CN108416080B - Composite material modeling method based on repetitive substructure - Google Patents
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Abstract
本发明公开了一种基于重复子结构的复合材料有限元建模方法，包括以下步骤：建立复合材料精细化的多组分单胞有限元模型；基于上述精细化的多组分单胞有限元模型，建立复合材料重复子结构模型；对重复子结构进行缩聚，然后将特征矩阵装配到单胞残余结构，得到全复合材料分析模型；此方法在保证计算精度的同时简化了复合材料精细化建模工程，极大的提高建模效率，具有十分重要的工程意义。
The invention discloses a composite material finite element modeling method based on repeated substructures, comprising the following steps: establishing a refined multi-component unit cell finite element model of composite materials; based on the above-mentioned refined multi-component unit cell finite element model Model, establish the composite material repeating substructure model; polycondensate the repeating substructure, and then assemble the feature matrix to the unit cell residual structure to obtain the full composite material analysis model; this method simplifies the fine-tuning construction of the composite material while ensuring the calculation accuracy. It is of great engineering significance to improve the modeling efficiency greatly.
Description
技术领域technical field
本发明属于计算材料学领域，具体涉及基于重复子结构的复合材料建模方法。The invention belongs to the field of computational materials science, in particular to a composite material modeling method based on repeated substructures.
背景技术Background technique
复合材料是由不同的材料复合而成，通常包含两种甚至两种以上的复合材料，内部结构复杂，且复合材料一般为各向异性材料，在有限元建模分析中较为困难。传统复合材料有限元建模方式为等效建模，简化了复合材料的有限元模型，一定程度上提高了建模效率和计算效率，但无可避免的会导致结果出现误差，不能够精确的反映出复合材料真实的动力学行为。Composite materials are composed of different materials, usually including two or more composite materials, the internal structure is complex, and composite materials are generally anisotropic materials, which is difficult in finite element modeling and analysis. The traditional finite element modeling method of composite materials is equivalent modeling, which simplifies the finite element model of composite materials and improves the modeling efficiency and calculation efficiency to a certain extent. Reflects the real dynamic behavior of composite materials.
近年来，大多数的研究对复合材料的编织工艺和流程进行分析，找出三维编织复合材料细观有规律的、具有代表性的体积单元用以反映出结构整体的宏观性能，该代表性体积单元反映了宏观整体结构的组分信息、编织工艺等参数，被称之为单胞。对于复合材料精细化建模，虽然能够更准确的反映复合材料的力学行为，但建模工作量大，有限元模型过于复杂，导致计算效率低，在工程应用中有一定局限性。所以建立一种更为有效可行的复合材料建模方法十分必要。In recent years, most studies have analyzed the weaving process and process of composite materials, and found the meso-regular and representative volume units of three-dimensional braided composite materials to reflect the macroscopic properties of the overall structure. The representative volume The unit reflects the component information of the macroscopic overall structure, weaving process and other parameters, and is called a unit cell. For the refined modeling of composite materials, although it can more accurately reflect the mechanical behavior of composite materials, the modeling workload is too large, and the finite element model is too complicated, resulting in low computational efficiency and certain limitations in engineering applications. Therefore, it is necessary to establish a more effective and feasible modeling method for composite materials.
发明内容SUMMARY OF THE INVENTION
为解决上述问题，本发明公开了一种基于重复子结构的复合材料建模方法，采用复合材料单胞映像子结构的的方法，在保证精度的同时能极大的提高建模效率，具有十分重要的工程意义。In order to solve the above problems, the present invention discloses a composite material modeling method based on repeated substructures. The method of using composite material unit cell mapping substructures can greatly improve the modeling efficiency while ensuring the accuracy, and has a very high efficiency. important engineering significance.
为实现上述目的，本发明中基于重复子结构的复合材料建模方法，包括以下步骤：In order to achieve the above object, the composite material modeling method based on repeated substructures in the present invention includes the following steps:
(1)建立复合材料精细化的多组分单胞有限元模型；(1) Establish a multi-component unit cell finite element model for the refinement of composite materials;
(2)基于上述精细化的多组分单胞有限元模型，建立复合材料重复子结构模型；(2) Based on the above refined multi-component unit cell finite element model, a repeating substructure model of the composite material is established;
(3)对重复子结构进行缩聚，然后将特征矩阵装配到单胞残余结构，得到全复合材料分析模型；(3) polycondensing the repeating substructures, and then assembling the feature matrix into the unit cell residual structure to obtain an analysis model of the full composite material;
(4)基于重复子结构的复合材料建模方法验证。(4) Verification of composite modeling method based on repeated substructure.
