CN108416080B - Composite material modeling method based on repetitive substructure - Google Patents
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- 239000002131 composite material Substances 0.000 title claims abstract description 79
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- 230000003252 repetitive effect Effects 0.000 title claims abstract description 9
- 238000006068 polycondensation reaction Methods 0.000 claims abstract description 3
- 239000011159 matrix material Substances 0.000 claims description 40
- 239000000463 material Substances 0.000 claims description 12
- 238000013016 damping Methods 0.000 claims description 6
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Abstract
The COMPOSITE FINITE ELEMENT modeling method based on repetitive substructure that the invention discloses a kind of, comprising the following steps: establish the multicomponent unit cell finite element model of composite material fining；Multicomponent unit cell finite element model based on above-mentioned fining, establishes composite material repetitive substructure model；Polycondensation is carried out to repetitive substructure, eigenmatrix is then assembled to unit cell relict texture, obtains full composite material analysis model；The method simplifies composite material fining modeling engineering while guaranteeing computational accuracy, greatly improves modeling efficiency, has highly important engineering significance.
Description
Technical Field
The invention belongs to the field of computational materials science, and particularly relates to a composite material modeling method based on a repeated substructure.
Background
The composite material is formed by compounding different materials, usually comprises two or even more than two composite materials, has a complex internal structure, is generally an anisotropic material, and is difficult to analyze in finite element modeling. The traditional composite finite element modeling mode is equivalent modeling, a finite element model of the composite is simplified, modeling efficiency and calculation efficiency are improved to a certain extent, but results are inevitably subject to error, and real dynamic behaviors of the composite cannot be accurately reflected.
In recent years, most researches analyze the weaving process and flow of the composite material, and find out a representative volume unit with regular mesoscopic appearance of the three-dimensional woven composite material to reflect the macroscopic performance of the whole structure, wherein the representative volume unit reflects the parameters of the component information, the weaving process and the like of the macroscopic structure and is called as a unit cell. For the fine modeling of the composite material, although the mechanical behavior of the composite material can be more accurately reflected, the modeling workload is large, and the finite element model is too complex, so that the calculation efficiency is low, and the method has certain limitation in engineering application. Therefore, it is necessary to establish a more effective and feasible composite material modeling method.
Disclosure of Invention
In order to solve the problems, the invention discloses a composite material modeling method based on a repeated substructure, which adopts a method of mapping a substructure by using a composite material unit cell, can greatly improve modeling efficiency while ensuring precision, and has very important engineering significance.
In order to achieve the above object, the method for modeling a composite material based on a repeating substructure according to the present invention comprises the following steps:
(1) establishing a refined multi-component unit cell finite element model of the composite material;
(2) establishing a composite material repetitive substructure model based on the refined multi-component unit cell finite element model;
(3) performing polycondensation on the repeated substructure, and assembling the characteristic matrix to a unit cell residual structure to obtain a full composite material analysis model;
(4) and (4) verifying a composite material modeling method based on the repeated substructure.
Wherein, the establishing of the multicomponent unit cell finite element model refined by the composite material in the step (1) comprises the following steps:
(1.1) finding out a unit cell geometric model with regular mesoscopic and representative volume units of the composite material according to the component materials and the weaving rule of the composite material, wherein the unit cell geometric model is used for reflecting the macroscopic performance of the whole structure;
and (1.2) analyzing the components of the unit cell material according to the unit cell geometric model, and establishing a refined multi-component unit cell finite element model.
Wherein, in the step (2), the composite material repetitive substructure model is established according to the unit cell finite element model, and the method comprises the following steps:
(2.1) analyzing the boundary form type of the unit cell model according to the arrangement rule of the unit cell model in the composite material, and establishing unit cell structures and residual structures with different boundary forms;
(2.2) mapping to obtain a composite material repeated substructure model according to the single cell substructure and by combining the arrangement rule and the position relation of the single cells in the composite material;
wherein, in the step (3), the feature matrix after the condensation polymerization of the repeated substructure is assembled and matched on the unit cell residual structure, and the method comprises the following steps:
(3.1) condensation polymerization of the substructure model to obtain a characteristic matrix and a kinetic equation under a modal coordinate; the equation of motion converted from the substructure at physical coordinates to the reduced modal coordinate p is:
wherein,
m, C and K respectively represent a mass matrix, a damping matrix and a rigidity matrix of the unit cell structure;respectively representing a mass matrix, a damping matrix and a rigidity matrix of the unit cell structure under a modal coordinate; u is the physical coordinate of the unit cell structure; p is a modal coordinate; h is a transformation matrix:
wherein o is the degree of freedom of the internal node, and b is the degree of freedom of the external node; [ phi ] ofoo]The interface is in a fixed interface main mode; [ psi]Is a constrained mode matrix;
(3.2) performing modal synthesis on all the substructures and the residual structure by utilizing a displacement coordination condition and a force balance condition among the substructures to obtain a motion equation of the overall structure, and solving the modal of the whole composite material; the motion equation of the overall structure under the generalized coordinate q is as follows:
wherein,
the characteristic matrix is a structural integral characteristic matrix under a generalized coordinate q; t is a transformation matrix.
