiber composite plate-shell structure, belongs to the technical field of optimization design of composite structures. Said method comprises the steps: 1) establishing an alternative material library; 2) establishing a three-dimensional finite element numerical model and performing geometric partition; 3) establishing a reduced-order numerical analysis model using a model order reduction method; and 4) establishing an optimization formulation, and performing dispersed material optimization design. A continuous interpolation function is used to represent dispersed materials in the material library; design variables are allocated according to geometric partitions of a model and the optimization target and constraint; a reduced-order model is used to perform numerical calculation, so as to obtain a target and constraint response; and a dispersed material optimization design is performed to achieve multi-variable collaborative optimization, and obtain an optimal design configuration. The method can achieve an integrated design of a hybrid fiber composite structure, and achieve a collaborative optimization design of multi-level variables such as structure topology, fiber content, fiber angle and ply stacking sequence, thereby reducing structure weight and reducing material costs while satisfying structure function requirements.
Description
本发明属于复合材料结构优化设计技术领域，涉及一种面向混杂纤维复合材料板壳结构的快速协同优化方法。The invention belongs to the technical field of composite material structure optimization design, and relates to a rapid collaborative optimization method for a hybrid fiber composite material plate and shell structure.
纤维增强复合材料是由增强纤维材料，如玻璃纤维、碳纤维、芳纶纤维等，与基体材料经过缠绕，模压或拉挤等成型工艺而形成的复合材料。由于纤维增强复合材料具有如下特点：(1)比强度高,比模量大；(2)材料性能具有可设计性；(3)抗腐蚀性和耐久性能好；(4)热膨胀系数与混凝土的相近。这些特点使得纤维增强复合材料能满足现代结构向大跨、高耸、重载、轻质高强以及在恶劣条件下工作发展的需要，同时也能满足现代建筑施工工业化发展的要求，因此被越来越广泛地应用于各种民用建筑、桥梁、公路、海洋、水工结构以及地下结构等领域中。纤维增强复合材料种类很多，每种增强纤维复合材料都有各自的有点和不足，比如碳纤维复合材料比强度大、比刚度高，但价格昂贵，并且延伸率低，因此在20世纪70年代出现了混杂纤维复合材料。混杂纤维复合材料是由两种及两种以上的纤维通过不同的混杂方式，形成的一种强韧性结构材料。它不仅保留了纤维的各自特点，兼容不同的属性，又表现出一些独特的优势。目前，混杂纤维复合材料被广泛应用于航空、航天、汽车、船舶、医疗等领域。混杂复合材料构件的设计自由度较单一纤维复合材料要大。混杂复合材料构件工艺实现的可能性超过单一纤维复合材料，相应又进一步扩大了构件的设计自由度。如玻璃纤维复合材料飞机机翼的翼尖部位刚度不够，可在翼尖部位适当使用碳纤维，制成混杂复合材料构件来增加刚度。而且这种混杂复合材料构件的设计在工艺上是不难实现的。混杂纤维复合材料可以根据结构使用性能要求， 通过不同类型纤维、不同纤维的相对含量、不同的混杂方式进行设计，以满足对复合材料结构和功能兼备的要求。在性能允许的情况下，用价格低的纤维取代部分高价纤维制成混杂复合材料构件可以降低材料成本。另一方面，使用适量高价但高性能的纤维制成混杂复合材料构件，获得材料的高性能/价格比，同样获得大的经济效益。混杂纤维复合材料的使用扩大了结构设计的自由度和材料的适用范围，能够减轻结构质量，降低材料成本，提高经济效益。因此，发明适用于混杂纤维复合材料结构的高效优化设计方法越发重要，这也是充分发挥混杂纤维复合材料潜在优势的有效途径，推动混杂纤维复合材料广泛应用的必要手段。Fiber-reinforced composite materials are composite materials formed by reinforcing fiber materials, such as glass fiber, carbon fiber, aramid fiber, etc., and matrix materials through forming processes such as winding, molding or pultrusion. Because fiber reinforced composite materials have the following characteristics: (1) high specific strength and large specific modulus; (2) material performance can be designed; (3) corrosion resistance and durability; (4) thermal expansion coefficient and concrete similar. These characteristics enable fiber-reinforced composite materials to meet the needs of modern structures for large-span, towering, heavy-load, light-weight and high-strength, and work under harsh conditions. At the same time, it can also meet the requirements of the industrial development of modern building construction. It is widely used in various civil buildings, bridges, highways, oceans, hydraulic structures and underground structures. There are many types of fiber-reinforced composite materials. Each type of fiber-reinforced composite material has its own advantages and disadvantages. For example, carbon fiber composite materials have high specific strength and high specific stiffness, but they are expensive and have low elongation. Therefore, they appeared in the 1970s. Hybrid fiber composite materials. Hybrid fiber composite material is a strong and tough structural material formed by two or more fibers through different hybrid methods. It not only retains the respective characteristics of the fiber and is compatible with different properties, but also shows some unique advantages. Currently, hybrid fiber composite materials are widely used in aviation, aerospace, automobiles, ships, medical and other fields. The design freedom of hybrid composite materials is greater than that of single fiber composite materials. The possibility of hybrid composite component technology is more than that of single fiber composite material, which further expands the design freedom of components. If the rigidity of the wingtip of the glass fiber composite aircraft wing is not enough, carbon fiber can be appropriately used in the wingtip to make a hybrid composite member to increase the rigidity. Moreover, the design of this hybrid composite material component is not difficult to achieve in the process. Hybrid fiber composite materials can be designed according to the structural performance requirements, through different types of fibers, the relative content of different fibers, and different hybrid methods to meet the requirements for both composite structure and function. Where performance permits, replacing some high-priced fibers with low-priced fibers to make hybrid composite components can reduce material costs. On the other hand, the use of appropriate amount of expensive but high-performance fibers to make hybrid composite components can achieve the high performance/price ratio of the material and also obtain large economic benefits. The use of hybrid fiber composite materials expands the freedom of structural design and the scope of application of materials, can reduce structural quality, reduce material costs, and improve economic benefits. Therefore, the invention of an efficient optimization design method suitable for the structure of hybrid fiber composite materials is becoming more and more important. This is also an effective way to give full play to the potential advantages of hybrid fiber composite materials and a necessary means to promote the wide application of hybrid fiber composite materials.
