CN112417621A - Method for analyzing influence of defects in truss structure on rigidity of structure in any direction - Google Patents
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Abstract
The invention provides an analysis method for influence of defects in a truss structure on rigidity of the structure in any direction, which comprises the following steps: calculating an overall stiffness matrix of the truss structure; establishing a node displacement field of the truss structure in any direction; obtaining node reaction force vectors in any direction of the truss structure according to the overall stiffness matrix and the node displacement field; applying a periodic boundary condition to the truss structure, and obtaining a characteristic displacement field in any direction and a node counterforce field in any direction of the truss structure according to the overall stiffness matrix, the node counterforce vector and the periodic boundary condition; constructing an analytic expression of equivalent stiffness of the truss structure in any direction according to the node displacement field, the characteristic displacement field, the node reaction force vector and the node reaction force field; and analyzing the influence of the defects in the truss structure on the rigidity of the structure in any direction according to the analytic expression of the equivalent rigidity. The analysis method provided by the disclosure can effectively analyze the influence of the defects on the rigidity of the truss structure in any direction.
Description
Technical Field
The disclosure relates to the field of structural defect calculation and analysis, in particular to an analysis method for influence of defects in a truss structure on rigidity of the structure in any direction.
Background
In recent years, with the rapid development of manufacturing technologies, particularly additive manufacturing technologies, high-performance and complex structures can be manufactured rapidly and at low cost, and a series of structures which have been designed only theoretically but cannot be manufactured are also manufactured in the process of the continuous development of the additive manufacturing technologies, and are successfully applied to various engineering fields.
However, these structures tend to produce geometric defects during the manufacturing process, particularly those made using additive manufacturing techniques, such as: the absence or increase in the cross-sectional area of the rod. These geometric defects may generate stress concentration during the whole structure stress process, which may have a great influence on the mechanical properties (such as rigidity, strength, etc.) of the structure.
At present, aiming at the problem of the geometric defects, the stress concentration problem caused by the geometric defects is calculated and analyzed in a basic mode. However, in practical applications of the structure, the above geometrical defects also have a significant effect on the stiffness of the structure in different directions. But at present, no analysis method aiming at the influence of geometric defects on the rigidity of the structure in different directions exists. Therefore, it is necessary to provide a method that can analyze the effect of geometric defects on stiffness of a structure in any direction.
The above information disclosed in the background section is only for enhancement of understanding of the background of the present disclosure and therefore it may contain information that does not constitute prior art that is known to a person of ordinary skill in the art.
Disclosure of Invention
The purpose of the present disclosure is to provide an analysis method capable of effectively analyzing the influence of defects on the performance of a truss structure in any direction, and analyzing the influence of defects in the truss structure on the rigidity of the truss structure in any direction.
In order to achieve the purpose, the technical scheme adopted by the disclosure is as follows:
according to the present disclosure, there is provided an analysis method for influence of defects in a truss structure on stiffness of the structure in any direction, comprising:
calculating an overall stiffness matrix of the truss structure;
establishing a node displacement field of the truss structure in any direction;
obtaining node reaction force vectors in any direction of the truss structure according to the overall stiffness matrix and the node displacement field;
applying a periodic boundary condition to the truss structure, and obtaining a characteristic displacement field in any direction and a node reaction field in any direction of the truss structure according to the overall stiffness matrix, the node reaction force vector and the periodic boundary condition;
constructing an analytic expression of equivalent stiffness of the truss structure in any direction according to the node displacement field, the characteristic displacement field, the node reaction force vector and the node reaction force field;
and analyzing the influence of the defects in the truss structure on the rigidity of the structure in any direction according to the analytic expression of the equivalent rigidity.
In an exemplary embodiment of the present disclosure, the calculating an overall stiffness matrix of the truss structure includes:
respectively calculating a local rigidity matrix of each rod piece according to the cross sectional area and the length of each rod piece in the truss structure;
adding the local stiffness matrix of each rod piece to obtain the overall stiffness matrix of the truss structure.
In an exemplary embodiment of the present disclosure, the local stiffness matrix is:
wherein k isiLocal stiffness matrix for the rod member of item i, EiThe modulus of elasticity of the rod member of the i-th line, AiThe cross-sectional area of the rod member of the i-thiThe length of the ith rod piece.
In an exemplary embodiment of the present disclosure, the establishing a node displacement field in any direction of the truss structure includes:
calculating coordinates of each node in the truss structure;
and integrating the coordinates of each node to establish a node displacement field in any direction of the truss structure.
