CN118070580A - Complex structure dynamics calculation method based on MATLAB - Google Patents
Complex structure dynamics calculation method based on MATLAB Download PDFInfo
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Abstract
The invention discloses a complex structure dynamics calculation method based on MATLAB, which comprises the following steps: performing geometric modeling, material attribute giving, finite element mesh subdivision and boundary condition setting on a complex structure by using ABAQUS software, and performing modal analysis calculation according to the established finite element model; reading and storing physical coordinates, modal shape data and natural circle frequency of finite element nodes in the calculation result; reading in physical coordinates, modal shape data and natural circle frequency from a stored calculation result by utilizing a data input function in MATLAB; indexing the serial numbers of the finite element nodes by using physical coordinates through the action positions of the external loads of the finite element nodes, and determining the mode shape data of the corresponding finite element nodes according to the serial numbers of the finite element nodes; calculating the modal force according to the determined modal shape data of the corresponding finite element node; and obtaining the regular response under each order of modes according to the calculated modal force and natural circle frequency, and obtaining the dynamic response of the complex structure according to the regular response.
Description
Technical Field
The invention relates to the technical field of Computer Aided Engineering (CAE), in particular to a complex structure dynamics calculation method based on MATLAB.
Background
Various large structures (such as aerospace vehicles, ocean platforms, ships, bridges, high-rise buildings, large-scale heavy equipment structures, etc.) are continuously developed towards the directions of complexity, high speed and high performance. In order to ensure good performance, accuracy, safety and reliability, the problem of structural dynamics has become an extremely important problem that must be solved.
The fundamental task of structural dynamics is to study the dynamic characteristics and dynamic response exhibited by a structure under dynamic loading. The main task of structural dynamics calculation is to predict the dynamic characteristics and dynamic response of a complex structure, and the method comprises the following steps: determining the dynamic load of external excitation, including the nature, the size and the change rule of the load and the excitation position; simplifying a complex structure into a physical model, and then, into a mathematical model of a differential equation set with a large degree of freedom; and solving on a computer by adopting a reasonable method and a reasonable program to give dynamic characteristics and dynamic response results of the complex structure.
For the dynamics calculation of a simple structure, MATLAB can be used for establishing a mass matrix and a rigidity matrix of a finite element, then numerical solution is carried out, and the calculation result is visualized and analyzed. For complex structural dynamics, analysis and calculation are usually carried out by means of commercial finite element software, wherein ABAQUS is commercial engineering analysis finite element software with strong functions and strong universality, and the problem of dynamic calculation of a complex structure can be solved.
However, MATLAB is cumbersome to solve the complex structural dynamics problem. For complex structural dynamics problems, MATLAB programming solution can involve a series of problems such as modeling of complex geometry, finite element subdivision of complex boundaries, numerical solution of large engineering problems and the like.
For ABAQUS, there are limitations in its computation result access and use: the large-scale encapsulation finite element software such as ABAQUS is used, and the external load accurate loading of complicated space-time distribution and the flexible access and use of calculation results have certain limitations.
In addition, the solution of the dynamics problem of the coupling structure is difficult to realize by using a single platform. For example, for the dynamics problems of coupling structures such as axle coupling and fluid-solid coupling, strong coupling often exists between the input and the output of the structure dynamics, and the solution of the problems is very complex whether MATLAB or ABAQUS is used.
Disclosure of Invention
The invention provides a complex structure dynamics calculation method based on MATLAB, which can solve the technical problems in the prior art.
The invention provides a complex structure dynamics calculation method based on MATLAB, wherein the method comprises the following steps:
Performing geometric modeling, material attribute giving, finite element mesh subdivision and boundary condition setting on a complex structure by using ABAQUS software, and performing modal analysis calculation according to the established finite element model;
Reading and storing physical coordinates, modal shape data and natural circle frequency of finite element nodes in the calculation result;
Reading in physical coordinates, modal shape data and natural circle frequency from a stored calculation result by utilizing a data input function in MATLAB;
Indexing the serial numbers of the finite element nodes by using physical coordinates through the action positions of the external loads of the finite element nodes, and determining the mode shape data of the corresponding finite element nodes according to the serial numbers of the finite element nodes;
calculating modal forces from the determined modal shape data for the corresponding finite element node;
and obtaining the regular response under each order of modes according to the calculated modal force and natural circle frequency, and obtaining the dynamic response of the complex structure according to the regular response.