随着有限元等数值分析方法的快速发展，基于数值模型的结构优化方法已成为复合材料结构优化设计的重要途径之一。在常规的复合材料结构设计中，一般按照拓扑、形状、尺寸优化的顺序，将复合材料的纤维角度、纤维含量、铺层顺序作为设计变量，逐级分步的将不同尺度的设计变量进行解耦式优化。变量分组解耦的方式虽然提高了优化效率，但忽视了变量间耦合关系对结构响应的影响，限制了设计空间，不能充分发挥混杂纤维复合材料的优势。根据文献调研，目前还缺少有效的混杂纤维板壳结构高效优化设计方法。因此，亟需发明一种面向混杂纤维复合材料板壳结构的快速协同优化方法，同时实现混杂复合材料结构拓扑、纤维含量、纤维角度、铺层顺序等跨尺度变量的高效协同优化设计，满足结构功能需要的同时，减轻结构质量，降低材料成本，提高经济效益。With the rapid development of numerical analysis methods such as finite element, structural optimization methods based on numerical models have become one of the important ways to optimize the design of composite structures. In the conventional composite material structure design, generally according to the order of topology, shape and size optimization, the fiber angle, fiber content, and layup order of the composite material are used as design variables, and the design variables of different scales are solved step by step. Coupling optimization. Although the method of variable grouping and decoupling improves the optimization efficiency, it ignores the influence of the coupling relationship between variables on the structure response, limits the design space, and cannot give full play to the advantages of hybrid fiber composites. According to literature research, there is still a lack of effective methods for the efficient optimization of hybrid fiber shell structures. Therefore, it is urgent to invent a rapid collaborative optimization method for hybrid fiber composite slab and shell structure, and realize the efficient collaborative optimization design of cross-scale variables such as hybrid composite structure topology, fiber content, fiber angle, and layup order to meet the structural requirements While the function is needed, the structure quality is reduced, the material cost is reduced, and the economic efficiency is improved.
发明内容Summary of the invention
本发明主要解决混杂纤维复合材料结构难以进行跨尺度设计变量协同优化问题，并解决工程中大规模结构计算优化效率低的问题，提出一种面向混杂纤 维复合材料板壳结构的快速协同优化方法。将纤维含量、纤维角度、拓扑变量等跨尺度、多层级设计变量统一到同一宏观尺度并建立备选材料库，使用离散材料优化方法实现混杂纤维复合材料结构的协同优化，解决不同结构功能要求下的复合材料一体化设计。并结合几何分区和模型降阶技术提高数值分析及优化效率，解决大规模结构优化效率低的问题。该方法充分考虑了不同尺度变量耦合关系对结构宏观响应的影响，通过材料分区布局优化得到一种宏观变刚度创新设计，扩大了设计空间，能够充分挖掘混杂纤维复合材料的潜力，提供满足设计要求并降低材料成本的创新设计构型，从而提高经济效益。The invention mainly solves the problem that the hybrid fiber composite material structure is difficult to carry out cross-scale design variable collaborative optimization, and solves the problem of low efficiency of large-scale structural calculation and optimization in engineering, and proposes a rapid collaborative optimization method for hybrid fiber composite material plate and shell structure. Unify the cross-scale and multi-level design variables such as fiber content, fiber angle, and topological variables into the same macro-scale and establish a candidate material library. Use discrete material optimization methods to achieve collaborative optimization of hybrid fiber composite structures to solve different structural functional requirements Integrated design of composite materials. And combined with geometric partition and model reduction technology to improve the efficiency of numerical analysis and optimization, to solve the problem of low efficiency in large-scale structural optimization. This method fully considers the influence of the coupling relationship between variables of different scales on the macro response of the structure. Through the optimization of the material partition layout, a macro-variable stiffness innovative design is obtained, which expands the design space and can fully tap the potential of the hybrid fiber composite material to meet the design requirements And reduce the material cost of the innovative design configuration, thereby improving economic efficiency.
为了达到上述目的，本发明的技术方案为：In order to achieve the above objective, the technical solution of the present invention is:
一种面向混杂纤维复合材料板壳结构的快速协同优化方法，具体包括以下步骤：A rapid collaborative optimization method for hybrid fiber composite plate and shell structure, which specifically includes the following steps:
第一步，建立备选材料库。The first step is to establish a library of candidate materials.