In an exemplary embodiment of the present disclosure, the obtaining a characteristic displacement field in any direction and a node reaction field in any direction of the truss structure according to the overall stiffness matrix, the node reaction vector and the periodic boundary condition includes:
constructing a conversion matrix according to the periodic boundary condition;
obtaining a characteristic displacement field of the truss structure in any direction through the conversion matrix, the overall stiffness matrix and the node reaction force vector;
and removing the periodic boundary condition, and obtaining a node reaction field of the truss structure in any direction according to the characteristic displacement field and the overall stiffness matrix.
In an exemplary embodiment of the present disclosure, the obtaining, through the transformation matrix, the overall stiffness matrix, and the node reaction force vector, a characteristic displacement field in any direction of the truss structure includes:
dividing nodes in the truss structure into a driving node and a driven node
Coupling degrees of freedom of the master node and the slave node in a periodic direction through the conversion matrix;
selecting one active node from the active nodes, and constraining the degrees of freedom of the active node in two directions;
and applying the node reaction force vector to the active node to obtain a characteristic displacement field of the truss structure in any direction.
In an exemplary embodiment of the present disclosure, the characteristic displacement field is:
χ(θ)＝TTχT(θ)，
wherein χ (θ) is the characteristic displacement field, T is the transformation matrix, χT(θ)＝KT -1fT(θ)，KT＝TTKT，fT(θ)＝TTf (theta), K is the overall stiffness matrix, and f (theta) is the node reaction force vector.
In an exemplary embodiment of the present disclosure, the nodal reaction force field is:
f*(θ)＝Kχ(θ)，
wherein f is*(θ) is the nodal reaction field, K is the overall stiffness matrix, and χ (θ) is the characteristic displacement field.
In an exemplary embodiment of the present disclosure, the analytical expression of the equivalent stiffness is:
wherein C (θ) is the equivalent stiffness, V is the volume of the truss structure, χ0(theta) is the nodal displacement field, χ (theta) is the characteristic displacement field, f (theta) is the nodal reaction force vector*(θ) is the nodal reaction field.
In one exemplary embodiment of the present disclosure,
analyzing the influence of the defects in the truss structure on the rigidity of the structure in any direction according to the analytic expression of the equivalent rigidity, wherein the analysis comprises the following steps:
calculating the relative density of the truss structure;
calculating the normalized equivalent stiffness of the truss structure according to the relative density of the truss structure and the analytic expression of the equivalent stiffness;
and analyzing the influence of the defects in the truss structure on the rigidity of the structure in any direction according to the normalized equivalent rigidity.
The technical scheme provided by the disclosure can achieve the following beneficial effects:
according to the analytical formula of the equivalent stiffness in any direction of the truss structure, the influence of the defects on the stiffness of the truss structure in any direction can be effectively analyzed according to the condition that the cross section area of the rod in the truss structure has the defects. And the analysis method provided by the disclosure can also theoretically carry out a method or reduce the defect degree so as to research the influence of the defects in the truss structure on the overall rigidity of the truss structure.
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The above and other features and advantages of the present disclosure will become more apparent by describing in detail exemplary embodiments thereof with reference to the attached drawings.
FIG. 1 illustrates a flow chart of a method of analyzing the effect of defects in a truss structure on structural stiffness in an exemplary embodiment of the disclosure;
FIG. 2 illustrates a schematic structural view of a dual square truss structure in an exemplary embodiment of the present disclosure;
FIG. 3 illustrates a schematic diagram of a biquad truss structure coupled by a transition matrix in an exemplary embodiment of the disclosure;
fig. 4 shows a schematic diagram of the equivalent stiffness of a binary square truss structure in any direction for different defect cases in exemplary embodiments of the present disclosure.
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of embodiments of the disclosure.
The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of embodiments of the disclosure. One skilled in the relevant art will recognize, however, that the embodiments of the disclosure can be practiced without one or more of the specific details, or with other methods, components, materials, and so forth. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring the primary technical ideas of the disclosure.
The terms "a," "an," "the," and the like are used to denote the presence of one or more elements/components/parts; the terms "comprising" and "having" are intended to be inclusive and mean that there may be additional elements/components/etc. other than the listed elements/components/etc.
The invention provides an analysis method for the influence of defects in a truss structure on the rigidity of the truss structure in any direction, which can effectively analyze the influence of the defects on the rigidity of the truss structure in any direction aiming at the condition that the cross section area of a rod piece in the truss structure has defects. And the analysis method provided by the disclosure can also theoretically carry out a method or reduce the defect degree so as to research the influence of the defects in the truss structure on the overall rigidity of the truss structure.