The verification of the composite material modeling method based on the repeated substructure in the step (4) comprises the following steps:
(4.1) calculating to obtain the natural frequency and the vibration mode of each order of the composite material based on the repeated substructure under free vibration;
(4.2) establishing a composite material integral refined finite element model to obtain each order natural frequency and vibration mode under free vibration;
and (4.3) comparing and verifying the natural frequency and the vibration mode of each order of the composite material under the two modeling methods.
The invention has the beneficial effects that:
the composite material modeling method based on the repeated substructure considers the difficulty in fine modeling of the composite material, only uses one composite material unit cell model as a residual structure, and uses four unit cells with different external nodes as main substructure; the modal information of the whole composite material is obtained by a repeated substructure method, and finite element analysis of the composite material can be well guided.
Drawings
FIG. 1 composite Material Unit cell geometric model;
FIG. 2 is a finite element model of a composite material unit cell;
FIG. 3 depicts the unit cell residue structure 0;
FIG. 4 depicts a unit cell structure 1;
FIG. 5 depicts unit cell structure 2;
FIG. 6 depicts unit cell structure 3;
FIG. 7 depicts unit cell structure 4;
FIG. 8 repeats a substructure composite model;
fig. 9 mode comparison MAC plots.
Detailed Description
The present invention will be further illustrated with reference to the accompanying drawings and specific embodiments, which are to be understood as merely illustrative of the invention and not as limiting the scope of the invention. It should be noted that the terms "front," "back," "left," "right," "upper" and "lower" used in the following description refer to directions in the drawings, and the terms "inner" and "outer" refer to directions toward and away from, respectively, the geometric center of a particular component.
The invention relates to a composite material modeling method based on a repeated substructure, which comprises the following steps:
(1) establishing a multi-component unit cell finite element model refined by a composite material, comprising the following steps:
(1.1) finding out a unit cell geometric model with regular mesoscopic and representative volume units of the composite material for reflecting the macroscopic performance of the whole structure according to the component materials and the weaving rule of the composite material, as shown in figure 1;
the unit cell model comprises an upper plate, a core layer, a lower plate and a suture line; as shown in fig. 1, the composite geometry parameters are as follows:
the geometric size of the unit cell is 30 x 15 x 11.5mm, the thickness of the upper panel is 1mm, the thickness of the lower panel is 0.5mm, the thickness of the core layer is 10mm, the upper panel, the lower panel and the core layer are sewn into a whole by adopting fiber materials, a zigzag sewing mode is mainly adopted, the diameter of the sewing material is 1mm, and the sewing step length is 15 mm; the panels of each layer in the structure are made of orthotropic materials, and the sewing lines are made of isotropic materials.
(1.2) analyzing the components of the unit cell material according to the unit cell geometric model, and establishing a refined multi-component unit cell finite element model as shown in figure 2;
(2) establishing a composite material repetitive substructure model based on the refined multi-component unit cell finite element model, which comprises the following steps:
(2.1) analyzing the boundary form type of the unit cell model according to the arrangement rule of the unit cell model in the composite material, and establishing four unit cell structures and unit cell residual structures with different boundary forms, as shown in figures 3-7;
(2.2) according to the single cell substructure, mapping to obtain a composite material repetitive substructure model by combining the arrangement rule and the position relation of the single cells in the composite material, as shown in FIG. 8;
(3) assembling the feature matrix after condensation polymerization of the repeating substructure onto a unit cell residual structure, comprising the steps of:
(3.1) condensation polymerization of the substructure model to obtain a characteristic matrix and a kinetic equation under a modal coordinate; the equation of motion converted from the substructure at physical coordinates to the reduced modal coordinate p is:
wherein,
m, C and K respectively represent a mass matrix, a damping matrix and a rigidity matrix of the unit cell structure;respectively representing a mass matrix, a damping matrix and a rigidity matrix of the unit cell structure under a modal coordinate; u is the physical coordinate of the unit cell structure; p is a modal coordinate; h is a transformation matrix:
wherein o is the degree of freedom of the internal node, and b is the degree of freedom of the external node; [ phi ] ofoo]The interface is in a fixed interface main mode; [ psi]Is a constrained mode matrix;
(3.2) performing modal synthesis on all the substructures and the residual structure by utilizing a displacement coordination condition and a force balance condition among the substructures to obtain a motion equation of the overall structure, and solving the modal of the whole composite material; the motion equation of the overall structure under the generalized coordinate q is as follows:
wherein,
the characteristic matrix is a structural integral characteristic matrix under a generalized coordinate q; t is a transformation matrix.