采用实验方法、解析方法或数值计算方法获得具有不同纤维体分比、不同微观纤维分布的复合材料的材料属性，并使用经典层合板理论计算不同纤维角度及铺层顺序层合板的一般壳刚度系数。将不同组合层合板的壳刚度系数作为备选材料(离散材料优化中的设计变量)，建立混杂纤维复合材料的备选材料库，为后续的离散材料优化做好准备。建立备选材料库，将具有不同强弱水平的材料收入备选材料库是本专利实现跨尺度协同优化的关键技术，可以将不同尺度的设计变量统一到同一层级，并充分考虑不同尺度变量间的耦合关系，从而实现混杂纤维复合材料结构的跨尺度、多层级变量协同优化设计。Use experimental methods, analytical methods or numerical calculation methods to obtain the material properties of composite materials with different fiber-to-body ratios and different micro-fiber distributions, and use classical laminate theory to calculate the general shell stiffness coefficients of laminates with different fiber angles and layup sequences . The shell stiffness coefficients of different composite laminates are used as candidate materials (design variables in the optimization of discrete materials), and a candidate material library of hybrid fiber composite materials is established to prepare for the subsequent optimization of discrete materials. Establishing a candidate material library and collecting materials with different strengths and weaknesses into the candidate material library is the key technology of this patent to achieve cross-scale collaborative optimization. It can unify design variables of different scales to the same level, and fully consider the difference between variables of different scales. In order to realize the cross-scale and multi-level variable collaborative optimization design of the hybrid fiber composite structure.
所述的解析方法为混合公式法，数值方法包括均匀化方法、代表体元法等。The analytical method is a mixed formula method, and the numerical method includes a homogenization method, a representative voxel method, and the like.
第二步，建立三维有限元数值模型并进行几何分区。The second step is to establish a three-dimensional finite element numerical model and perform geometric partitioning.
建立复合材料板壳结构三维有限元数值模型，根据结构的几何形状、功能 要求将有限元数值模型进行几何分区处理。几何分区不仅可以加速优化进程，还可以使优化结果满足加工制造工艺，得到易于加工制造的新颖的结构设计形式。对板壳结构进行分区优化设计可以扩大结构的设计空间，后续通过离散材料优化可以获得每个相邻区域都为不同备选材料的变刚度板壳结构。A three-dimensional finite element numerical model of composite plate and shell structure is established, and the finite element numerical model is geometrically partitioned according to the geometric shape and functional requirements of the structure. The geometric partition can not only accelerate the optimization process, but also make the optimization results meet the manufacturing process, and obtain a novel structural design form that is easy to process and manufacture. The partition optimization design of the plate and shell structure can expand the design space of the structure, and subsequent optimization of discrete materials can obtain a variable stiffness plate and shell structure with different candidate materials for each adjacent area.
第三步，使用模型降阶方法，建立降阶数值分析模型。The third step is to use the model reduction method to establish a reduced-order numerical analysis model.
对于具有复杂结构细节的混杂纤维板壳结构，基于精细模型开展有限元分析需要大量的计算资源和计算时长，为加速优化进程，本发明使用模型降阶的方法降低有限元数值模型的维度，降低数值分析的计算成本，从而实现混杂复合材料快速协同优化设计。所述的模型降阶方法包括：特征正价本征正交分解(Proper Orthogonal Decomposition，POD)方法、动力学模态分解(Dynamic Mode Decomposition，DMD)方法。For hybrid fiber slabs and shell structures with complex structural details, finite element analysis based on fine models requires a lot of computing resources and calculation time. In order to accelerate the optimization process, the present invention uses model reduction methods to reduce the dimensions of the finite element numerical model and reduce the value Analyze the computational cost to achieve rapid collaborative optimization design of hybrid composite materials. The model reduction methods include: feature orthovalent intrinsic orthogonal decomposition (Proper Orthogonal Decomposition, POD) method, and dynamic mode decomposition (Dynamic Mode Decomposition, DMD) method.
建立降阶模型步骤主要包括：首先，使用拉丁超立方、正交采样等抽样方法在离散设计空间中抽取一定数目的样本点，并对选取样本点进行精细有限元数值分析，基于上述精细分析的结果建立初始减缩基。其次，通过主成分分析等数学方法从初始减缩基中提取结构的关键成分，构造减缩基向量。最后，基于减缩基向量，对精细有限元数值模型进行自由度减缩，构造出降阶模型，使降阶模型在能计算满足精度响应的同时减少分析时间。The steps to establish a reduced-order model mainly include: First, use sampling methods such as Latin hypercube and orthogonal sampling to extract a certain number of sample points in the discrete design space, and perform fine finite element numerical analysis on the selected sample points, based on the above-mentioned fine analysis As a result, an initial reduction base is established. Secondly, the key components of the structure are extracted from the initial reduced basis through mathematical methods such as principal component analysis, and the reduced basis vector is constructed. Finally, based on the reduced basis vector, the degree of freedom of the fine finite element numerical model is reduced, and a reduced-order model is constructed, so that the reduced-order model can calculate the response to the accuracy while reducing the analysis time.