The truss structure can be composed of a plurality of rod pieces, and the number of the rod pieces in the truss structure is not limited by the disclosure and is within the protection scope of the disclosure. The defects in the truss structure may be geometric defects, such as: absence or increase of the cross-sectional area of the rod member, and the like. It should be noted that, in the above-mentioned truss structure, at least one rod member has a defect.
As shown in fig. 1, the analysis method provided by the present disclosure may include the following steps:
step S10, calculating an overall stiffness matrix of the truss structure;
step S20, establishing a node displacement field in any direction of the truss structure;
step S30, obtaining node reaction force vectors in any direction of the truss structure according to the overall stiffness matrix and the node displacement field;
step S40, applying a periodic boundary condition to the truss structure, and obtaining a characteristic displacement field in any direction and a node reaction field in any direction of the truss structure according to the overall stiffness matrix, the node reaction force vector and the periodic boundary condition;
s50, constructing an analytic expression of equivalent stiffness in any direction of the truss structure according to the node displacement field, the characteristic displacement field, the node reaction force vector and the node reaction force field;
and S60, analyzing the influence of the defects in the truss structure on the rigidity of the structure in any direction according to the analytic expression of the equivalent rigidity.
The above steps are explained in detail below:
in step S10, an overall stiffness matrix of the truss structure may be calculated.
Specifically, the local stiffness matrix of each rod member can be calculated according to the cross-sectional area and the length of each rod member in the truss structure. After calculating the local stiffness matrix for each rod, the local stiffness matrices for each rod may be added to obtain the overall stiffness matrix for the truss structure.
Wherein the local stiffness matrix of each rod may be:
wherein k isiLocal stiffness matrix for the ith rod piece, EiIs the elastic modulus of the i-th bar member, AiThe cross-sectional area of the ith rod member, /)iIs the length of the ith rod piece. It should be noted that the value range of i in the above formula may be determined according to the class of the truss structure to be analyzedThe type decision, for example, when the truss structure is a structure composed of 8 bars, the value of i may range from 1, 2, 3, 4, 5, 6, 7, 8; when the truss structure is a structure composed of 9 bars, the value range of i may be 1, 2, 3, 4, 5, 6, 7, 8, 9, and so on, which are all within the protection scope of the present disclosure.
Further, the overall stiffness matrix of the truss structure may be:
K＝∑ki
wherein K is the overall stiffness matrix of the truss structure, KiIs the local stiffness matrix of the ith rod piece.
In addition, for better calculation at a later stage, the cross-sectional area of a structurally complete bar can be designated as a, and the cross-sectional area of a bar with a structure defect can be designated as ad. Thus, the rod member having the defect can be distinguished from the rod member having the complete structure.
In step S20, a node displacement field in any direction of the truss structure may be established.
Specifically, the coordinates of each node in the truss structure can be calculated, and the coordinates of each node are integrated, so that a node displacement field in any direction of the truss structure can be established.
For example: the abscissa and the ordinate of each node in the truss structure can be expressed by using an angle theta, the abscissa and the ordinate of each node are integrated into a matrix, and the transposition of the matrix is taken, so that a node displacement field in any direction of the truss structure can be obtained. Wherein the angle θ may be the direction of the node displacement field. The angle θ may take any value between 0 ° and 360 °, which is within the scope of the present disclosure.
It should be noted that the nodes in the truss structure may be connection points of the respective rods.
In step S30, node reaction force vectors in any direction of the truss structure can be obtained from the overall stiffness matrix and the node displacement field.
In particular, the above-described nodal displacement field may be imposed on each node in the truss structure. Therefore, the total stiffness matrix and the node displacement field can be multiplied to obtain node reaction force vectors in any direction of the truss structure. The node reaction force vector may be:
f(θ)＝Kχ0(θ)，
wherein f (theta) is a node reaction force vector, K is an overall rigidity matrix, and x0And (theta) is the node displacement field.
In step S40, a periodic boundary condition may be applied to the truss structure, and a characteristic displacement field in any direction and a node reaction field in any direction of the truss structure may be obtained according to the overall stiffness matrix, the node reaction force vector, and the periodic boundary condition.
Specifically, the periodic boundary condition may be a condition that the displacement of each node is kept equal in a periodic direction, where the periodic direction may be a horizontal direction and a vertical direction, but is not limited thereto, and may also be other directions, such as: the orientation of the cell array, etc., are within the scope of the present disclosure.
