CN113704881A - Method for applying inertial load to structural finite element model - Google Patents

Method for applying inertial load to structural finite element model Download PDF

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CN113704881A
CN113704881A CN202110904666.XA CN202110904666A CN113704881A CN 113704881 A CN113704881 A CN 113704881A CN 202110904666 A CN202110904666 A CN 202110904666A CN 113704881 A CN113704881 A CN 113704881A
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inertial load
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CN113704881B (en
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汤春尧
周健
李振国
张研
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Shenyang Aircraft Design and Research Institute Aviation Industry of China AVIC
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Abstract

The application belongs to the technical field of finite element analysis of aircraft thin-wall box section structures, and particularly relates to a method for applying inertial load to a structural finite element model, which comprises the following steps: constructing a structure finite element model; configuring the material density of each component in the structural finite element model, and constructing a mass finite element model; configuring mass weighting coefficients of all components in the mass finite element model, enabling the mass of each component to be consistent with the expected mass, and configuring the direction of the structure inertial load and the acceleration coefficient thereof; and dispersing the inertial load borne by the structure to the nodes of the finite element model of the structure.

Description

Method for applying inertial load to structural finite element model
Technical Field
The application belongs to the technical field of finite element analysis of airplane thin-wall box section structures, and particularly relates to an inertial load applying method of a structural finite element model.
Background
In order to improve the performance and reduce the weight, the wing parts and the empennage parts on the airplane adopt a large number of thin-wall box section structures, and the thin-wall box section structures are thin-wall reinforced structures and have higher bearing efficiency.
In the design stage of the airplane, the structure finite element model is mostly adopted to carry out simulation aided design on the thin-wall box section structure, the structure finite element model describes the deformation and the internal load of the structure under the action of the external load, wherein the inertial load is an important component of the airplane load, and when the structure finite element model is adopted to carry out simulation aided design on the thin-wall box section structure, the inertial load needs to be accurately applied on the structure finite element model, however, the accurate application of the inertial load on the structure finite element model is difficult to realize based on the existing technical scheme, and the accuracy of the analysis on the thin-wall box section structure is seriously influenced.
The present application has been made in view of the above-mentioned technical drawbacks.
It should be noted that the above background disclosure is only for the purpose of assisting understanding of the inventive concept and technical solutions of the present invention, and does not necessarily belong to the prior art of the present patent application, and the above background disclosure should not be used for evaluating the novelty and inventive step of the present application without explicit evidence to suggest that the above content is already disclosed at the filing date of the present application.
Disclosure of Invention
The present application aims to provide a method for applying inertial loads to a structural finite element model, which overcomes or alleviates the technical disadvantages of at least one aspect of the known existing method.
The technical scheme of the application is as follows:
a method for applying inertial load to a structural finite element model comprises the following steps:
constructing a structure finite element model;
configuring the material density of each component in the structural finite element model, and constructing a mass finite element model;
configuring mass weighting coefficients of all components in the mass finite element model, enabling the mass of each component to be consistent with the expected mass, and configuring the direction of the structure inertial load and the acceleration coefficient thereof;
and dispersing the inertial load borne by the structure to 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 structural finite element model, discretizing the inertial load applied to the structure onto a node of the structural finite element model includes:
the method comprises the following steps of dispersing the concentrated inertial load borne by the structure to the nodes of a finite element model of the structure, specifically:
and based on Lagrange multiplier method, dispersing the concentrated inertial load borne by the structure to the nodes of the structure finite element model.
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 concentrated inertial load applied to the structure to nodes of the structural finite element model based on a Lagrange multiplier method specifically includes:
Figure BDA0003201145140000021
Figure BDA0003201145140000022
Figure BDA0003201145140000023
Figure BDA0003201145140000024
wherein,
Pjdistributing the concentrated inertial load borne by the structure in j nodes of a finite element model of the structure;
Ljthe distance from the point of the concentrated inertial load borne by the structure to the j node of the finite element model of the structure is calculated;
λ，λx，λzis Lagrange multiplier;
xjas structural finite elementsCoordinates of model j nodes in the x direction;
zjthe coordinate of a j node of the structure finite element model in the z direction is shown;
n is the number of nodes of the structural finite element model;
xAthe coordinate of the point of the structure which bears the concentrated inertial load in the x direction;
zAthe coordinate of the point of the structure which bears the concentrated inertial load in the z direction;
PAis the concentrated inertial load experienced by the structure.