第四步，建立优化列式，进行离散材料优化设计。The fourth step is to establish an optimized column formula and perform an optimized design of discrete materials.
根据设计要求建立优化列式和离散材料优化模型，目标和约束依据设计初期的具体要求，一般包括刚度、频率、屈曲等力学响应。优化列式的一般形式如下：Establish optimized columns and discrete material optimization models according to the design requirements. The objectives and constraints are based on the specific requirements at the initial stage of the design, which generally include mechanical responses such as stiffness, frequency, and buckling. The general form of the optimized column is as follows:
优化目标:minF(u(x),x)Optimization goal: minF(u(x),x)
优化约束:G
i(x)≤0 (1)
Optimization constraint: G i (x)≤0 (1)
0≤x
i≤1,i＝1,...,L
0≤x i ≤1,i＝1,...,L
其中，x为设计变量，x
i为设计变量第i个分量，L为设计变量的数量，u为力学控制方程，F为目标函数，G为约束函数。
Among them, x is the design variable, x i is the i-th component of the design variable, L is the number of design variables, u is the mechanical control equation, F is the objective function, and G is the constraint function.
将第一步获得的备选材料库中的离散材料作为设计变量，使用连续插值函数表征备选材料库中的离散材料。将第二步获得的分区化三维有限元数值模型作为设计的几何模型，依据模型的几何分区和优化目标及约束分配设计变量。将第三步获得的降阶模型作为优化过程中使用的数值分析模型，使用降阶模型进行数值计算获得目标和约束响应，进行离散材料优化设计，实现纤维体分比、纤维角度、铺层顺序等多尺度变量的协同优化设计，获得满足功能要求的最优设计构型。具体步骤包括：The discrete materials in the candidate material library obtained in the first step are used as design variables, and a continuous interpolation function is used to characterize the discrete materials in the candidate material library. The partitioned three-dimensional finite element numerical model obtained in the second step is used as the geometric model of the design, and the design variables are allocated according to the geometric partition of the model and the optimization objectives and constraints. Use the reduced-order model obtained in the third step as the numerical analysis model used in the optimization process, use the reduced-order model to perform numerical calculations to obtain the target and constraint response, and perform the discrete material optimization design to realize the fiber body fraction, fiber angle, and layer sequence The collaborative optimization design of other multi-scale variables obtains the optimal design configuration that meets the functional requirements. The specific steps include:
(1)使用连续插值公式将离散材料连续化表征，材料插值格式如公式(2)所示。(1) Use continuous interpolation formula to continuously characterize discrete materials, and the material interpolation format is shown in formula (2).
其中，C
e为单元本构矩阵，w
i为备选材料的权重系数，C
i为备选材料的等效壳刚度矩阵，
为单元e对应备选材料j的设计变量,i为备选材料编号，n
e为有限元模型单元总数，p为罚值。
Among them, C e is the element constitutive matrix, w i is the weight coefficient of the candidate material, C i is the equivalent shell stiffness matrix of the candidate material, Alternatively the material units e j corresponding to the design variable, i is an alternative numbers, n e is the number of the finite element model unit, p is the penalty value.
(2)基于有限元降阶模型计算目标函数和约束，并计算灵敏度信息。其中灵敏度信息的计算方法包括直接法，伴随法和差分法。(2) Calculate the objective function and constraints based on the finite element reduced-order model, and calculate the sensitivity information. The calculation methods of sensitivity information include direct method, adjoint method and difference method.
(3)使用梯度类优化方法求解优化问题，直至优化问题收敛。其中优化方法包括牛顿法、拟牛顿法、移动渐近线法等。(3) Use gradient optimization methods to solve the optimization problem until the optimization problem converges. The optimization methods include Newton's method, quasi-Newton's method, moving asymptote method and so on.
(4)消除优化结果中的中间密度，获得材料选择明确的设计结果。(4) Eliminate the intermediate density in the optimization result, and obtain a clear design result for material selection.
本发明的有益效果为：本发明针对混杂纤维复合材料结构具有跨尺度、多层级设计变量问题，通过建立备选材料库将不同尺度的设计变量统一至同一层级，通过开展离散材料优化设计，获得新颖的结构材料布局构型，从而实现混杂纤维复合材料的协同优化设计。并通过几何分区和模型降阶方法，加速了优化进程，实现快速优化设计。本发明提出的方法能实现混杂纤维复合材料结构的一体化设计，实现结构拓扑、纤维含量、纤维角度、铺层顺序等跨尺度、多变量的协同优化设计，满足结构功能需要的同时，减轻结构质量，降低材料成本，提高经济效益。The beneficial effects of the present invention are: in view of the cross-scale and multi-level design variables of the hybrid fiber composite material structure, the present invention unifies the design variables of different scales to the same level by establishing a candidate material library, and develops discrete material optimization design to obtain Novel structural material layout configuration, so as to realize the collaborative optimization design of hybrid fiber composite materials. And through geometric partition and model reduction methods, the optimization process is accelerated, and rapid optimization design is realized. The method proposed in the present invention can realize the integrated design of the hybrid fiber composite material structure, realize the cross-scale and multivariable collaborative optimization design of structure topology, fiber content, fiber angle, layup sequence, etc., and meet the needs of structural functions while reducing the structure Quality, reduce material costs and improve economic efficiency.
