CN113704881B - Inertial load application method for finite element model of structure - Google Patents
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Abstract
The application belongs to the technical field of finite element analysis of airplane thin-wall box section structures, and particularly relates to a method for applying inertial load of a structural finite element model, which comprises the following steps: constructing a structural finite element model; configuring material density of each component in the structure finite element model, and constructing a quality finite element model; the method comprises the steps of configuring mass weighting coefficients of all components in a mass finite element model, enabling the mass of each component to be consistent with expected mass, and configuring the direction of inertial load of a structure and acceleration coefficients of the inertial load; the inertial load to which the structure is subjected is discretized onto nodes of the finite element model of the structure.
Description
Technical Field
The application belongs to the technical field of finite element analysis of a thin-wall box section structure of an airplane, and particularly relates to a method for applying inertial load of a finite element model of the structure.
Background
In order to improve the performance and reduce the weight, a large number of thin-wall box section structures are adopted at the positions of wings and tail wings on an aircraft, and the thin-wall box section structures are thin-wall reinforced structures, so that the bearing efficiency is high.
In the aircraft design stage, a structural finite element model is adopted to carry out simulation aided design on a thin-wall box section structure, the structural finite element model describes deformation and internal load of the structure under the action of external load, wherein inertial load is an important component of the aircraft load, and when the structural finite element model is adopted to carry out simulation aided design on the thin-wall box section structure, the inertial load is required to be accurately applied on the thin-wall box section structure, however, the accurate application of the inertial load on the structural finite element model is difficult to realize based on the prior technical scheme, and the accuracy of analyzing the thin-wall box section structure is seriously influenced.
The present application has been made in view of the existence of the above-mentioned technical drawbacks.
It should be noted that the above disclosure of the background art is only for aiding in understanding the inventive concept and technical solution of the present invention, which is not necessarily prior art to the present application, and should not be used for evaluating the novelty and the creativity of the present application in the case where no clear evidence indicates that the above content has been disclosed at the filing date of the present application.
Disclosure of Invention
It is an object of the present application to provide a method of inertial load application of a structural finite element model that overcomes or mitigates at least one of the known technical drawbacks.
The technical scheme of the application is as follows:
a method of inertial load application for a structural finite element model, comprising:
constructing a structural finite element model;
configuring material density of each component in the structure finite element model, and constructing a quality finite element model;
the method comprises the steps of configuring mass weighting coefficients of all components in a mass finite element model, enabling the mass of each component to be consistent with expected mass, and configuring the direction of inertial load of a structure and acceleration coefficients of the inertial load;
the inertial load to which the structure is subjected is discretized onto nodes of the finite element model of the structure.
According to at least one embodiment of the present application, in the method for applying an inertial load to a finite element model of a structure, the dispersing the inertial load to a node of the finite element model of the structure includes:
the concentrated inertial load borne by the structure is scattered to the nodes of the finite element model of the structure, and the method specifically comprises the following steps:
based on Lagrange's multiplier method, the concentrated inertial load to which the structure is subjected is scattered onto the nodes of the finite element model of the structure.
According to at least one embodiment of the present application, in the method for applying an inertial load to a finite element model of a structure, the method for dispersing a concentrated inertial load applied to the structure to a node of the finite element model of the structure based on lagrangian (Lagrange) multiplier is specifically as follows:
wherein,,
P j distributing concentrated inertial load to the structure in the j node of the finite element model;
L j the distance from the point of the concentrated inertial load of the structure to the j node of the finite element model of the structure;
λ，λ x ，λ z is Lagrange multiplier;
x j the coordinates of j nodes of the structure finite element model in the x direction;
z j the coordinate of the j node of the finite element model of the structure in the z direction;
n is the number of structural finite element model nodes;
x A coordinates in the x-direction of points of concentrated inertial load to the structure;
z A coordinates in the z-direction of points of concentrated inertial load to the structure;
P A is subject to concentrated inertial loads.