According to at least one embodiment of the present application, in the method for applying an inertial load to a structural finite element model, discretizing the inertial load applied to the structure onto a node of the structural finite element model includes:
dispersing the continuously distributed inertial load borne by the structure to the vertex of the triangular unit of the finite element model of the structure; or,
and dispersing the continuously distributed inertial load borne by the structure to the vertexes of the quadrilateral units 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 of a finite element model of a structure, the discretization of the continuously distributed inertial load applied to the structure on the vertices of the triangular units of the finite element model of the structure specifically includes:
Figure BDA0003201145140000031
Figure BDA0003201145140000032
Figure BDA0003201145140000033
Figure BDA0003201145140000034
Figure BDA0003201145140000035
Figure BDA0003201145140000036
Figure BDA0003201145140000041
Figure BDA0003201145140000042
Figure BDA0003201145140000043
wherein,
Fi、Fj、Fmdistributing the continuously distributed inertial loads borne by the structure at the vertices i, j and m of the triangular units of the finite element model of the structure;
Ni，Nj，Nmis Lagrange multiplier, and is a triangle unit shape function of the structure finite element model;
xi, eta are used for constructing N in a triangular unit of a finite element model of the structurei、Nj、NmIso-parametric transformation parameters of (1);
p (xi, eta) is the distribution of the continuously distributed inertial load borne by the structure in the triangle unit of the finite element model of the structure;
j is a Jacobi matrix determinant;
xi、yi，xj、yj，xm、ymcoordinates of the vertices i, j and m of the triangular unit of the structural finite element model.
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 discretizing a continuously distributed inertial load borne by the structure onto vertices of quadrilateral elements of the finite element model of the structure specifically includes:
Figure BDA0003201145140000044
Figure BDA0003201145140000045
Figure BDA0003201145140000046
Figure BDA0003201145140000047
Figure BDA0003201145140000051
Figure BDA0003201145140000052
Figure BDA0003201145140000053
Figure BDA0003201145140000054
Figure BDA0003201145140000055
Figure BDA0003201145140000056
Figure BDA0003201145140000057
wherein,
Fi、Fj、Fk、Fldistributing the continuously distributed inertial loads borne by the structure at the vertices i, j, k and l of quadrilateral units of the finite element model of the structure;
Ni，Nj，Nk，Nlis Lagrange multiplier, which is a quadrilateral element shape function of the structure finite element model;
xi, eta are used for constructing N in quadrilateral unit of finite element model with structurei、Nj、Nk、NlIso-parametric transformation parameters of (1);
p (xi, eta) is the distribution of the continuously distributed inertial load borne by the structure in the quadrilateral unit of the finite element model of the structure;
j is a Jacobi matrix determinant;
xi、yi，xj、yj，xk、yk，xl、yland (3) coordinates of the vertices i, j, k and l of the triangular unit of the structural finite element model.
Drawings
FIG. 1 is a flow chart of a method for applying an inertial load to a structural finite element model according to an embodiment of the present application;
FIG. 2 is a schematic diagram illustrating a discretization of a concentrated inertial load experienced by a structure onto a node of a finite element model of the structure according to an embodiment of the present disclosure;
FIG. 3 is a schematic diagram of a two-dimensional shell unit or a three-dimensional unit in a finite element model with a structure, where the inertial loads are continuously distributed and are defined by specifying the size of the distributed loads on the units;
FIG. 4 is a schematic diagram of a triangle unit in a global coordinate system provided in an embodiment of the present application being converted into a regular triangle in a natural coordinate system by an interpolation method;
fig. 5 is a schematic diagram illustrating that a quadrilateral unit in a global coordinate system is converted into a regular quadrilateral in a natural coordinate system by an interpolation method according to an embodiment of the present application.