图1为本发明实施例提供的一种面向混杂纤维复合材料板壳结构的快速协同优化方法的实现流程图；FIG. 1 is an implementation flow chart of a method for rapid collaborative optimization of hybrid fiber composite material plate and shell structure provided by an embodiment of the present invention;
图2为本发明矩形薄板实例提供的优化结果概念图；(a)为混杂纤维复合材料板宏观材料分布；(b)为纤维角度铺层顺序及内部纤维体和纤维分布。Figure 2 is a conceptual diagram of optimization results provided by an example of the rectangular thin plate of the present invention; (a) is the macroscopic material distribution of the hybrid fiber composite plate; (b) is the order of fiber angle layup and the internal fiber body and fiber distribution.
图3为本发明矩形薄板实例提供设计域，载荷边界及几何分区示意图；Fig. 3 is a schematic diagram of the design domain, load boundary and geometric division of the rectangular thin plate of the present invention;
图4为本发明矩形薄板实例提供的初始设计构型；(a)为层合板第一层铺层角度分布图；(b)为层合板第二层铺层角度分布图；Figure 4 is the initial design configuration provided by the example of the rectangular thin plate of the present invention; (a) is the angle distribution of the first layer of the laminate; (b) is the angle distribution of the second layer of the laminate;
图5为本发明矩形薄板实例提供的一种面向混杂纤维复合材料板壳结构的快速协同优化方法中获得的创新构型示意图；(a)为层合板第一层铺层角度分布图；(b)为层合板第二层铺层角度分布图；Figure 5 is a schematic diagram of an innovative configuration obtained in a method for rapid collaborative optimization of hybrid fiber composite slab and shell structure provided by the example of the rectangular thin plate of the present invention; (a) is the angle distribution diagram of the first layer of the laminate; (b) ) Is the angle distribution diagram of the second layer of laminate;
为使本发明解决的方法问题、采用的方法方案和达到的方法效果更加清楚，下面结合附图和实施例对本发明作进一步的详细说明。In order to make the method problem solved by the present invention, the method scheme adopted and the method effect achieved by the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.
图1为本发明实施例提供的一种面向混杂纤维复合材料板壳结构的快速协 同优化方法的实现流程图。如图1所示，本发明实施例提供的一种面向混杂纤维复合材料板壳结构的快速协同优化方法包括：1)建立备选材料库；2)建立三维有限元数值模型并进行几何分区；3)使用模型降阶方法，建立降阶数值分析模型；4)建立优化列式，进行离散材料优化设计。使用连续插值函数表征离散备选材料库中的离散材料，依据模型的几何分区和优化目标及约束分配设计变量，使用降阶模型进行数值计算获得目标和约束响应，进行离散材料优化设计，实现纤维体分比、纤维角度、铺层顺序等多变量协同优化，获得满足功能要求的最优设计构型。具体步骤如下：Fig. 1 is a flow chart of the implementation of a method for rapid collaborative optimization of hybrid fiber composite material slab and shell structure provided by an embodiment of the present invention. As shown in FIG. 1, a method for rapid collaborative optimization of hybrid fiber composite slab-shell structure provided by an embodiment of the present invention includes: 1) establishing a candidate material library; 2) establishing a three-dimensional finite element numerical model and performing geometric partitioning; 3) Use the model reduction method to establish a reduced-order numerical analysis model; 4) Establish an optimized formula to optimize the design of discrete materials. Use continuous interpolation function to characterize the discrete materials in the discrete candidate material library, assign design variables according to the model's geometric partition and optimization goals and constraints, use the reduced-order model to perform numerical calculations to obtain targets and constraint responses, and perform discrete material optimization design to achieve fiber Multi-variable collaborative optimization, such as volume ratio, fiber angle, and layering sequence, obtains the optimal design configuration that meets the functional requirements. Specific steps are as follows:
第一步，建立备选材料库。The first step is to establish a library of candidate materials.
确定混杂纤维复合材料可选的纤维体分比和纤维角度，使用解析法计算不同纤维体分比的材料属性，并基于经典层合理论计算拥有不同纤维角度和铺层顺序排列组合层合板的等效壳刚度系数，将所有设计变量统一至宏观尺度，建立备选材料库，供后续离散材料优化使用。图2为混杂复合材料结构协同优化结果的概念示意图。Determine the optional fiber fraction and fiber angle of the hybrid fiber composite material, use the analytical method to calculate the material properties of different fiber fractions, and calculate the composite laminates with different fiber angles and layup sequences based on classical lamination theory. Effective shell stiffness coefficient, unify all design variables to the macro-scale, establish a candidate material library for subsequent optimization of discrete materials. Figure 2 is a conceptual diagram of the results of collaborative optimization of hybrid composite structures.
第二步，建立三维有限元数值模型并进行几何分区。The second step is to establish a three-dimensional finite element numerical model and perform geometric partitioning.