Preferably, calculating the modal forces from the determined modal shape data of the corresponding finite element node comprises:
the mode force is obtained by multiplying the determined mode shape data of the corresponding finite element node with the external load of the finite element node.
Preferably, the canonical response in each order mode is obtained from the calculated modal forces by:
Wherein r is the order of the multi-degree-of-freedom system, and xi r is the r-order damping ratio; omega nr is the frequency of the r-order natural circle, m r is the mass of the r-order mode, F r is the force of the r-order mode, q 0r is the initial value of the canonical response, omega dr is the frequency of the r-order damping circle, and q r is the canonical response of the r-order.
Preferably, deriving the complex structural dynamics response from the canonical response comprises:
and obtaining the dynamic response of the complex structure according to the regular response and the modal shape data.
Preferably, the complex structural dynamic response is obtained by:
Where x is the complex structural dynamics response, phi r is the r-order mode shape data, and q r is the r-order canonical response.
Preferably, the physical coordinates of the finite element nodes, the mode shape data and the natural circle frequency in the calculation result are stored in the format of txt, csv or dat.
By the technical scheme, the advantages of MATLAB and ABAQUS can be brought into play, repeated data interaction between the MATLAB and the ABAQUS is not needed, and the modal dynamics calculation function of the ABAQUS is integrated into the MATLAB, so that the complexity of loading of external load, access and use of calculation results and visualization is greatly reduced. Meanwhile, a general interface exists between most simulation software and MATLAB, and the invention takes MATLAB as a main platform, so that a foundation can be laid for solving multidisciplinary coupling dynamics problems of large structures in the fields of civil engineering, transportation, aerospace and the like.
Drawings
The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention. It is evident that the drawings in the following description are only some embodiments of the present invention and that other drawings may be obtained from these drawings without inventive effort for a person of ordinary skill in the art.
FIG. 1 shows a flow chart of a MATLAB-based complex structure dynamics calculation method in accordance with an embodiment of the present invention;
FIGS. 2A and 2B are diagrams illustrating a load mode of action versus load time history according to embodiments of the present invention;
FIG. 3 shows a schematic diagram of a bridge mode frequency, mode shape distribution according to an embodiment of the invention;
FIGS. 4A and 4B show schematic diagrams of vertical Y and lateral Z displacements of multiple nodes of a prior art ABAQUS direct integration method;
Fig. 5A and 5B are schematic diagrams showing vertical Y and lateral Z displacements of a plurality of nodes based on MATLAB complex structure dynamics calculation methods according to embodiments of the present invention.
Detailed Description
It should be noted that, without conflict, the embodiments of the present application and features of the embodiments may be combined with each other. The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. The following description of at least one exemplary embodiment is merely exemplary in nature and is in no way intended to limit the application, its application, or uses. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present application. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
The relative arrangement of the components and steps, numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless it is specifically stated otherwise. Meanwhile, it should be understood that the sizes of the respective parts shown in the drawings are not drawn in actual scale for convenience of description. Techniques, methods, and apparatus known to one of ordinary skill in the relevant art may not be discussed in detail, but should be considered part of the specification where appropriate. In all examples shown and discussed herein, any specific values should be construed as merely illustrative, and not a limitation. Thus, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numerals and letters denote like items in the following figures, and thus once an item is defined in one figure, no further discussion thereof is necessary in subsequent figures.
The motion differential equation of the classical viscous damping multi-degree-of-freedom system is as follows:
Wherein M is a mass matrix; c is a damping matrix; k is a stiffness matrix, x is a dynamic response, and f (t) is the external load of the finite element node.
Kinetic response calculation was performed using a modal displacement method, and the displacement was decomposed into a function of the modal and response, i.e., the following equation (5).
Substituting equation (5) into equation (1), equation (1) can be decoupled into n single degree of freedom equations:
Wherein r is the order of the multi-degree-of-freedom system, and xi r is the r-order damping ratio; omega nr is the r-order natural circle frequency, m r is the r-order modal mass, F r is the r-order modal force, and q r is the r-order canonical response.
Neglecting the higher order mode, taking the former L-order mode, and applying Du A Mel integration to obtain the analytical solution of the equation (2) as shown in the following equation (4).
Fig. 1 shows a flow chart of a MATLAB-based complex structure dynamics calculation method according to an embodiment of the present invention.