(4) The verification of the composite material modeling method based on the repeated substructure comprises the following steps:
(4.1) calculating to obtain the natural frequency and the vibration mode of each order of the composite material based on the repeated substructure under free vibration, wherein the composite material has 25 unit cells in the example;
(4.2) establishing a composite material integral refined finite element model to obtain the natural frequency and the vibration mode of each order under free vibration, wherein the geometric dimension of the composite material is 150 x 75 x 11.5 mm;
(4.3) comparing and verifying the natural frequency and the vibration mode of each order of the composite material under the two modeling methods, wherein the result is as follows:
table 4 composite modeling method validation based on repeating substructures
As can be seen from table 4 and fig. 9, the composite material modeling method based on the repeated substructure can ensure the accuracy of the composite material at the low-order modal frequency under the condition of reducing the composite material modeling engineering.
The technical means disclosed in the invention scheme are not limited to the technical means disclosed in the above embodiments, but also include the technical scheme formed by any combination of the above technical features.
Claims (1)
1. The composite material modeling method based on the repeated substructure is characterized by comprising the following steps of:
(1) establishing a multi-component unit cell finite element model refined by a composite material, comprising the following steps:
(1.1) finding out a unit cell geometric model with regular mesoscopic and representative volume units of the composite material according to the component materials and the weaving rule of the composite material, wherein the unit cell geometric model is used for reflecting the macroscopic performance of the whole structure;
(1.2) analyzing the components of the unit cell material according to the unit cell geometric model, and establishing a refined multi-component unit cell finite element model;
(2) establishing a composite material repetitive substructure model based on the refined multi-component unit cell finite element model; the method comprises the following steps:
(2.1) analyzing the boundary form type of the unit cell model according to the arrangement rule of the unit cell model in the composite material, and establishing unit cell structures with different boundary forms;
(2.2) mapping to obtain a composite material repeated substructure model according to the single cell substructure and by combining the arrangement rule and the position relation of the single cells in the composite material;
(3) performing polycondensation on the repeated substructure, and assembling the characteristic matrix to a unit cell residual structure to obtain a full composite material analysis model; the method comprises the following steps:
(3.1) condensation polymerization of the substructure model to obtain a characteristic matrix and a kinetic equation under a modal coordinate; the equation of motion converted from the substructure at physical coordinates to the reduced modal coordinate p is:
wherein,
m, C and K respectively represent a mass matrix, a damping matrix and a rigidity matrix of the unit cell structure;respectively representing a mass matrix, a damping matrix and a rigidity matrix of the unit cell structure under a modal coordinate; u is the physical coordinate of the unit cell structure; p is a modal coordinate; h is a transformation matrix:
where subscript o is the set of internal nodes, b is the set of external nodes, [ phi ]oo]The interface is in a fixed interface main mode; [ psi]Is a constrained mode matrix;
(3.2) performing modal synthesis on all the substructures and the residual structure by utilizing a displacement coordination condition and a force balance condition among the substructures to obtain a motion equation of the overall structure, and solving the modal of the whole composite material; the motion equation of the overall structure under the generalized coordinate q is as follows:
wherein,
the characteristic matrix is a structural integral characteristic matrix under a generalized coordinate q; t is a conversion matrix;
(4) the composite material modeling method verification based on the repeated substructure comprises the following steps:
(4.1) calculating to obtain the natural frequency and the vibration mode of each order of the composite material based on the repeated substructure under free vibration;
(4.2) establishing a composite material integral refined finite element model to obtain each order natural frequency and vibration mode under free vibration;
and (4.3) comparing and verifying the natural frequency and the vibration mode of each order of the composite material under the two modeling methods.
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