其中，上述步骤(1)中建立复合材料精细化的多组分单胞有限元模型，包括以下步骤：Wherein, establishing the multi-component unit cell finite element model of composite material refinement in the above step (1) includes the following steps:
(1.1)根据复合材料组分材料和编织规律找出复合材料细观有规律的、具有代表性的体积单元用以反映出结构整体的宏观性能的单胞几何模型；(1.1) According to the composite material component materials and the weaving law, find the unit cell geometric model of the composite material with regular and representative volume units to reflect the macroscopic performance of the overall structure;
(1.2)根据单胞几何模型，分析单胞材料组分，建立精细化的多组分单胞有限元模型。(1.2) According to the geometric model of the unit cell, analyze the components of the unit cell material, and establish a refined multi-component unit cell finite element model.
其中，上述步骤(2)中根据所述单胞有限元模型建立复合材料重复子结构模型，包括以下步骤：Wherein, in the above step (2), the composite material repeating substructure model is established according to the unit cell finite element model, including the following steps:
(2.1)根据单胞模型在复合材料中排布规律，分析单胞模型的边界形式类型，建立具有不同边界形式的单胞子结构和残余结构；(2.1) According to the arrangement rule of the unit cell model in the composite material, analyze the boundary form types of the unit cell model, and establish the unit cell substructure and residual structure with different boundary forms;
(2.2)根据所述单胞子结构，结合单胞在复合材料中排布规律和位置关系，映像得到复合材料重复子结构模型；(2.2) According to the unit cell substructure, combined with the arrangement rule and positional relationship of the unit cells in the composite material, the repeating substructure model of the composite material is obtained by mapping;
其中，上述步骤(3)中将重复子结构缩聚后特征矩阵装匹配到单胞残余结构上，包括以下步骤：Wherein, in the above-mentioned step (3), the feature matrix after the polycondensation of the repeating substructure is assembled and matched to the unit cell residual structure, including the following steps:
(3.1)子结构模型缩聚，得到模态坐标下的特征矩阵和动力学方程；由子结构在物理坐标下运动方程转换到缩减的模态坐标p下的运动方程为：(3.1) The substructure model is condensed to obtain the characteristic matrix and dynamic equation in modal coordinates; the motion equation converted from the substructure motion equation in physical coordinates to the reduced modal coordinates p is:
其中，in,
M，C，K分别表示单胞子结构的质量矩阵，阻尼矩阵和刚度矩阵；分别表示单胞子结构在模态坐标下的质量矩阵，阻尼矩阵和刚度矩阵；u为单胞子结构物理坐标；p为模态坐标；H为转换矩阵：M, C, K represent the mass matrix, damping matrix and stiffness matrix of the single-cell substructure, respectively; Represent the mass matrix, damping matrix and stiffness matrix of the single-cell substructure in modal coordinates; u is the physical coordinate of the single-cell substructure; p is the modal coordinate; H is the transformation matrix:
其中o为内部节点自由度，b为外部节点自由度；[φoo]为固定界面主模态；[ψ]为约束模态矩阵；where o is the degree of freedom of the internal node, b is the degree of freedom of the external node; [φ oo ] is the main mode of the fixed interface; [ψ] is the constraint mode matrix;
(3.2)利用子结构间位移协调条件及力平衡条件，将所有子结构和残余结构进行模态综合，得到整体结构的运动方程，求解整块复合材料的模态；整体结构在广义坐标q下的运动方程为：(3.2) Using the displacement coordination conditions and force balance conditions between the substructures, the modal synthesis of all the substructures and the residual structure is carried out to obtain the motion equation of the overall structure, and the modal of the entire composite material is solved; the overall structure is under the generalized coordinate q. The equation of motion is:
其中，in,
为在广义坐标q下的结构整体特征矩阵；T为转换矩阵。 is the overall characteristic matrix of the structure under the generalized coordinate q; T is the transformation matrix.
其中，上述步骤(4)中基于重复子结构的复合材料建模方法的验证，包括以下步骤：Wherein, the verification of the composite material modeling method based on the repeated substructure in the above step (4) includes the following steps:
(4.1)计算得到基于重复子结构的复合材料自由振动下各阶固有频率和振型；(4.1) Calculate the natural frequency and mode shape of each order under the free vibration of the composite material based on the repeated substructure;
(4.2)建立复合材料整体精细化有限元模型，得到自由振动下各阶固有频及振型；(4.2) Establish the overall refined finite element model of the composite material, and obtain the natural frequencies and mode shapes of each order under free vibration;
(4.3)对两种建模方法下复合材料各阶固有频率和振型对比验证。(4.3) Contrast and verify the natural frequencies and mode shapes of composite materials under the two modeling methods.