The obtaining of the characteristic displacement field in any direction and the node reaction field in any direction of the truss structure according to the overall stiffness matrix, the node reaction vector and the periodic boundary condition may include:
according to the periodic boundary conditions, a transformation matrix can be constructed;
obtaining a characteristic displacement field of the truss structure in any direction through the conversion matrix, the total rigidity matrix and the node reaction force vector;
and removing the periodic boundary condition, and obtaining a node reaction field of the truss structure in any direction according to the characteristic displacement field and the overall stiffness matrix.
It will be appreciated that the transformation matrix may be determined by the type of the periodic boundary condition and the truss structure, i.e., the periodic boundary condition and the truss structure are different, and the transformation matrix is different.
The obtaining of the characteristic displacement field of the truss structure in any direction by converting the matrix, the total stiffness matrix and the node reaction force vector may include:
the nodes in the truss structure can be divided into driving nodes and driven nodes;
the degrees of freedom of the driving node and the driven node in the periodic direction can be coupled through the conversion matrix;
one active node in the active nodes can be selected, and the degrees of freedom of the active node in two directions are restrained;
and applying the node reaction force vector to the active node to obtain a characteristic displacement field of the truss structure in any direction.
It should be noted that, the number of the driving nodes and the number of the driven nodes may be multiple, and the number of the driving nodes and the number of the driven nodes are not limited in the present disclosure and are within the protection scope of the present disclosure.
The characteristic displacement field may be:
χ(θ)＝TTχT(θ)，
wherein, χ (theta) is characteristic displacement field, T is transformation matrix, χT(θ)＝KT -1fT(θ)，KT＝TTKT，fT(θ)＝TTf (theta), K is the overall rigidity matrix, and f (theta) is a node reaction force vector.
The node counterforce field can be as follows:
f*(θ)＝Kχ(θ)，
wherein f is*(theta) is a nodal reaction force field, K is an overall stiffness matrix, and χ (theta) is a characteristic displacement field.
In step S50, an analytical expression of equivalent stiffness in any direction of the truss structure may be constructed from the nodal displacement field, the characteristic displacement field, the nodal reaction force vector, and the nodal reaction force field.
Specifically, the equivalent stiffness may be given by the analytic formula:
wherein C (theta) is equivalent stiffness, V is volume of the truss structure, and chi0(theta) is a node displacement field, chi (theta) is a characteristic displacement field, f (theta) is a node reaction force vector,f*and (theta) is a nodal reaction force field.
In step S60, the influence of the defect in the truss structure on the stiffness in any direction of the structure can be analyzed according to the equivalent stiffness analytic expression.
Specifically, the angles θ of various values can be substituted into the equivalent stiffness formula, so that the equivalent stiffness of the truss structure in any direction can be calculated, and the influence of the defects in the truss structure on the stiffness of the structure in any direction can be analyzed.
In one embodiment of the present disclosure, the relative density of the truss structure may be calculated, the normalized equivalent stiffness of the truss structure may be calculated according to the relative density of the truss structure and the analytic expression of the equivalent stiffness, and the influence of the defect in the truss structure on the stiffness of the structure in any direction may be analyzed according to the normalized equivalent stiffness.
By calculating the relative density of the truss structure and solving the normalized equivalent stiffness, the influence of defects in the truss structures with different densities on the stiffness of the structure in any direction can be conveniently and visually compared in the later period.
The following takes a binary square truss structure composed of 8 rods as an example, and illustrates an analysis method for the influence of defects in the truss structure on the rigidity of the structure in any direction.
As shown in fig. 2 and 3, the rod 001 is a defective rod, and the rest of the rods are structurally complete rods. Thus, the cross-sectional area of the rod 001 can be denoted as adThe cross sectional areas of the remaining rod pieces may be all denoted as a.
So that it is possible to use the formula,
and respectively calculating local rigidity matrixes of the defective rod piece 001 and the structurally complete rod piece, and adding the local rigidity matrixes of the defective rod piece 001 and the structurally complete rod piece to obtain an overall rigidity matrix K of the truss structure.
