WO2014201984A1

WO2014201984A1 - Super-unit construction method based structure-function analysis method and device therefor

Info

Publication number: WO2014201984A1
Application number: PCT/CN2014/079933
Authority: WO
Inventors: 丁桦
Original assignee: 深圳市网蓝实业有限公司
Priority date: 2013-06-18
Filing date: 2014-06-16
Publication date: 2014-12-24
Also published as: CN104239588A; CN104239588B

Abstract

The present invention relates to a structure-function analysis method and device therefor, based on a super-unit construction method. The present method and device, based on a super-unit construction method, use a deformation characteristic matrix to further simplify a system. Computational processing of structural units greatly simplifies the parameters of the structural characteristics, and better maintains computational accuracy.

Description

Structural function analysis method based on super unit construction method and device thereof

TECHNICAL FIELD The present invention relates to the field of structural dynamics, and more particularly to a structural function analysis method based on a super-cell construction method and an apparatus therefor.

BACKGROUND OF THE INVENTION Any structure involved in the field of structural mechanics has its specific mechanical function. For a long time, simple structures have been described by their unique mechanical functions, such as: springs, which are described by their overall spring coefficient in the direction of use; rods and beams have corresponding mechanical characteristic parameters to describe. These descriptions make the problem simple and straightforward, and express the function of the structure with relatively straightforward parameters, which brings great convenience and efficiency to the application. But a simple and effective description of its function for more complex structures would be very difficult. The key to this is how to describe the function of the structure with as few parameters as possible while maintaining a certain degree of precision.

For a simpler structure, under the action of a specific load, the structural function parameters are generally determined by a certain assumption of the deformation of the structure, or by a certain approximation, establishing the relationship between the equivalent generalized force and the generalized deformation. Such as, beams, plates, shells, etc. Due to the existence of assumptions, these structures are subject to many limitations in their use. From another perspective, when the structure and load conditions differ greatly from the assumptions, the accuracy of the results does not meet the requirements.

For the structural statics problem, under certain conditions, the substructure method can be used to define the structural function parameters: establish the relationship between the external nodes of the substructure part and the external node forces. The corresponding structural function parameter is the stiffness matrix of the substructure.

For the structural dynamics problem, the traditional substructure method is difficult to give the relationship between the external nodes and the nodal forces of the substructure, so it is difficult to establish a structure similar to the structural static problem. Function definition.

The research and application of the simplified method of dynamic system model has always been an important topic in the theoretical research and structural design of large dynamic systems. Similarly, in the field of structural dynamics, model simplification is also a very critical technique in structural dynamic analysis. The fundamental purpose of the structural dynamics model simplification is to obtain a low-order, efficient computational model that meets the engineering accuracy requirements, so that the simplified model can be used for performance analysis and simulation of the original complex model. The existing structural dynamic model simplification methods can be mainly divided into the following three categories.

(I) The method of reducing the degree of freedom, the basic idea is to start from the general motion equation or characteristic equation of the structure, and use the degree of freedom to express the degree of freedom of the polycondensation, so as to simplify the model. Typical such methods are the Guyan-Irons method, the Kuhar method, the IRS method, and the mode polycondensation method.

(2) Dynamic substructure methods, which are methods that directly obtain low-order models. Firstly, the low-order dynamic characteristics of each substructure are obtained, and then the comprehensive vibration equation of the whole structure expressed by low-order modal coordinates is obtained by the double coordination condition of displacement and force between substructures.

(3) Structural equivalence method. From the structural mechanics analysis, such a method obtains a simplified force model for a specific structure and uses the main features of a simple structural equivalent complex structure.

The new dynamic model simplification technology, based on the deformation-corrected power reduction method, can better solve the various limitations and inconveniences in the traditional model simplification technology while maintaining high efficiency. Under certain assumptions, this method can be used to define and simplify the structural dynamics, stiffness and quality of substructures.

Once the definition of the structural function is completed, it can be used to perform structural design, analysis, and validation of the experimental protocol. It is very useful to develop complex structures and make alternative structural designs.