本发明的有益效果是：The beneficial effects of the present invention are:
本发明中基于重复子结构的复合材料建模方法考虑了复合材料精细化建模困难，只运用一个复合材料单胞模型作为残余结构，四种具有不同外部节点单胞作为主子结构；通过重复子结构方法得到整块复合材料模态信息，能够很好的指导复合材料有限元分析。The composite material modeling method based on repeated substructures in the present invention takes into account the difficulty of fine modeling of composite materials, and only uses one composite material unit cell model as the residual structure, and four unit cells with different external nodes as the main substructure; The structural method obtains the modal information of the whole composite material, which can well guide the finite element analysis of the composite material.
附图说明Description of drawings
图1复合材料单胞几何模型；Figure 1. The geometric model of the composite material unit cell;
图2复合材料单胞有限元模型；Figure 2. The composite material unit cell finite element model;
图3单胞残余结构0；Figure 3. Unit cell residual structure 0;
图4单胞子结构1；Figure 4 Single cell substructure 1;
图5单胞子结构2；Figure 5 Single cell substructure 2;
图6单胞子结构3；Fig. 6 single cell substructure 3;
图7单胞子结构4；Fig. 7 single cell substructure 4;
图8重复子结构复合材料模型；Fig. 8 Repeated substructure composite material model;
图9振型比较MAC图。Figure 9 Mode shape comparison MAC plot.
具体实施方式Detailed ways
下面结合附图和具体实施方式，进一步阐明本发明，应理解下述具体实施方式仅用于说明本发明而不用于限制本发明的范围。需要说明的是，下面描述中使用的词语“前”、“后”、“左、”“右”、“上”和“下”指的是附图中的方向，词语“内”和“外”分别指的是朝向或远离特定部件几何中心的方向。The present invention will be further clarified below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. It should be noted that the words "front", "rear", "left," "right", "upper" and "lower" used in the following description refer to the directions in the drawings, and the words "inner" and "outer" ” refer to directions towards or away from the geometric center of a particular part, respectively.
本发明所述的基于重复子结构的复合材料建模方法，包括以下步骤：The composite material modeling method based on repeated substructures of the present invention includes the following steps:
(1)建立复合材料精细化的多组分单胞有限元模型，包括以下步骤：(1) Establish a refined multi-component unit cell finite element model of composite materials, including the following steps:
(1.1)根据复合材料组分材料和编织规律找出复合材料细观有规律的、具有代表性的体积单元用以反映出结构整体的宏观性能的单胞几何模型，如图1所示；(1.1) According to the composite material component materials and weaving laws, find out the meso-regular and representative volume units of the composite material to reflect the unit cell geometric model of the overall macroscopic properties of the structure, as shown in Figure 1;
所述单胞模型包括上层板，芯层，下层板和缝合线；如图1中所示，该复合材料几何参数如下：The unit cell model includes an upper layer, a core layer, a lower layer and a suture; as shown in Figure 1, the composite geometry parameters are as follows:
单胞几何尺寸为30*15*11.5mm，上面板厚度为1mm，下面板厚度为0.5mm，芯层厚度为10mm，上下面板和芯层之间采用纤维材料缝合为一体，主要采用“几”字型缝合方式，缝合材料直径1mm，缝合步长为15mm；结构中各层面板为正交各向异性材料，缝合线为各向同性材料。The geometric size of the unit cell is 30*15*11.5mm, the thickness of the upper panel is 1mm, the thickness of the lower panel is 0.5mm, and the thickness of the core layer is 10mm. In the font stitching method, the diameter of the stitching material is 1mm, and the stitching step length is 15mm; the panels of each layer in the structure are orthotropic materials, and the stitching lines are isotropic materials.