For the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; further, the drawings are for illustrative purposes, and terms describing positional relationships are limited to illustrative illustrations only and are not to be construed as limiting the patent.
Detailed Description
In order to make the technical solutions and advantages of the present application clearer, the technical solutions of the present application will be further clearly and completely described in the following detailed description with reference to the accompanying drawings, and it should be understood that the specific embodiments described herein are only some of the embodiments of the present application, and are only used for explaining the present application, but not limiting the present application. It should be noted that, for convenience of description, only the parts related to the present application are shown in the drawings, other related parts may refer to general designs, and the embodiments and technical features in the embodiments in the present application may be combined with each other to obtain a new embodiment without conflict.
In addition, unless otherwise defined, technical or scientific terms used in the description of the present application shall have the ordinary meaning as understood by one of ordinary skill in the art to which the present application belongs. The terms "upper", "lower", "left", "right", "center", "vertical", "horizontal", "inner", "outer", and the like used in the description of the present application, which indicate orientations, are used only to indicate relative directions or positional relationships, and do not imply that the devices or elements must have a specific orientation, be constructed and operated in a specific orientation, and when the absolute position of the object to be described is changed, the relative positional relationships may be changed accordingly, and thus, should not be construed as limiting the present application. The use of "first," "second," "third," and the like in the description of the present application is for descriptive purposes only to distinguish between different components and is not to be construed as indicating or implying relative importance. The use of the terms "a," "an," or "the" and similar referents in the context of describing the application is not to be construed as an absolute limitation on the number, but rather as the presence of at least one. The word "comprising" or "comprises", and the like, when used in this description, is intended to specify the presence of stated elements or items, but not the exclusion of other elements or items.
Further, it is noted that, unless expressly stated or limited otherwise, the terms "mounted," "connected," and the like are used in the description of the invention in a generic sense, e.g., connected as either a fixed connection or a removable connection or integrally connected; can be mechanically or electrically connected; they may be directly connected or indirectly connected through an intermediate medium, or they may be connected through the inside of two elements, and those skilled in the art can understand their specific meaning in this application according to the specific situation.
The present application is described in further detail below with reference to fig. 1 to 5.
A method for applying inertial load to a structural finite element model comprises the following steps:
constructing a structure finite element model;
configuring the material density of each component in the structural finite element model, and constructing a mass finite element model;
configuring mass weighting coefficients of all components in the mass finite element model, enabling the mass of each component to be consistent with the expected mass, and configuring the direction of the structure inertial load and the acceleration coefficient thereof;
and dispersing the inertial load borne by the structure to the nodes of the finite element model of the structure.
For the method for applying the inertial load to the structural finite element model disclosed in the above embodiment, it can be understood by those skilled in the art that, on the basis of constructing the finite element model, the material density of each component is configured to construct a mass finite element model, the mass of each component is made to conform to the expected mass by configuring the mass weighting coefficient of each component, the direction and the acceleration coefficient of the structural inertial load are configured, and the inertial load borne by the structure is dispersed to the node of the structural finite element model, so that the inertial load is accurately applied to the structural finite element model.
In some optional embodiments, in the method for applying an inertial load to a finite element model of a structure, discretizing the inertial load applied to the structure on a node of the finite element model of the structure includes:
the method comprises the following steps of dispersing the concentrated inertial load borne by the structure to the nodes of a finite element model of the structure, specifically:
and based on Lagrange multiplier method, dispersing the concentrated inertial load borne by the structure to the nodes of the structure finite element model.