The invention name of the application No. 200810102136.8 is "power reduction algorithm based on deformation correction and super unit construction method". Chinese patent application discloses a power reduction algorithm based on deformation correction and a super unit construction method, which is hereby incorporated by reference in its entirety. Although this method can simplify the model of complex structure well, the computational complexity is greatly reduced. But right In terms of structural parts, it contains relatively many parameters, so that it is rather cumbersome to characterize the structure.

Based on the above drawbacks, the present invention proposes a structural function analysis method based on a super-cell construction method and an apparatus using the same. SUMMARY OF THE INVENTION In view of the above problems in the prior art, an object of the present invention is to provide a structural function analysis method based on a super-cell construction method, which simplifies parameters.

In order to achieve the above object, the present invention provides the following technical solutions: A structural function analysis method based on a super-cell construction method, specifically: Step 1: According to a super-cell construction method, a simplified super-cell model is generated by a structural unit, and an approximating original limited is obtained. An optimized approximation of the displacement of the metamodel = , where g is the generalized displacement vector of the superelement, T is the optimized displacement mode matrix, and the stiffness, mass and damping matrix corresponding to g can be obtained by transformation;

Step 2 According to the displacement characteristics of the boundary of the structural member, the displacement of the boundary node is further simplified, namely:

q = Bq , where g is a super-unit generalized displacement vector, 7j and β are respectively a generalized displacement vector and a component deformation characteristic matrix determined according to the deformation characteristics of the member; using β to construct a structural member stiffness similar to the super-cell method, Mass and damping matrices, which are used as mechanical functions or characteristic parameters of structural members.

Preferably, when the deformation matrix can sufficiently approximate the true displacement, S is a deformation feature matrix that can directly select the component; when further precision is required, it can be obtained by optimization similar to the method of constructing Τ.

According to the geometry of the original model, the structure is divided into several parts, each part is regarded as a super unit, and then divided into several motion synchronization areas according to the motion characteristics of each part, the part boundary nodes are reserved and the feature points of each part of the synchronization area are Add a super node. The super unit construction method is then used to generate a simplified super unit model for the structural unit. The present invention further simplifies the system based on the super-element construction method using the deformation feature matrix. The calculation processing of the structural unit by this method can greatly simplify the parameters of the structural features and better maintain the accuracy of the calculation. The simplest case is to directly use the aforementioned dynamic substructure method, the mass matrix of the substructure, the damping matrix of the substructure ⁽ ', the stiffness matrix ^A ' of the substructure, directly as the functional parameters of the substructure;

(I) In the case that the substructure is more complicated, the substructure can be divided into several smaller substructures. The structural function parameters of each substructure are obtained by the above method, and the overall matrix integration is performed by splicing, that is, similar to finite element. Method, obtaining functional parameters of the substructure;

(2) For substructures with prominent geometric and load characteristics, external loads and nodal displacements can be further modeled to reduce degrees of freedom. That is, the external boundary displacement is further limited, and the boundary displacement synchronization model is used to model the boundary displacement, and the generalized displacement and the corresponding generalized force are obtained, such as the neutral surface displacement, the end surface rotation angle and the corresponding force of the beam end. With torque. Based on the above method, the present invention also provides an apparatus using the above method, the structural function analysis apparatus based on the super unit construction method comprising the following structural unit: a super unit model forming unit, which simplifies the structural unit generation according to the super unit construction method Super element model, an optimized approximation of the displacement approximating the original finite element model

^Ή , , where is the generalized displacement vector of the superelement, τ is the optimal displacement mode matrix, and the corresponding stiffness, mass and damping matrix can be obtained by transformation; the node displacement simplification unit, the displacement of the boundary node according to the displacement feature of the structural member boundary Further simplification, that is, '.q, where ^ is a super-unit generalized displacement vector, ^ is a generalized displacement vector and a component deformation characteristic matrix determined according to the deformation characteristics of the member; and the structural member can be constructed by using a super-cell-like method Stiffness, mass and damping matrix, which are used as mechanical functions or characteristic parameters of structural members.

Preferably, when the deformation matrix can sufficiently approximate the true displacement, s is a deformation feature matrix of the component directly selected; when it is required to further improve the precision, the structure and the tau can be similarly constructed. The method is obtained by optimization.

The present invention further simplifies the system based on the superelement construction method using the deformation feature matrix. The calculation processing of the structural unit by this method can greatly simplify the parameters of the structural features and better maintain the accuracy of the calculation.