As shown in fig. 1, an embodiment of the present invention provides a MATLAB-based complex structure dynamics calculation method, where the method includes:
performing geometric modeling, material attribute giving, finite element mesh division (mesh division) and boundary condition setting on a complex structure by using ABAQUS software, and performing modal analysis calculation according to the established finite element model;
The geometric modeling, the material attribute assignment, the finite element mesh division and the boundary condition setting all belong to the conventional operation of the finite element modeling of the structure, so that the invention is not confused and will not be repeated herein.
Reading and storing physical coordinates, modal shape data (field variable) and natural circle frequency (modal frequency) of finite element nodes in the calculation result;
For example, the above may be read using a PYTHON script. The physical coordinates and the mode shape data (field variable) can be read from ABAQUS calculation result.
Reading in physical coordinates, modal shape data and natural circle frequency from a stored calculation result by utilizing a data input function in MATLAB;
that is, the calculation result is imported into MATLAB as input of MATLAB modal dynamics.
Indexing the serial numbers of the finite element nodes by using physical coordinates through the action positions of the external loads of the finite element nodes, and determining the mode shape data of the corresponding finite element nodes according to the serial numbers of the finite element nodes;
wherein the number of the finite element node corresponds to the physical coordinates one by one.
Calculating modal forces from the determined modal shape data for the corresponding finite element node;
and obtaining the regular response under each order of modes according to the calculated modal force and natural circle frequency, and obtaining the dynamic response of the complex structure according to the regular response.
By the technical scheme, the advantages of MATLAB and ABAQUS can be brought into play, repeated data interaction between the MATLAB and the ABAQUS is not needed, and the modal dynamics calculation function of the ABAQUS is integrated into the MATLAB, so that the complexity of loading of external load, access and use of calculation results and visualization is greatly reduced. Meanwhile, a general interface exists between most simulation software and MATLAB, and the invention takes MATLAB as a main platform, so that a foundation can be laid for solving multidisciplinary coupling dynamics problems of large structures in the fields of civil engineering, transportation, aerospace and the like.
Wherein, performing modal analysis calculation according to the established finite element model may include: in the ABAQUS software, frequency analysis (namely frequency analysis) in the linear perturbation analysis step is carried out, COORD is selected and output at the output of the mode shape, and the mode analysis calculation result of quality normalization is obtained.
According to one embodiment of the invention, calculating modal forces from the determined modal shape data of the corresponding finite element node comprises:
the mode force is obtained by multiplying the determined mode shape data of the corresponding finite element node with the external load of the finite element node.
That is, F r＝φr F, where F r is the r-order modal force, φ r is the r-order modal shape data, and F is the external load of the finite element node.
Wherein the external load of the finite element node may be the dynamic response at the previous time.
Thus, modal forces can be obtained.
According to one embodiment of the invention, a canonical response in each order of mode is obtained from the calculated modal forces by:
Wherein r is the order of the multi-degree-of-freedom system, and xi r is the r-order damping ratio; omega nr is the frequency of the r-order natural circle, m r is the mass of the r-order mode, F r is the force of the r-order mode, q 0r is the initial value of the canonical response, omega dr is the frequency of the r-order damping circle, and q r is the canonical response of the r-order.
According to one embodiment of the invention, obtaining a complex structural dynamics response from a canonical response includes:
and obtaining the dynamic response of the complex structure according to the regular response and the modal shape data.
That is, the dynamic response of each node can be reconstructed from the canonical response and the mode shape data.
According to one embodiment of the invention, the complex structural dynamics response is obtained by:
Where x is the complex structural dynamics response, phi r is the r-order mode shape data, and q r is the r-order canonical response.
According to one embodiment of the invention, the physical coordinates, mode shape data and natural circle frequency of the finite element nodes in the calculation result are stored in the format of txt, csv or dat.
It will be appreciated by those skilled in the art that the above format is merely exemplary and is not intended to limit the present invention.
A complex structural dynamics calculation method based on MATLAB according to the present invention is described below with reference to examples. The method can be used for calculating the structural dynamics of the bridge in the vehicle-bridge coupling calculation. The feasibility and accuracy of the invention are illustrated below by comparing the prior art ABAQUS direct integration method (implicit dynamics algorithm) with the modal displacement method of the MATLAB of the invention.