According to at least one embodiment of the present application, in the method for applying an inertial load to a finite element model of a structure, the dispersing the inertial load to a node of the finite element model of the structure includes:
dispersing the continuously distributed inertial load borne by the structure to the vertexes of the triangular units of the finite element model of the structure; or,
and dispersing the continuously distributed inertial load to the vertices of the quadrilateral unit of the finite element model of the structure.
According to at least one embodiment of the present application, in the method for applying an inertial load to a finite element model of a structure, the dispersing a continuously distributed inertial load to the vertices of a triangle unit of the finite element model of the structure specifically includes:
wherein,,
F i 、F j 、F m distributing continuous distributed inertial load to the structure at vertexes i, j and m of the triangular unit of the finite element model;
N i ，N j ，N m is Lagrange multiplier, which is a triangle unit shape function of the structure finite element model;
ζ, η are used to construct N in a structural finite element model triangle unit i 、N j 、N m Parameter transformation parameters of (2);
p (ζ, eta) is the distribution of the continuously distributed inertial load to which the structure is subjected in the triangular unit of the finite element model of the structure;
j is Jacobi matrix determinant;
x i 、y i ，x j 、y j ，x m 、y m coordinates of vertices i, j and m of triangle units of the finite element model are obtained.
According to at least one embodiment of the present application, in the method for applying an inertial load to a structural finite element model, the dispersing a continuously distributed inertial load to a vertex of a quadrilateral unit of the structural finite element model, specifically:
wherein,,
F i 、F j 、F k 、F l distribution of continuously distributed inertial loads to the structure at the vertices i, j, k, l of the quadrilateral elements of the finite element model of the structure;
N i ，N j ，N k ，N l the Lagrange multiplier is a quadrilateral unit shape function of a structural finite element model;
ζ, eta is used for constructing N in the quadrilateral unit of the finite element model i 、N j 、N k 、N l Parameter transformation parameters of (2);
p (ζ, eta) is the distribution of the continuously distributed inertial load to which the structure is subjected in the quadrangle unit (ζ, eta) of the finite element model of the structure;
j is Jacobi matrix determinant;
x i 、y i ，x j 、y j ，x k 、y k ，x l 、y l coordinates of the vertices i, j, k, l of the triangular elements of the structural finite element model.
Drawings
FIG. 1 is a flow chart of a method of inertial load application of a structural finite element model provided in an embodiment of the present application;
FIG. 2 is a schematic diagram of a structure according to an embodiment of the present application for discretizing the concentrated inertial loads experienced by the structure onto nodes of a finite element model of the structure;
FIG. 3 is a schematic diagram of a finite element model with a continuous distribution of inertial loads for two-dimensional shell elements or three-dimensional elements, defined by specifying the magnitude of the distributed loads on the elements, according to an embodiment of the present application;
FIG. 4 is a schematic diagram of triangle units in an overall coordinate system converted into regular triangles in a natural coordinate system by interpolation according to the embodiment of the present application;
fig. 5 is a schematic diagram of a quadrilateral unit in an overall coordinate system according to an embodiment of the present application converted into a regular quadrilateral in a natural coordinate system by an interpolation method.
For the purpose of better illustrating the embodiments, certain elements of the drawings may be omitted, enlarged or reduced and do not represent the actual product dimensions; further, the drawings are for illustrative purposes, wherein the terms describing the positional relationship are limited to the illustrative description only and are not to be construed as limiting the present patent.
Detailed Description
In order to make the technical solution of the present application and the advantages thereof more apparent, the technical solution of the present application will be more fully described in detail below with reference to the accompanying drawings, it being understood that the specific embodiments described herein are only some of the embodiments of the present application, which are for explanation of the present application, not for limitation of the present application. It should be noted that, for convenience of description, only the portion relevant to the present application is shown in the drawings, and other relevant portions may refer to a general design, and without conflict, the embodiments and technical features in the embodiments may be combined with each other to obtain new embodiments.