The simplest case is to directly use the aforementioned dynamic substructure method, the mass matrix of the substructure, the damping matrix of the substructure ⁽ ', the stiffness matrix ^A ' of the substructure, directly as the functional parameters of the substructure;

(1) In the case that the substructure is more complicated, the substructure can be divided into several smaller substructures, and the structural function parameters of each substructure are obtained by the foregoing method, and the overall matrix integration is performed by splicing, that is, similar finite element. Method, obtaining functional parameters of the substructure;

(2) For substructures with prominent geometric and load characteristics, external loads and nodal displacements can be further modeled to reduce degrees of freedom. That is, the external boundary displacement is further limited, and the boundary displacement synchronization model is used to model the boundary displacement, and the generalized displacement and the corresponding generalized force are obtained, such as the neutral surface displacement, the end surface rotation angle and the corresponding force of the beam end. With torque.

Beneficial effect

The invention will utilize a new dynamic model simplification technique, based on the dynamic reduction method of deformation correction, and give a dynamic substructure method, thereby realizing the characterization of structural function parameters.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a substructure mass condensation model obtained by a super unit analysis method; FIG. 2 is a frequency error curve of the embodiment of FIG. 1;

Figure 3 is a super unit obtained by a super unit construction method;

Figure 4 is an overall structure composed of super units;

Figure 5 is a structural unit obtained by simplification; Figure 6 is an overall structure composed of structural units.

The more compact lung type of the present invention is a structural function analysis method of the present invention, specifically:

1) According to the super-cell construction method, the simplified super-cell model is generated by the structural unit, and an optimized approximation of the displacement of the original finite element model is obtained, where g is the generalized displacement vector of the super element, and T is the optimized displacement mode matrix. The corresponding stiffness, mass and damping matrix can be obtained by transformation;

2) The displacement of the boundary node is further simplified according to the displacement characteristics of the boundary of the structural member, namely:

q = Bq , where g is a super-unit generalized displacement vector, 7 Ϊ, β are respectively a generalized displacement vector and a component deformation characteristic matrix determined according to the deformation characteristics of the member; using β to construct a structural member stiffness similar to the super-cell method, Mass and damping matrices, which are used as mechanical functions or characteristic parameters of structural members.

When the deformation matrix can fully approximate the real displacement, the deformed feature matrix of the component can be directly selected; when the precision needs to be further improved, the method can be similarly optimized by the method of constructing Τ.

The structural function analysis device based on the super unit construction method includes the following structural unit:

The super-cell model forming unit generates a simplified super-cell model from the structural unit according to the super-cell construction method, and obtains an optimized approximation ^逼 which approximates the displacement of the original finite element model, where is the generalized displacement vector of the super-unit, and Τ is optimized Displacement mode matrix, by which the corresponding stiffness, mass and damping matrix can be obtained;

The node displacement simplification unit further simplifies the boundary node displacement according to the displacement feature of the structural member boundary, that is, C, wherein the super-unit generalized displacement vector J and s are respectively the generalized displacement vector and the component deformation determined according to the deformation characteristics of the member. Characteristic moment Array; the structural stiffness, mass and damping matrix of structural members can be constructed by using S-like super-cell method, and they are used as mechanical functions or characteristic parameters of structural members.

Preferably, when the deformation matrix can sufficiently approximate the true displacement, ^ is the deformation feature matrix of the component directly selected; when the precision needs to be further improved, it can be obtained by optimization similar to the method of constructing T.

The following is further illustrated by specific examples.

Plane cantilever beam

The quality of each dynamic substructure is concentrated in the internal super node.

1 is shown. The frequency solution results are shown in Table I, and the frequency error is shown in Figure 2. On the basis of the previous model, similar to the previous dynamic substructure example, the nodes above and below the single substructure are also treated as internal nodes, and the substructure shown in Fig. 3 can be obtained. After splicing, it is obtained as shown in Fig. 2. It is the overall structure.