After the overall stiffness matrix is obtained, a node displacement field in any direction of the truss structure can be established, and the node displacement field in any direction can be as follows:
χ0(θ)＝[x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8]Twherein, in the step (A),
x3＝L cos2θ，y3＝L cosθsinθ，
x6＝L sinθcosθ，y6＝L sin2θ，
x8＝L cos2θ+L sinθcosθ，y8＝L cosθsinθ+L sin2θ。
it should be noted that epsilon in the above formula is a strain value, and the value of the strain value has no influence on the calculation result and can be offset in the subsequent calculation process. As shown in fig. 3, the numbers 1, 2, 3, 4, 5, 6, 7, and 8 are numbers of the truss nodes. In FIG. 3, x is the abscissa and y is the ordinate, and x is the above1May be the abscissa, y, of the first node1May be the ordinate, x, of the first node2May be the abscissa of the second node,y2may be the ordinate of the second node and so on.
The node displacement field can be applied to each node in the truss structure, so that a node reaction force vector in any direction of the truss structure is obtained: f (theta) ═ K chi0(θ)。
A periodic boundary condition is imposed on the truss structure, which may be the same for each node in the truss structure in displacement in a periodic direction. Thus, a transition matrix under this periodic condition can be obtained, which can be:
through the conversion matrix, the degrees of freedom of the driving node and the driven node in the periodic direction can be coupled, so that the degree of freedom of each driven node is the same as that of the driving node, wherein the driving node can be a node 1, a node 2 and a node 4, and the rest nodes can be driven nodes. To prevent the truss structure from moving, the node 1 may be chosen and the degrees of freedom of the node 1 in both directions may be constrained. And then applying the node reaction force vector to the active node, thereby obtaining a characteristic displacement field of the truss structure in any direction: χ (θ) ═ TTχT(θ)。
After the characteristic displacement field is obtained, the periodic boundary condition can be removed, and the characteristic displacement field is applied to the truss structure, so that a node reaction field in any direction of the truss structure can be obtained according to the characteristic displacement field and the overall stiffness matrix: f. of*(θ)＝Kχ(θ)。
An analytic expression of equivalent stiffness in any direction of the truss structure can be constructed according to the node displacement field, the characteristic displacement field, the node reaction force vector and the node reaction force field, and the analytic expression of the equivalent stiffness can be as follows:
the parameters are brought into an analytic expression of the equivalent stiffness, so that an analytic expression of the equivalent stiffness in any direction of the truss structure can be obtained, and the analytic expression can be as follows:
different angles theta are substituted into the analytical expression of the equivalent stiffness, and the equivalent stiffness of the truss structure in any direction can be calculated. Therefore, the influence of the defects in the truss structure on the structural rigidity of the truss structure in any direction can be analyzed.
Further, the relative density of the truss structure may be calculated as:
according to the relative density and the analytical expression of the equivalent stiffness, the normalized equivalent stiffness of the truss structure can be calculated, so that the influence of the defects in the truss structure on the stiffness of the structure in any direction can be analyzed according to the normalized equivalent stiffness.
Specifically, the normalized equivalent stiffness of the truss structure in any direction can be analyzed under the following defects:
1. case where the cross-sectional area of the rod member containing the defect is increased: namely Ad＝10A、Ad＝3A；
2. Case of decrease in cross-sectional area of rod member containing defect: namely 10Ad＝A、3Ad＝A；
3. Containing no or very little defects, i.e. Ad＝A；
4. Absence of a rod, i.e. Ad＝0。
And the equivalent stiffness of the truss structure in any direction under different defect conditions can be visually seen through the graph 4, so that the influence of different defects in the truss structure on the stiffness of the structure in any direction can be rapidly analyzed.
The defect of the truss structure is not limited to this, and other defects may be used, for example: a. thed5A, etc., are within the scope of the present disclosure. Meanwhile, the above is only an example of a truss structure composed of 8 bars, and an analysis method of the influence of defects in the truss structure on the structural rigidity is illustrated. In practical applications, the truss structure formed by 8 bars is not limited, and can be changed according to practical needs, which is within the protection scope of the present disclosure.
In addition, it should be further noted that the above-mentioned node reaction force vectors related individually are node reaction force vectors in any direction of the truss structure, the node displacement fields are node displacement fields in any direction of the truss structure, the characteristic displacement fields are characteristic displacement fields in any direction of the truss structure, the node reaction fields are node reaction fields in any direction of the truss structure, and the analytic expressions of the equivalent stiffness are analytic expressions of the equivalent stiffness in any direction of the truss structure.