In some optional embodiments, in the method for applying an inertial load to a structural finite element model, the discretizing a concentrated inertial load borne by the structure on nodes of the structural finite element model based on a Lagrange multiplier method specifically includes:
Figure BDA0003201145140000081
Figure BDA0003201145140000082
Figure BDA0003201145140000083
Figure BDA0003201145140000084
wherein,
Pjdistributing the concentrated inertial load borne by the structure in j nodes of a finite element model of the structure;
Ljthe distance from the point of the concentrated inertial load borne by the structure to the j node of the finite element model of the structure is calculated;
λ，λx，λzis Lagrange multiplier;
xjthe coordinates of j nodes of the structure finite element model in the x direction are shown;
zjthe coordinate of a j node of the structure finite element model in the z direction is shown;
n is the number of nodes of the structural finite element model;
xAthe coordinate of the point of the structure which bears the concentrated inertial load in the x direction;
zAthe coordinate of the point of the structure which bears the concentrated inertial load in the z direction;
PAis the concentrated inertial load experienced by the structure.
For the method for applying the inertial load of the finite element model of the structure disclosed in the above embodiments, it can be understood by those skilled in the art that, according to the deformation theory, referring to fig. 2, the structure is subjected to a concentrated inertial load PAIs a cantilever beam supported fixedly, the finite element node j on the free end of which is distributed to the load PjThe deformation energy in time was:
Figure BDA0003201145140000091
wherein EJ is the bending rigidity of the cantilever beam;
the deformation energy of the whole space is as follows:
Figure BDA0003201145140000092
in order to minimize the deformation energy of the whole space, the following static equivalent conditions are satisfied:
Figure BDA0003201145140000093
Figure BDA0003201145140000094
Figure BDA0003201145140000095
lagrange (Lagrange) multiplier methods are used to establish the Lagrange function as follows:
Figure BDA0003201145140000096
Figure BDA0003201145140000097
Figure BDA0003201145140000098
let F (λ)x λz) Taking the minimum value as follows:
Figure BDA0003201145140000099
the following results were obtained:
Figure BDA00032011451400000910
Figure BDA0003201145140000101
in some optional embodiments, in the method for applying an inertial load to a finite element model of a structure, discretizing the inertial load applied to the structure on a node of the finite element model of the structure includes:
dispersing the continuously distributed inertial load borne by the structure to the vertex of the triangular unit of the finite element model of the structure; or,
and dispersing the continuously distributed inertial load borne by the structure to the vertexes of the quadrilateral units 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 discretization of the continuously distributed inertial load applied to the structure on the vertices of the triangular units of the finite element model of the structure specifically includes:
Figure BDA0003201145140000102
Figure BDA0003201145140000103
Figure BDA0003201145140000104
Figure BDA0003201145140000105
Figure BDA0003201145140000106
Figure BDA0003201145140000107
Figure BDA0003201145140000108
Figure BDA0003201145140000109
Figure BDA0003201145140000111
wherein,
Fi、Fj、Fmdistributing the continuously distributed inertial loads borne by the structure at the vertices i, j and m of the triangular units of the finite element model of the structure;
Ni，Nj，Nmis Lagrange multiplier, and is a triangle unit shape function of the structure finite element model;
xi, eta are used for constructing N in a triangular unit of a finite element model of the structurei、Nj、NmIso-parametric transformation parameters of (1);
p (xi, eta) is the distribution of the continuously distributed inertial load borne by the structure in the triangle unit of the finite element model of the structure;
j is a Jacobi matrix determinant;
xi、yi，xj、yj，xm、ymcoordinates of the vertices i, j and m of the triangular unit of the structural finite element model.