本发明实例为混杂纤维矩形薄板优化设计。基于ANASYS,ABAQUS等商用有限元软件或者自编有限元程序建立结构的三维有限元数值模型，施加边界条件和载荷，并按照经验和功能需求进行几何分区。本实例中分区为5*5的矩形规则分区。图3为有限元模型的边界条件和几何分区示意图。The example of the present invention is the optimized design of the hybrid fiber rectangular thin plate. Based on commercial finite element software such as ANASYS, ABAQUS or self-compiled finite element program, a three-dimensional finite element numerical model of the structure is established, boundary conditions and loads are applied, and geometrical partitioning is performed according to experience and functional requirements. The partition in this example is a 5*5 rectangular regular partition. Figure 3 is a schematic diagram of the boundary conditions and geometric partitions of the finite element model.
第三步，使用模型降阶方法，建立降阶数值分析模型。The third step is to use the model reduction method to establish a reduced-order numerical analysis model.
首先，在离散设计域中使用最优拉丁超立方方法抽取一百个样本点，基于样本点进行线性屈曲分析，获取初始向量基。本实例使用本征正交分解(Proper Orthogonal Decomposition，POD)方法分析提取模型的主要成分，构造减缩基向 量，建立降阶模型，实现快速数值分析。First, use the optimal Latin hypercube method to extract one hundred sample points in the discrete design domain, and perform linear buckling analysis based on the sample points to obtain the initial vector basis. This example uses the Proper Orthogonal Decomposition (POD) method to analyze and extract the main components of the model, construct a reduced base vector, establish a reduced-order model, and achieve rapid numerical analysis.
第四步，建立优化列式，进行离散材料优化设计。The fourth step is to establish an optimized column formula and perform an optimized design of discrete materials.
建立以最大屈曲载荷为优化目标，材料成本为约束的优化列式：Establish an optimization formula with the maximum buckling load as the optimization goal and material cost as the constraint:
其中，P为结构的屈曲载荷，λ
j为线性屈曲分析得到的第j个特征值,N
λ为模型的自由度总数，K为模型刚度矩阵，K
σ为模型的几何刚度矩阵，Φ
j为第j个特征值对应的特征向量，x
i为设计变量，
x
i
为设计变量的下限值，
为设计变量的上限值，C为结构的材料成本，
为材料成本上限约束。
Among them, P is the buckling load of the structure, λ j is the j-th eigenvalue obtained from linear buckling analysis, N λ is the total number of degrees of freedom of the model, K is the model stiffness matrix, K σ is the geometric stiffness matrix of the model, and Φ j is The eigenvector corresponding to the j-th eigenvalue, x i is the design variable, x i is the lower limit of the design variable, Is the upper limit of the design variable, C is the material cost of the structure, Constraint for the upper limit of material cost.
将第一步获得的备选材料库中的离散材料作为设计变量，使用连续插值函数表征备选材料库中的离散材料；将第二步获得的分区化三维有限元数值模型作为设计的几何模型，依据模型的几何分区和优化目标及约束分配设计变量；将第三步获得的降阶模型作为优化过程中使用的数值分析模型，使用降阶模型进行数值计算获得目标和约束响应，进行离散材料优化设计，实现纤维体分比、纤维角度、铺层顺序等多尺度变量的协同优化设计，获得满足功能要求的最优设计构型。图4为初始设计构型，图5为优化后创新构型设计，优化具体步骤包括：Use the discrete materials in the candidate material library obtained in the first step as design variables, and use continuous interpolation functions to characterize the discrete materials in the candidate material library; use the partitioned three-dimensional finite element numerical model obtained in the second step as the geometric model of the design , Assign design variables according to the model’s geometric partition and optimization goals and constraints; use the reduced-order model obtained in the third step as the numerical analysis model used in the optimization process, use the reduced-order model to perform numerical calculations to obtain the target and constraint responses, and perform discrete materials Optimize the design to realize the collaborative optimization design of multi-scale variables such as fiber body fraction, fiber angle, layup sequence, etc., and obtain the optimal design configuration that meets the functional requirements. Figure 4 is the initial design configuration, and Figure 5 is the optimized innovative configuration design. The specific steps of optimization include:
(1)使用连续插值公式将离散材料连续化表征，材料插值格式如下所示。(1) Use continuous interpolation formula to continuously characterize discrete materials. The material interpolation format is shown below.
其中C
e为单元本构矩阵，w
i为备选材料的权重系数，C
i为备选材料的等效 壳刚度矩阵，
为单元e对应备选材料j的设计变量,i为备选材料编号，n
e为有限元模型单元总数，p为罚值。
Where C e is the element constitutive matrix, w i is the weight coefficient of the candidate material, and C i is the equivalent shell stiffness matrix of the candidate material, Alternatively the material units e j corresponding to the design variable, i is an alternative numbers, n e is the number of the finite element model unit, p is the penalty value.
(2)基于有限元降阶模型进行线性屈曲分析，计算结构的屈曲载荷，并使用伴随法计算灵敏度信息。(2) Perform linear buckling analysis based on the finite element reduced-order model, calculate the buckling load of the structure, and use the adjoint method to calculate the sensitivity information.
(3)使用数学规划方法中的移动渐近线(MMA)方法对优化问题进行求解，直至优化问题收敛。(3) Use the moving asymptote (MMA) method in the mathematical programming method to solve the optimization problem until the optimization problem converges.
(4)消除优化结果中的中间密度，获得材料选择明确的设计结果，如图5所示。(4) Eliminate the intermediate density in the optimization result, and obtain the design result with clear material selection, as shown in Figure 5.