Furthermore, unless defined otherwise, technical or scientific terms used in the description of this application should be given the ordinary meaning as understood by one of ordinary skill in the art to which this application belongs. The terms "upper," "lower," "left," "right," "center," "vertical," "horizontal," "inner," "outer," and the like as used in this description are merely used to indicate relative directions or positional relationships, and do not imply that a device or element must have a particular orientation, be configured and operated in a particular orientation, and that the relative positional relationships may be changed when the absolute position of the object being described is changed, and thus should not be construed as limiting the present application. The terms "first," "second," "third," and the like, as used in the description herein, are used for descriptive purposes only and are not to be construed as indicating or implying any particular importance to the various components. The use of the terms "a," "an," or "the" and similar referents in the description of the invention are not to be construed as limited in number to the precise location of at least one. As used in this description, the terms "comprises," "comprising," or the like are intended to cover an element or article that appears before the term and that is listed after the term and its equivalents, without excluding other elements or articles.
Furthermore, unless specifically stated and limited otherwise, the terms "mounted," "connected," and the like in the description herein are to be construed broadly and refer to either a fixed connection, a removable connection, or an integral connection, for example; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can also be communicated with the inside of two elements, and the specific meaning of the two elements can be understood by a person skilled in the art according to specific situations.
The present application is described in further detail below with reference to fig. 1-5.
A method of inertial load application for a structural finite element model, comprising:
constructing a structural finite element model;
configuring material density of each component in the structure finite element model, and constructing a quality finite element model;
the method comprises the steps of configuring mass weighting coefficients of all components in a mass finite element model, enabling the mass of each component to be consistent with expected mass, and configuring the direction of inertial load of a structure and acceleration coefficients of the inertial load;
the inertial load to which the structure is subjected is discretized onto nodes of the finite element model of the structure.
As for the method for applying the inertial load of the finite element model of the structure disclosed by the embodiment, as can be understood by those skilled in the art, the method can be used for accurately applying the inertial load on the finite element model of the structure by configuring the material density of each component on the basis of the finite element model of the structure, constructing a mass finite element model, configuring the mass weighting coefficient of each component to enable the mass of each component to be consistent with the expected mass, configuring the direction and the acceleration coefficient of the inertial load of the structure, and dispersing the inertial load born by the structure on the nodes of the finite element model of the structure.
In some optional embodiments, in the method for applying inertial load to a finite element model of a structure, the dispersing the inertial load to the nodes of the finite element model of the structure includes:
the concentrated inertial load borne by the structure is scattered to the nodes of the finite element model of the structure, and the method specifically comprises the following steps:
based on Lagrange's multiplier method, the concentrated inertial load to which the structure is subjected is scattered onto the nodes of the finite element model of the structure.
In some optional embodiments, in the method for applying the inertial load to the finite element model of the structure, the concentrated inertial load applied to the structure is scattered onto nodes of the finite element model of the structure based on lagrangian (Lagrange) multiplier method, specifically:
wherein,,
P j distributing concentrated inertial load to the structure in the j node of the finite element model;
L j the distance from the point of the concentrated inertial load of the structure to the j node of the finite element model of the structure;
λ，λ x ，λ z is Lagrange multiplier;
x j the coordinates of j nodes of the structure finite element model in the x direction;
z j the coordinate of the j node of the finite element model of the structure in the z direction;
n is the number of structural finite element model nodes;
x A coordinates in the x-direction of points of concentrated inertial load to the structure;
z A coordinates in the z-direction of points of concentrated inertial load to the structure;
P A is subject to concentrated inertial loads.