For the method for applying inertial load to structural finite element model disclosed in the above embodiments, it can be understood by those skilled in the art that, in the structural finite element model, the inertial load of the two-dimensional shell unit or the three-dimensional unit is a continuously distributed inertial load, which can be defined by specifying the size of the distributed load on the unit, and the pressure intensity on each unit node is different, as shown in fig. 3, in the application of the structural finite element model inertial load, it is necessary to convert any continuously distributed load applied on the unit surface into a concentrated load on the unit node;
any triangle unit in the global coordinate system can be converted into a regular triangle in the natural coordinate system by an interpolation method, as shown in fig. 4:
Figure BDA0003201145140000112
Figure BDA0003201145140000113
Figure BDA0003201145140000114
Figure BDA0003201145140000121
Figure BDA0003201145140000122
at this time, the equivalent nodal force in any triangle unit can be calculated as follows:
Figure BDA0003201145140000123
Figure BDA0003201145140000124
Figure BDA0003201145140000125
Figure BDA0003201145140000126
in some optional embodiments, in the method for applying the inertial load of the finite element model of the structure, the discretization of the continuously distributed inertial load applied to the structure on the vertices of the quadrilateral elements of the finite element model of the structure specifically includes:
Figure BDA0003201145140000127
Figure BDA0003201145140000128
Figure BDA0003201145140000129
Figure BDA00032011451400001210
Figure BDA00032011451400001211
Figure BDA00032011451400001212
Figure BDA00032011451400001213
Figure BDA0003201145140000131
Figure BDA0003201145140000132
Figure BDA0003201145140000133
Figure BDA0003201145140000134
Figure BDA0003201145140000135
wherein,
Fi、Fj、Fk、Fldistributing the continuously distributed inertial loads borne by the structure at the vertices i, j, k and l of quadrilateral units of the finite element model of the structure;
Ni，Nj，Nk，Nlis Lagrange multiplier, which is a quadrilateral element shape function of the structure finite element model;
xi, eta are used for constructing N in quadrilateral unit of finite element model with structurei、Nj、Nm、NlIso-parametric transformation parameters of (1);
p (xi, eta) is the distribution of the continuously distributed inertial load borne by the structure in the quadrilateral unit of the finite element model of the structure;
j is a Jacobi matrix determinant;
xi、yi，xj、yj，xk、yk，xl、yland (3) coordinates of the vertices i, j, k and l of the triangular unit of the structural finite element model.
For the method for applying the inertial load to the finite element model of the structure disclosed in the above embodiments, it can be understood by those skilled in the art that any quadrilateral element in the global coordinate system can be converted into a regular square in the natural coordinate system by an interpolation method, as shown in fig. 5:
Figure BDA0003201145140000136
Figure BDA0003201145140000137
Figure BDA0003201145140000138
Figure BDA0003201145140000141
Figure BDA0003201145140000142
Figure BDA0003201145140000143
at this time, the equivalent node force in an arbitrary quadrilateral unit can be calculated as follows:
Figure BDA0003201145140000144
Figure BDA0003201145140000145
Figure BDA0003201145140000146
Figure BDA0003201145140000147
Figure BDA0003201145140000148
Figure BDA0003201145140000149
the embodiments are described in a progressive manner in the specification, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other.
Having thus described the present application in connection with the preferred embodiments illustrated in the accompanying drawings, it will be understood by those skilled in the art that the scope of the present application is not limited to those specific embodiments, and that equivalent modifications or substitutions of related technical features may be made by those skilled in the art without departing from the principle of the present application, and those modifications or substitutions will fall within the scope of the present application.

Claims (6)

1. A method for applying inertial load to a structural finite element model is characterized by comprising the following steps:
constructing a structure finite element model;
configuring the material density of each component in the structural finite element model, and constructing a mass finite element model;
configuring mass weighting coefficients of all components in the mass finite element model, enabling the mass of each component to be consistent with the expected mass, and configuring the direction of the structure inertial load and the acceleration coefficient thereof;
and dispersing the inertial load borne by the structure to the nodes of the finite element model of the structure.
2. The structural finite element model inertial load applying method according to claim 1,
the discretization of the inertial load borne by the structure on the nodes of the finite element model of the structure comprises the following steps:
the method comprises the following steps of dispersing the concentrated inertial load borne by the structure to the nodes of a finite element model of the structure, specifically:
and based on a Lagrange multiplier method, dispersing the concentrated inertial load borne by the structure to the nodes of the finite element model of the structure.