本发明提供一种面向混杂纤维复合材料板壳结构的快速协同优化方法，针对混杂纤维复合材料结构具有跨尺度、多层级设计变量问题，通过建立备选材料库将不同尺度的设计变量统一至同一层级，通过开展离散材料优化设计，获得新颖的结构材料布局构型，从而实现混杂纤维复合材料的协同优化设计。并通过几何分区和模型降阶方法，加速了优化进程，实现快速优化设计。本发明提出的方法能实现混杂纤维复合材料结构的一体化设计，实现结构拓扑、纤维含量、纤维角度、铺层顺序等跨尺度、多变量的协同优化设计，满足结构功能需要的同时，减轻结构质量，降低材料成本，提高经济效益。The present invention provides a rapid collaborative optimization method for hybrid fiber composite material plate and shell structure, aiming at the problem of cross-scale and multi-level design variables of hybrid fiber composite material structure, and unified design variables of different scales to the same by establishing a candidate material library At the level, through the development of discrete material optimization design, novel structural material layout configurations are obtained, so as to realize the collaborative optimization design of hybrid fiber composite materials. And through geometric partition and model reduction methods, the optimization process is accelerated, and rapid optimization design is realized. The method proposed in the present invention can realize the integrated design of the hybrid fiber composite material structure, realize the cross-scale and multivariable collaborative optimization design of structure topology, fiber content, fiber angle, layup sequence, etc., and meet the needs of structural functions while reducing the structure Quality, reduce material costs and improve economic efficiency.
最后应说明的是：以上各实施例仅用以说明本发明的方法方案，而非对其限制；尽管参照前述各实施例对本发明进行了详细的说明，本领域的普通方法人员应当理解：其对前述各实施例所记载的方法方案进行修改，或者对其中部分或者全部方法特征进行等同替换，并不使相应方法方案的本质脱离本发明各实施例方法方案的范围。Finally, it should be noted that the above embodiments are only used to illustrate the method scheme of the present invention, not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand: Modifying the method solutions described in the foregoing embodiments, or equivalently replacing some or all of the method features therein, does not deviate from the essence of the corresponding method solutions from the scope of the method solutions of the embodiments of the present invention.
Claims (5)
- 一种面向混杂纤维复合材料板壳结构的快速协同优化方法，其特征在于包括以下步骤：A rapid collaborative optimization method for hybrid fiber composite material plate and shell structure is characterized by comprising the following steps:第一步，建立备选材料库；The first step is to establish a database of candidate materials;采用实验方法、解析方法或数值计算方法获得具有不同纤维体分比、不同微观纤维分布的复合材料的材料属性，并使用经典层合板理论计算不同纤维角度及铺层顺序层合板的一般壳刚度系数；将不同组合层合板的壳刚度系数作为离散材料优化中的设计变量，建立混杂纤维复合材料的备选材料库，为后续的离散材料优化做好准备；Use experimental methods, analytical methods or numerical calculation methods to obtain the material properties of composite materials with different fiber-to-body ratios and different micro-fiber distributions, and use classical laminate theory to calculate the general shell stiffness coefficients of laminates with different fiber angles and layup sequences ; Use the shell stiffness coefficients of different composite laminates as design variables in the optimization of discrete materials, and establish a candidate material library for hybrid fiber composite materials to prepare for subsequent optimization of discrete materials;通过建立备选材料库，将具有不同强弱水平的材料收入备选材料库，将不同尺度的设计变量统一到同一层级，以实现混杂纤维复合材料结构的跨尺度、多层级变量协同优化设计；Through the establishment of a candidate material library, materials with different strengths and weaknesses are included in the candidate material library, and design variables of different scales are unified to the same level, so as to realize the cross-scale and multi-level variable collaborative optimization design of the hybrid fiber composite structure;第二步，建立三维有限元数值模型并进行几何分区；The second step is to establish a three-dimensional finite element numerical model and perform geometric partitioning;建立复合材料板壳结构三维有限元数值模型，根据板壳结构的几何形状、功能要求将有限元数值模型进行几何分区处理；对板壳结构进行分区优化设计可以扩大结构的设计空间，后续通过离散材料优化可以获得每个相邻区域都为不同备选材料的变刚度板壳结构；Establish a three-dimensional finite element numerical model of the composite plate and shell structure, and perform geometric partitioning of the finite element numerical model according to the geometric shape and functional requirements of the plate and shell structure; the partition optimization design of the plate and shell structure can expand the design space of the structure, and follow-up through discrete Material optimization can obtain a variable-rigidity plate and shell structure with different candidate materials for each adjacent area;第三步，使用模型降阶方法，建立降阶数值分析模型；The third step is to use the model reduction method to establish a reduced-order numerical analysis model;使用模型降阶的方法降低有限元数值模型的维度，降低数值分析的计算成本，实现混杂复合材料快速协同优化设计；Use the method of model reduction to reduce the dimensionality of the finite element numerical model, reduce the calculation cost of numerical analysis, and realize the rapid collaborative optimization design of hybrid composite materials;第四步，建立优化列式，进行离散材料优化设计；The fourth step is to establish an optimized column formula and conduct an optimized design