Further, assuming that the two ends of the substructure conform to the (beam cross section) plane hypothesis (straight normal line), the displacement of both sides of the substructure shown in Fig. 2 is the translational displacement and rotation angle of the two midpoints (u, w, Θ) (al )

(Each side is approximated by the above formula) where y is the coordinate of the node i now parallel to the boundary direction of the midpoint of the boundary. Using ( a2 ), we can construct the relationship between the displacement vector of the boundary points on both sides of the substructure shown in Fig. 1 and the sum of the corners of the two sides.

Using the patents 2008 1 0102 1 36.8 similar to equations (23) to ij (26), a simplified substructure system can be given (Fig. 5 simplified substructure, Fig. 6 corresponds to the overall structure). Table I compares with ANSYS results, and the explanation is basically the same. Table 1 Comparison of the frequency results of the embodiment of Figure 6 with the results of ANSYS solution

Order

ANSYS Solution Results (Hz) Plane Simplified Frequency Results Relative Errors Times (Hz) (%)

1 4.7858 4.7992 0.28%

2 28.792 28.802 0.03%

3 74.608 74.667 0.08%

4 76.135 75.826 -0.41%

5 139 1 37.9 -0.79%

6 213.02 2 1 1 .04 -0.93%

7 223.79 224.58 0.35%

8 294.7 1 291.55 -1.07%

9 372.85 374.93 0.56%

10 381.78 377.86 -1.03%

1 1 472.68 468.27 -0.93%

12 521.61 532.03 2.00%

13 566.33 554.32 -2.12%

14 661.9 647.85 -2.12%

15 669.75 690.05 3.03%

It should be noted that the above-described embodiments are merely illustrative of the present invention and are not intended to limit the embodiments. Other variations or modifications of the various forms may be made by those of ordinary skill in the art. There is no need and no way to exhaust all of the implementations. Obvious changes or variations resulting therefrom are still within the scope of this application. Industrial Applicability The present invention further simplifies the system based on the super-element construction method using the deformation feature matrix. It can better solve various limitations and inconveniences in the traditional model simplification technology. Under certain assumptions, the structural dynamics function, stiffness and quality of the substructure can be performed by calculating the structural unit by this method. It is defined and greatly simplified, and it is better able to maintain the accuracy of the calculation while maintaining high efficiency.

Claims

Claim

1. A structural function analysis method based on a super-cell construction method, characterized in that: the steps are as follows

Step 1 generates a simplified super element model based on the super element construction method to obtain a simplified approximation of the displacement of the original finite element model, where g is the generalized displacement vector of the super element and T is the optimized displacement mode matrix. The stiffness, mass and damping matrix corresponding to g can be obtained by transformation;

Step 2 further simplifies the displacement of the boundary node according to the displacement characteristics of the boundary of the structural member, namely: q - B f , where g is a super-unit generalized displacement vector, and Ίί, β are respectively generalized displacement vectors determined according to the deformation characteristics of the member And the deformation characteristic matrix of the member; the stiffness, mass and damping matrix of the structural member can be constructed by using the method of super-element, which is used as the mechanical function or characteristic parameter of the structural member.

2. The method according to claim 1, wherein when the deformation matrix can sufficiently approximate the true displacement, the deformation characteristic matrix of the component is directly selected; when the precision needs to be further improved, the method capable of similarly constructing the flaw can be optimized. Come to get S.

3. A structural function analysis device based on a super-cell construction method, comprising: a super-cell model forming unit, which generates a simplified super-cell model according to a super-cell construction method, and obtains a displacement approximating the displacement of the original finite element model The approximate approximation u = Tq , where g is the generalized displacement vector of the superelement, T is the optimal displacement mode matrix, and the stiffness, mass and damping matrix corresponding to g can be obtained by transformation; the node displacement simplification unit, according to the boundary of the structural member The displacement feature further simplifies the displacement of the boundary node, namely -. q - Bci , where the super-unit generalized displacement vector, q β is the generalized displacement vector and the component deformation characteristic matrix determined according to the deformation characteristics of the member respectively; Unit method to construct structural members for stiffness, mass and damping Matrices, which are used as mechanical functions or characteristic parameters of structural members.

4. The device according to claim 3, wherein when the deformation matrix can sufficiently approximate the true displacement, the deformation characteristic matrix of the component is directly selected; when the precision needs to be further improved, the method can be optimized similarly to the construction flaw. Come to get S.