It is to be understood that the disclosure is not limited in its application to the details of construction and the arrangements of the components set forth in the specification. The present disclosure is capable of other embodiments and of being practiced and carried out in various ways. The foregoing variations and modifications are within the scope of the present disclosure. It should be understood that the disclosure disclosed and defined in this specification extends to all alternative combinations of two or more of the individual features mentioned or evident from the text and/or drawings. All of these different combinations constitute various alternative aspects of the present disclosure. The embodiments of this specification illustrate the best mode known for carrying out the disclosure and will enable those skilled in the art to utilize the disclosure.
Claims (10)
1. A method for analyzing the influence of defects in a truss structure on the rigidity of the structure in any direction is characterized by comprising the following steps:
calculating an overall stiffness matrix of the truss structure;
establishing a node displacement field of the truss structure in any direction;
obtaining node reaction force vectors in any direction of the truss structure according to the overall stiffness matrix and the node displacement field;
applying a periodic boundary condition to the truss structure, and obtaining a characteristic displacement field in any direction and a node reaction field in any direction of the truss structure according to the overall stiffness matrix, the node reaction force vector and the periodic boundary condition;
constructing an analytic expression of equivalent stiffness of the truss structure in any direction according to the node displacement field, the characteristic displacement field, the node reaction force vector and the node reaction force field;
and analyzing the influence of the defects in the truss structure on the rigidity of the structure in any direction according to the analytic expression of the equivalent rigidity.
2. The method of analysis of claim 1, wherein the calculating an overall stiffness matrix of the truss structure comprises:
respectively calculating a local rigidity matrix of each rod piece according to the cross sectional area and the length of each rod piece in the truss structure;
adding the local stiffness matrix of each rod piece to obtain the overall stiffness matrix of the truss structure.
3. The analytical method of claim 2, wherein the local stiffness matrix is:
wherein k isiLocal stiffness matrix for the rod member of item i, EiThe modulus of elasticity of the rod member of the i-th line, AiThe cross-sectional area of the rod member of the i-thiThe length of the ith rod piece.
4. The method of claim 2, wherein the establishing a nodal displacement field in any direction of the truss structure comprises:
calculating coordinates of each node in the truss structure;
and integrating the coordinates of each node to establish a node displacement field in any direction of the truss structure.
5. The analysis method according to claim 4, wherein the obtaining a characteristic displacement field in any direction and a node reaction field in any direction of the truss structure according to the overall stiffness matrix, the node reaction force vector and the periodic boundary condition comprises:
constructing a conversion matrix according to the periodic boundary condition;
obtaining a characteristic displacement field of the truss structure in any direction through the conversion matrix, the overall stiffness matrix and the node reaction force vector;
and removing the periodic boundary condition, and obtaining a node reaction field of the truss structure in any direction according to the characteristic displacement field and the overall stiffness matrix.
6. The analysis method according to claim 5, wherein the obtaining a characteristic displacement field in any direction of the truss structure through the transformation matrix, the overall stiffness matrix and the node reaction force vector comprises:
dividing nodes in the truss structure into a driving node and a driven node
Coupling degrees of freedom of the master node and the slave node in a periodic direction through the conversion matrix;
selecting one active node from the active nodes, and constraining the degrees of freedom of the active node in two directions;
and applying the node reaction force vector to the active node to obtain a characteristic displacement field of the truss structure in any direction.
7. The analytical method of claim 6, wherein the characteristic displacement field is:
χ(θ)＝TTχT(θ)，
wherein χ (θ) is the characteristic displacement field, T is the transformation matrix, χT(θ)＝KT -1fT(θ)，KT＝TTKT，fT(θ)＝TTf (theta), K is the overall stiffness matrix, and f (theta) is the node reaction force vector.
8. The analysis method of claim 6, wherein the nodal reaction force field is:
f*(θ)＝Kχ(θ)，
wherein f is*(θ) is the nodal reaction field, K is the overall stiffness matrix, and χ (θ) is the characteristic displacement field.
9. The analytical method of claim 6, wherein the equivalent stiffness is analytically expressed as:
wherein C (θ) is the equivalent stiffness, V is the volume of the truss structure, χ0(theta) is the nodal displacement field, χ (theta) is the characteristic displacement field, f (theta) is the nodal reaction force vector*(θ) is the nodal reaction field.
10. The method of claim 1, wherein the analyzing the effect of the defect in the truss structure on the stiffness in any direction of the structure according to the analytical expression of the equivalent stiffness comprises:
calculating the relative density of the truss structure;
calculating the normalized equivalent stiffness of the truss structure according to the relative density of the truss structure and the analytic expression of the equivalent stiffness;
and analyzing the influence of the defects in the truss structure on the rigidity of the structure in any direction according to the normalized equivalent rigidity.
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