3. The structural finite element model inertial load applying method according to claim 2,
the method is characterized in that the concentrated inertial load borne by the structure is dispersed to the nodes of the finite element model of the structure based on the Lagrange multiplier method, and specifically comprises the following steps:
Figure FDA0003201145130000011
Figure FDA0003201145130000012
Figure FDA0003201145130000013
Figure FDA0003201145130000014
wherein,
Pjdistributing the concentrated inertial load borne by the structure in j nodes of a finite element model of the structure;
Ljthe distance from the point of the concentrated inertial load borne by the structure to the j node of the finite element model of the structure is calculated;
λ，λx，λzis Lagrange multiplier;
xjthe coordinates of j nodes of the structure finite element model in the x direction are shown;
zjthe coordinate of a j node of the structure finite element model in the z direction is shown;
n is the number of nodes of the structural finite element model;
xAthe coordinate of the point of the structure which bears the concentrated inertial load in the x direction;
zAthe coordinate of the point of the structure which bears the concentrated inertial load in the z direction;
PAis the concentrated inertial load experienced by the structure.
4. The structural finite element model inertial load applying method according to claim 2,
the discretization of the inertial load borne by the structure on 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 vertex of the triangular unit of the finite element model of the structure; or,
and dispersing the continuously distributed inertial load borne by the structure to the vertexes of the quadrilateral units of the finite element model of the structure.
5. The structural finite element model inertial load applying method according to claim 4,
the method for dispersing the continuously distributed inertial load borne by the structure to the vertex of the triangular unit of the finite element model of the structure specifically comprises the following steps:
Figure FDA0003201145130000021
Figure FDA0003201145130000022
Figure FDA0003201145130000031
Figure FDA0003201145130000032
Figure FDA0003201145130000033
Figure FDA0003201145130000034
Figure FDA0003201145130000035
Figure FDA0003201145130000036
Figure FDA0003201145130000037
wherein,
Fi、Fj、Fmis subject to the structureContinuously distributing the distribution of the inertial load at the vertices i, j and m of the triangular units of the finite element model of the structure;
Ni，Nj，Nmis Lagrange multiplier, and is a triangle unit shape function of the structure finite element model;
xi, eta are used for constructing N in a triangular unit of a finite element model of the structurei、Nj、NmIso-parametric transformation parameters of (1);
p (xi, eta) is the distribution of the continuously distributed inertial load borne by the structure in the triangle unit of the finite element model of the structure;
j is a Jacobi matrix determinant;
xi、yi，xj、yj，xm、ymcoordinates of the vertices i, j and m of the triangular unit of the structural finite element model.
6. The structural finite element model inertial load applying method according to claim 4,
the method for dispersing the continuously distributed inertial load borne by the structure to the vertex of the quadrilateral unit of the finite element model of the structure specifically comprises the following steps:
Figure FDA0003201145130000041
Figure FDA0003201145130000042
Figure FDA0003201145130000043
Figure FDA0003201145130000044
Figure FDA0003201145130000045
Figure FDA0003201145130000046
Figure FDA0003201145130000047
Figure FDA0003201145130000048
Figure FDA0003201145130000049
Figure FDA00032011451300000410
Figure FDA00032011451300000411
wherein,
Fi、Fj、Fk、Fldistributing the continuously distributed inertial loads borne by the structure at the vertices i, j, k and l of quadrilateral units of the finite element model of the structure;
Ni，Nj，Nk，Nlis Lagrange multiplier, which is a quadrilateral element shape function of the structure finite element model;
xi, eta are used for constructing N in quadrilateral unit of finite element model with structurei、Nj、Nk、NlIso-parametric transformation parameters of (1);
p (xi, eta) is the distribution of the continuously distributed inertial load borne by the structure in the quadrilateral unit of the finite element model of the structure;
j is a Jacobi matrix determinant;
xi、yi，xj、yj，xk、ykxl、yland (3) coordinates of the vertices i, j, m and l of the triangular unit of the structural finite element model.
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