The structural finite element disclosed for the above embodimentThe method of applying the model inertial load, as will be appreciated by those skilled in the art, is based on deformation theory, see FIG. 2, to concentrate the inertial load P to which the structure is subjected A Is a solid cantilever beam with a finite element node j at its free end assigned to a load P j The deformation energy is as follows:
wherein EJ is the bending stiffness of the cantilever beam;
the deformation energy of the whole space is as follows:
in order to minimize the deformation energy of the whole space, the following static equivalent conditions are satisfied:
the lagrangian (Lagrange) multiplier method is used to build the lagrangian function as follows:
let F (lambda x lambda) z The minimum value of 0 is:
the method can obtain the following steps:
in some optional embodiments, in the method for applying inertial load to a finite element model of a structure, the dispersing the inertial load to the nodes of the finite element model of the structure includes:
dispersing the continuously distributed inertial load borne by the structure to the vertexes of the triangular units of the finite element model of the structure; or,
and dispersing the continuously distributed inertial load to the vertices of the quadrilateral unit of the finite element model of the structure.
In some optional embodiments, in the method for applying the inertial load of the finite element model of the structure, the continuously distributed inertial load applied to the structure is dispersed onto the vertices of the triangular unit of the finite element model of the structure, specifically:
wherein,,
F i 、F j 、F m distributing continuous distributed inertial load to the structure at vertexes i, j and m of the triangular unit of the finite element model;
N i ，N j ，N m is Lagrange multiplier, which is a triangle unit shape function of the structure finite element model;
ζ, η are used to construct N in a structural finite element model triangle unit i 、N j 、N m Parameter transformation parameters of (2);
p (ζ, eta) is the distribution of the continuously distributed inertial load to which the structure is subjected in the triangular unit of the finite element model of the structure;
j is Jacobi matrix determinant;
x i 、y i ，x j 、y j ，x m 、y m coordinates of vertices i, j and m of triangle units of the finite element model are obtained.
For the method for applying inertial load to the finite element model of structure disclosed in the above embodiment, it will be understood by those skilled in the art that in the finite element model of structure, the inertial load of the two-dimensional shell element or the three-dimensional element is a continuous distributed inertial load, which can be defined by specifying the magnitude of the distributed load on the element, and the magnitude of the pressure on each element node is different, as shown in fig. 3, in the application of inertial load to the finite element model of structure, it is necessary to convert any continuous distributed load applied to the element surface into a concentrated load on the element node;
any triangle element in the global coordinate system can be converted into a regular triangle in the natural coordinate system by interpolation, as shown in fig. 4:
at this time, the equivalent node force in any triangle unit can be calculated as follows:
in some optional embodiments, in the method for applying the inertial load to the finite element model of the structure, the continuously distributed inertial load applied to the structure is dispersed onto the vertices of the quadrilateral unit of the finite element model of the structure, specifically:
wherein,,
F i 、F j 、F k 、F l distribution of continuously distributed inertial loads to the structure at the vertices i, j, k, l of the quadrilateral elements of the finite element model of the structure;
N i ，N j ，N k ，N l the Lagrange multiplier is a quadrilateral unit shape function of a structural finite element model;
ζ, eta is used for constructing N in the quadrilateral unit of the finite element model i 、N j 、N m 、N l Parameter transformation parameters of (2);
p (ζ, eta) is the distribution of the continuously distributed inertial load to which the structure is subjected in the quadrangle unit (ζ, eta) of the finite element model of the structure;
j is Jacobi matrix determinant;
x i 、y i ，x j 、y j ，x k 、y k ，x l 、y l coordinates of the vertices i, j, k, l of the triangular elements of the structural finite element model.
For the structural finite element model inertial load application method disclosed in the above embodiment, it will be understood by those skilled in the art that any quadrilateral element in the overall coordinate system can be converted into a regular square in the natural coordinate system by interpolation, as shown in fig. 5:
at this time, the equivalent node force in any quadrilateral unit can be calculated as follows:
in the description, each embodiment is described in a progressive manner, and each embodiment is mainly described by the differences from other embodiments, so that the same similar parts among the embodiments are mutually referred.
Having thus described the technical aspects of the present application with reference to the preferred embodiments illustrated in the accompanying drawings, it should be understood by those skilled in the art that the scope of the present application is not limited to the specific embodiments, and those skilled in the art may make equivalent changes or substitutions to the relevant technical features without departing from the principles of the present application, and those changes or substitutions will now fall within the scope of the present application.