(1.2)根据单胞几何模型，分析单胞材料组分，建立精细化的多组分单胞有限元模型，如图2所示；(1.2) According to the unit cell geometric model, analyze the unit cell material components, and establish a refined multi-component unit cell finite element model, as shown in Figure 2;
(2)基于上述精细化的多组分单胞有限元模型，建立复合材料重复子结构模型，包括以下步骤：(2) Based on the above refined multi-component unit cell finite element model, establish a composite material repeating substructure model, including the following steps:
(2.1)根据单胞模型在复合材料中排布规律，分析单胞模型的边界形式类型，建立四种具有不同边界形式的单胞子结构和单胞残余结构，如图3-7所示；(2.1) According to the arrangement rule of the unit cell model in the composite material, analyze the boundary form types of the unit cell model, and establish four unit cell substructures and unit cell residual structures with different boundary forms, as shown in Figure 3-7;
(2.2)根据所述单胞子结构，结合单胞在复合材料中排布规律和位置关系，映像得到复合材料重复子结构模型，如图8所示；(2.2) According to the unit cell substructure, combined with the arrangement rule and positional relationship of the unit cells in the composite material, the repeating substructure model of the composite material is obtained by mapping, as shown in Figure 8;
(3)将重复子结构缩聚后特征矩阵装配到单胞残余结构上，包括以下步骤：(3) Assembling the feature matrix after the polycondensation of the repeating substructures onto the unit cell residual structure, including the following steps:
(3.1)子结构模型缩聚，得到模态坐标下的特征矩阵和动力学方程；由子结构在物理坐标下运动方程转换到缩减的模态坐标p下的运动方程为：(3.1) The substructure model is condensed to obtain the characteristic matrix and dynamic equation in modal coordinates; the motion equation converted from the substructure motion equation in physical coordinates to the reduced modal coordinates p is:
其中，in,
M，C，K分别表示单胞子结构的质量矩阵，阻尼矩阵和刚度矩阵；分别表示单胞子结构在模态坐标下的质量矩阵，阻尼矩阵和刚度矩阵；u为单胞子结构物理坐标；p为模态坐标；H为转换矩阵：M, C, K represent the mass matrix, damping matrix and stiffness matrix of the single-cell substructure, respectively; Represent the mass matrix, damping matrix and stiffness matrix of the single-cell substructure in modal coordinates; u is the physical coordinate of the single-cell substructure; p is the modal coordinate; H is the transformation matrix:
其中o为内部节点自由度，b为外部节点自由度；[φoo]为固定界面主模态；[ψ]为约束模态矩阵；where o is the degree of freedom of the internal node, b is the degree of freedom of the external node; [φ oo ] is the main mode of the fixed interface; [ψ] is the constraint mode matrix;
(3.2)利用子结构间位移协调条件及力平衡条件，将所有子结构和残余结构进行模态综合，得到整体结构的运动方程，求解整块复合材料的模态；整体结构在广义坐标q下的运动方程为：(3.2) Using the displacement coordination conditions and force balance conditions between the substructures, the modal synthesis of all the substructures and the residual structure is carried out to obtain the motion equation of the overall structure, and the modal of the entire composite material is solved; the overall structure is under the generalized coordinate q. The equation of motion is:
其中，in,
为在广义坐标q下的结构整体特征矩阵；T为转换矩阵。 is the overall characteristic matrix of the structure under the generalized coordinate q; T is the transformation matrix.
(4)基于重复子结构的复合材料建模方法的验证，包括以下步骤：(4) Validation of the composite modeling method based on repeated substructures, including the following steps:
(4.1)计算得到基于重复子结构的复合材料自由振动下各阶固有频率和振型，算例中复合材料有25个单胞；(4.1) The natural frequencies and mode shapes of each order under the free vibration of the composite material based on the repeated substructure are calculated, and the composite material has 25 unit cells in the calculation example;
(4.2)建立复合材料整体精细化有限元模型，得到自由振动下各阶固有频率及振型，复合材料几何尺寸为150*75*11.5mm；(4.2) Establish the overall refined finite element model of the composite material, and obtain the natural frequencies and mode shapes of each order under free vibration. The geometric size of the composite material is 150*75*11.5mm;
(4.3)对两种建模方法下复合材料各阶固有频率和振型对比验证，结果如下：(4.3) Comparing and verifying the natural frequencies and mode shapes of composite materials under the two modeling methods, the results are as follows:
表4基于重复子结构的复合材料建模方法验证Table 4 Verification of composite modeling method based on repeating substructure
由表4和图9可以看出，基于重复子结构的复合材料建模方法在缩减复合材料建模工程的情况下，可以保证复合材料在低阶模态频率的精度。It can be seen from Table 4 and Figure 9 that the composite modeling method based on repeated substructures can ensure the accuracy of composite materials at low-order modal frequencies while reducing the composite modeling engineering.
本发明方案所公开的技术手段不仅限于上述实施方式所公开的技术手段，还包括由以上技术特征任意组合所组成的技术方案。The technical means disclosed in the solution of the present invention are not limited to the technical means disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features.
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