In this example, the operating conditions are: the interaction points of the vehicle-bridge are distributed on the left side and the right side of the bridge, 31 nodes are arranged on each side, triangular pulses are applied, FX peak value of a single node is 2KN, FY is 10KN, FZ is 1KN, and the load action mode and load time course are shown in figures 2A and 2B (wherein, figure 2A is the load action mode, and figure 2B is the load time course).
Fig. 3 shows the modal frequencies, modes of the bridge, and the calculation results can be imported into MATLAB as input to the MATLAB modal dynamics.
Fig. 4A and 4B are displacement graphs of the vertical Y and the lateral Z of the vehicle-bridge interaction point extracted from the ODB file generated by ABAQUS calculation (fig. 4A is a displacement graph of the vertical Y and fig. 4B is a displacement graph of the lateral Z). Fig. 5A and 5B are vertical Y versus lateral Z displacement maps (fig. 5A is a vertical Y displacement map and fig. 5B is a lateral Z displacement map) of the vehicle-bridge interaction point of the first 50 th order mode using MATLAB. It can be seen from the figure that the results of the calculation method based on the complex structural dynamics of MATLAB are consistent with the calculation results of the commercial finite element software ABAQUS.
In the description of the present invention, it should be understood that the azimuth or positional relationships indicated by the azimuth terms such as "front, rear, upper, lower, left, right", "lateral, vertical, horizontal", and "top, bottom", etc., are generally based on the azimuth or positional relationships shown in the drawings, merely to facilitate description of the present invention and simplify the description, and these azimuth terms do not indicate and imply that the apparatus or elements referred to must have a specific azimuth or be constructed and operated in a specific azimuth, and thus should not be construed as limiting the scope of protection of the present invention; the orientation word "inner and outer" refers to inner and outer relative to the contour of the respective component itself.
Spatially relative terms, such as "above … …," "above … …," "upper surface on … …," "above," and the like, may be used herein for ease of description to describe one device or feature's spatial location relative to another device or feature as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as "above" or "over" other devices or structures would then be oriented "below" or "beneath" the other devices or structures. Thus, the exemplary term "above … …" may include both orientations "above … …" and "below … …". The device may also be positioned in other different ways (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
In addition, the terms "first", "second", etc. are used to define the components, and are only for convenience of distinguishing the corresponding components, and the terms have no special meaning unless otherwise stated, and therefore should not be construed as limiting the scope of the present invention.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A complex structure dynamics calculation method based on MATLAB is characterized by comprising the following steps:
Performing geometric modeling, material attribute giving, finite element mesh subdivision and boundary condition setting on a complex structure by using ABAQUS software, and performing modal analysis calculation according to the established finite element model;
Reading and storing physical coordinates, modal shape data and natural circle frequency of finite element nodes in the calculation result;
Reading in physical coordinates, modal shape data and natural circle frequency from a stored calculation result by utilizing a data input function in MATLAB;
Indexing the serial numbers of the finite element nodes by using physical coordinates through the action positions of the external loads of the finite element nodes, and determining the mode shape data of the corresponding finite element nodes according to the serial numbers of the finite element nodes;
calculating modal forces from the determined modal shape data for the corresponding finite element node;
and obtaining the regular response under each order of modes according to the calculated modal force and natural circle frequency, and obtaining the dynamic response of the complex structure according to the regular response.
2. The method of claim 1, wherein calculating modal forces from the determined modal shape data for the corresponding finite element node comprises:
the mode force is obtained by multiplying the determined mode shape data of the corresponding finite element node with the external load of the finite element node.
3. The method of claim 1, wherein the canonical response in each order of modality is obtained from the calculated modal forces by:
Wherein r is the order of the multi-degree-of-freedom system, and xi r is the r-order damping ratio; omega nr is the frequency of the r-order natural circle, m r is the mass of the r-order mode, F r is the force of the r-order mode, q 0r is the initial value of the canonical response, omega dr is the frequency of the r-order damping circle, and q r is the canonical response of the r-order.
4. A method according to claim 3, wherein deriving the complex structural dynamics response from the canonical response comprises:
and obtaining the dynamic response of the complex structure according to the regular response and the modal shape data.
5. The method of claim 4, wherein the complex structural dynamic response is obtained by:
Where x is the complex structural dynamics response, phi r is the r-order mode shape data, and q r is the r-order canonical response.
6. The method according to any of claims 1-5, wherein the physical coordinates of the finite element nodes, the mode shape data and the natural circle frequency in the calculation result are stored in a format of txt, csv or dat.
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