Claims (3)
1. A method of inertial load application for a structural finite element model, comprising:
constructing a structural finite element model;
configuring material density of each component in the structure finite element model, and constructing a quality finite element model;
the method comprises the steps of configuring mass weighting coefficients of all components in a mass finite element model, enabling the mass of each component to be consistent with expected mass, and configuring the direction of inertial load of a structure and acceleration coefficients of the inertial load;
dispersing inertial load born by the structure to nodes of a finite element model of the structure;
the dispersing the inertial load of the structure to the nodes of the finite element model of the structure comprises the following steps:
the concentrated inertial load borne by the structure is scattered to the nodes of the finite element model of the structure, and the method specifically comprises the following steps:
based on the Lagrangian multiplier method, the concentrated inertial load borne by the structure is scattered to the nodes of the finite element model of the structure;
the dispersing the inertial load of the structure to the nodes of the finite element model of the structure comprises the following steps:
dispersing the continuously distributed inertial load borne by the structure to the vertexes of the triangular units of the finite element model of the structure; or,
dispersing continuously distributed inertial load borne by the structure to the vertexes of quadrilateral units of the finite element model of the structure;
the continuous distribution inertial load borne by the structure is scattered to the vertex of the triangle unit of the finite element model of the structure, and the continuous distribution inertial load borne by the structure is specifically:
wherein,,
F i 、F j 、F m distributing continuous distributed inertial load to the structure at vertexes i, j and m of the triangular unit of the finite element model;
N i ，N j ，N m is Lagrange multiplier, which is a triangle unit shape function of the structure finite element model;
ζ, η are used to construct N in a structural finite element model triangle unit i 、N j 、N m Parameter transformation parameters of (2);
p (ζ, eta) is the distribution of the continuously distributed inertial load to which the structure is subjected in the triangular unit of the finite element model of the structure;
j is Jacobi matrix determinant;
x i 、y i ，x j 、y j ，x m 、y m coordinates of vertices i, j and m of triangle units of the finite element model are obtained.
2. The method for inertial load application of a structural finite element model according to claim 1, wherein,
the Lagrangian multiplier method is based on dispersing the concentrated inertial load borne by the structure to the nodes of the finite element model of the structure, and specifically comprises the following steps:
wherein,,
P j distributing concentrated inertial load to the structure in the j node of the finite element model;
L j the distance from the point of the concentrated inertial load of the structure to the j node of the finite element model of the structure;
λ，λ x ，λ z is Lagrange multiplier;
x j the coordinates of j nodes of the structure finite element model in the x direction;
z j the coordinate of the j node of the finite element model of the structure in the z direction;
n is the number of structural finite element model nodes;
x A coordinates in the x-direction of points of concentrated inertial load to the structure;
z A coordinates in the z-direction of points of concentrated inertial load to the structure;
P A is subject to concentrated inertial loads.
3. The method for inertial load application of a structural finite element model according to claim 1, wherein,
the continuously distributed inertial load borne by the structure is scattered to the vertexes of the quadrilateral unit of the finite element model of the structure, and the continuously distributed inertial load borne by the structure is specifically:
wherein,,
F i 、F j 、F k 、F l distribution of continuously distributed inertial loads to the structure at the vertices i, j, k, l of the quadrilateral elements of the finite element model of the structure;
N i ，N j ，N k ，N l the Lagrange multiplier is a quadrilateral unit shape function of a structural finite element model;
ζ, eta is used for constructing N in the quadrilateral unit of the finite element model i 、N j 、N k 、N l Parameter transformation parameters of (2);
p (ζ, eta) is the distribution of the continuously distributed inertial load to which the structure is subjected in the quadrangle unit (ζ, eta) of the finite element model of the structure;
j is Jacobi matrix determinant;
x i 、y i ，x j 、y j ，x k 、y k x l 、y l coordinates of the vertices i, j, m, l of the triangular elements of the structural finite element model.
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