of discrete materials;根据设计要求建立优化列式和离散材料优化模型，目标和约束依据设计初期的具体要求，包括刚度、频率、屈曲力学响应；优化列式的一般形式如下：Establish optimized formulation and discrete material optimization models according to design requirements. The objectives and constraints are based on the specific requirements at the initial design stage, including stiffness, frequency, and buckling mechanical response; the general form of the optimized formulation is as follows:优化目标:min F(u(x),x)Optimization goal: min F(u(x),x)优化约束:G i(x)≤0 (1) Optimization constraint: G i (x)≤0 (1)0≤x i≤1,i＝1,...,L 0≤x i ≤1,i＝1,...,L其中，x为设计变量，x i为设计变量第i个分量，L为设计变量的数量，u为力学控制方程，F为目标函数，G为约束函数； Among them, x is the design variable, x i is the i-th component of the design variable, L is the number of design variables, u is the mechanical control equation, F is the objective function, and G is the constraint function;将第一步获得的备选材料库中的离散材料作为设计变量，使用连续插值函数表征备选材料库中的离散材料；将第二步获得的分区化三维有限元数值模型作为设计的几何模型，依据模型的几何分区和优化目标及约束分配设计变量；将第三步获得的降阶模型作为优化过程中使用的数值分析模型，使用降阶模型进行数值计算获得目标和约束响应，进行离散材料优化设计，同时进行混杂纤维复合材料纤维体分比、纤维角度、铺层顺序多变量、跨尺度协同优化设计，获得满足功能要求的最优设计构型。Use the discrete materials in the candidate material library obtained in the first step as design variables, and use continuous interpolation functions to characterize the discrete materials in the candidate material library; use the partitioned three-dimensional finite element numerical model obtained in the second step as the geometric model of the design , Assign design variables according to the model’s geometric partition and optimization goals and constraints; use the reduced-order model obtained in the third step as the numerical analysis model used in the optimization process, use the reduced-order model to perform numerical calculations to obtain the target and constraint responses, and perform discrete materials Optimize the design, and carry out the multi-variable, cross-scale collaborative optimization design of the hybrid fiber composite fiber body ratio, fiber angle, and layup sequence to obtain the optimal design configuration that meets the functional requirements.
- 根据权利要求1所述的一种面向混杂纤维复合材料板壳结构的快速协同优化方法，其特征在于，第四步具体步骤包括：The method for rapid collaborative optimization of hybrid fiber composite slab and shell structure according to claim 1, characterized in that the fourth step includes:(1)使用连续插值公式将离散材料连续化表征，材料插值格式如公式(2)所示；(1) Use continuous interpolation formula to continuously characterize discrete materials, and the material interpolation format is shown in formula (2);
其中，C e为单元本构矩阵，w i为备选材料的权重系数，C i为备选材料的等效壳刚度矩阵，为单元e对应备选材料j的设计变量,i为备选材料编号，n e为有限元模型单元总数，p为罚值； Among them, C e is the element constitutive matrix, w i is the weight coefficient of the candidate material, C i is the equivalent shell stiffness matrix of the candidate material,
Alternatively the material units e j corresponding to the design variable, i is an alternative numbers, n e is the number of the finite element model unit, p is the penalty value;(2)基于有限元降阶模型计算目标函数和约束，并计算灵敏度信息；其中 灵敏度信息的计算方法包括直接法，伴随法和差分法；(2) Calculate the objective function and constraints based on the finite element reduced-order model, and calculate the sensitivity information; the sensitivity information calculation methods include direct method, adjoint method and difference method;(3)使用梯度类优化方法求解优化问题，直至优化问题收敛；其中优化方法包括牛顿法、拟牛顿法、移动渐近线法等；(3) Use gradient optimization methods to solve the optimization problem until the optimization problem converges; the optimization methods include Newton method, quasi-Newton method, moving asymptote method, etc.;(4)消除优化结果中的中间密度，获得材料选择明确的设计结果。(4) Eliminate the intermediate density in the optimization result, and obtain a clear design result for material selection. - 根据权利要求1或2所述的一种面向混杂纤维复合材料板壳结构的快速协同优化方法，其特征在于，第一步中所述的解析方法为混合公式法，数值方法包括均匀化方法、代表体元法。According to claim 1 or 2, a rapid collaborative optimization method for hybrid fiber composite material plate and shell structure, wherein the analytical method in the first step is a hybrid formula method, and the numerical method includes a homogenization method, Represents the voxel method.
- 根据权利要求1或2所述的一种面向混杂纤维复合材料板壳结构的快速协同优化方法，其特征在于，第二步中所述的模型降阶方法包括：特征正价本征正交分解POD方法、动力学模态分解DMD方法。According to claim 1 or 2, a rapid collaborative optimization method for hybrid fiber composite material slab and shell structure, wherein the model reduction method in the second step comprises: characteristic normal valence eigen orthogonal decomposition POD method, dynamic modal decomposition DMD method.
- 根据权利要求3所述的一种面向混杂纤维复合材料板壳结构的快速协同优化方法，其特征在于，第二步中所述的模型降阶方法包括：特征正价本征正交分解POD方法、动力学模态分解DMD方法。The method for rapid collaborative optimization of hybrid fiber composite slab and shell structure according to claim 3, characterized in that the model reduction method in the second step comprises: characteristic normal valence eigen orthogonal decomposition POD method , Dynamic modal decomposition DMD method.
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