CN111783348A - Finite element analysis-based variable thickness shell unit mass center drift amount calculation method - Google Patents
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Abstract
The invention provides a method for calculating the mass center drift of variable thickness shell units based on finite element analysis, which belongs to the field of structural finite element analysis and comprises the following steps of S1, establishing a shell section with variable thickness property; s2, establishing a secondary development program, extracting mesh nodes before deformation, and dispersing quadrilateral units into triangular units; s3, establishing a local coordinate system O 'X' Y 'Z'; s4, establishing a coordinate transformation matrix M1 of a local coordinate system and a whole coordinate system, and acquiring a function g (x ', y ', z ',) -0 of the thickness of the shell section of the local coordinate system changing along with the space coordinate; s5, obtaining the volume of the triangular unit, and calculating the integral mass center of the structure before deformation by using a mass center formula; s6, determining a local coordinate system O 'X' Y 'Z' of the deformed triangular unit; and S7, calculating the mass center drift amount before and after deformation by applying a space distance formula. The invention has the advantages of strengthened transverse rigidity and reduced interference torque of the air bearing table.
Description
Technical Field
The invention belongs to the field of structural finite element analysis, and relates to a method for calculating the mass center drift of a variable-thickness shell unit based on finite element analysis.
Background
The triaxial air bearing table is core equipment for full physical simulation of a spacecraft attitude control system, when a large triaxial air bearing table is adopted on the ground for physical simulation, the structural deformation of the air bearing table causes the micro-deviation of the whole mass center, and the micro-deviation can cause gravity to generate an interference moment on the triaxial air bearing table. Whether the interference torque can meet the technical index or not is one of key technologies for determining success or failure of design, and the 10t triaxial air bearing table requires that the interference torque under no-load is better than 0.01 N.m, and the interference torque under large inertia is better than 0.02 N.m.
The method is characterized in that the shifting amount of the center of mass caused by gravity when the three-axis air bearing table structure rotates to any angle is very important to accurately calculate, the position of the center of mass of the structure before deformation can be directly obtained by using abaqus software, the structure after deformation can be obtained by leading in a calculation result odb file, and the center of mass of the structure after deformation can be obtained after material attributes are given, however, the quality attributes of shell units with variable thicknesses can not be obtained by the abaqus software, and the positions of the center of mass before and after deformation can not be directly extracted by the shell units with variable thicknesses in a finite element model of the three-axis air bearing table through the.
Through the search of the prior art, only a method for calculating the centroid drift of a triangular unit and a tetrahedral unit is disclosed, a method for calculating the centroid drift of a variable thickness shell unit is not involved, and a method for calculating the centroid drift of a deformable body through the secondary development of finite element software MSC Patran is also disclosed, but the calculation method and the calculation of the centroid drift of the variable thickness shell unit are not specifically given.
Disclosure of Invention
The invention aims to solve the problem of providing a method for calculating the mass center drift amount of a variable-thickness shell unit based on finite element analysis, so that the transverse rigidity is enhanced, and the interference moment of an air bearing table is reduced.
In order to solve the technical problems, the invention adopts the technical scheme that: the method for calculating the mass center drift of the variable-thickness shell unit based on finite element analysis comprises the following steps,
s1, establishing a shell section with variable thickness properties, wherein the thickness of the shell section is 0 as a function f (x, y, z) of a space coordinate, distributing the variable thickness section properties to a geometric model with the shell properties, dividing a grid based on the geometric model, setting boundary conditions and submitting calculation;
s2, establishing a secondary development program, extracting mesh nodes before deformation, and dispersing quadrilateral units into triangular units;
s3, establishing a local coordinate system O ' X ' Y ' Z ', taking the long edge of the triangle as the X ' axis of the local coordinate system, taking the axis where the height of the long edge is as the Y ' axis of the local coordinate system, and determining the Z ' axis according to the right-hand rule;
s4, establishing a coordinate transformation matrix M1 of a local coordinate system and a whole coordinate system, and acquiring a function g (x ', y ', z ',) -0 of the thickness of the shell section of the local coordinate system changing along with the space coordinate;
s5, integrating the triangular units under a local coordinate system to obtain the volumes of the triangular units, obtaining the mass of the triangular units and the mass center position under the local coordinate system by combining the material density, obtaining the mass center position of the triangular units under the global coordinate system according to the coordinate conversion matrix, and calculating the overall mass center of the structure before deformation by using a mass center formula;
s6, dispersing the deformed quadrilateral units into triangular units according to the method in the step 2, and determining the local coordinate system O 'X' Y 'Z' of the deformed triangular units according to the method in the step 3;
and S7, calculating the mass center drift amount before and after deformation by applying a space distance formula.
Further, in step S4, the coordinate conversion matrix is expressed as follows:
and replacing x, y and z parameters in f (x, y, z ') -0 with x ', y ' and z ' through a coordinate transformation matrix to obtain a shell thickness spatial distribution function g (x ', y ', z ') -0 in a local coordinate system.
Further, in step S5, the local coordinate system volume and centroid formula is as follows:
further, in step S6, when the cell feature size is not greater than the structural feature size 1/50, the deformation of the size of a single triangle cell is a high-order small quantity compared with the overall displacement of the triangle cell, the mass and the position of the centroid of the triangle cell in the local coordinate system after deformation are considered to be the same as those before deformation, the coordinate of the centroid position of the triangle cell before deformation determined in step S5 is used as the coordinate of the centroid of the triangle cell in the local coordinate system after deformation, the mass of the triangle cell before deformation determined in step S5 is used as the mass of the triangle cell after deformation, the position of the centroid of the triangle cell after deformation in the overall coordinate system is calculated according to the coordinate transformation matrix M2 of the local coordinate system of the triangle cell after deformation and the overall coordinate system, and the overall centroid position of the centroid of the.
Further, the coordinate transformation matrix is expressed as follows,
further, the centroid formula is as follows,
compared with the prior art, the invention has the following advantages and positive effects.
1. The transverse rigidity of the invention is strengthened, and the interference torque of the air bearing table is reduced;
2. the invention expands the centroid migration calculation method, provides an efficient and accurate centroid drift calculation method for the variable thickness shell unit, and greatly saves the calculation workload of finite elements compared with the volume unit;
3. the invention combines a finite element method and a numerical calculation method, and can realize rapid calculation through a programming method.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate an embodiment of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a schematic diagram of a local coordinate system of a triangle unit according to the present invention;
FIG. 2 is a variable thickness cylinder model of the present invention;
fig. 3 is a cross-section of a variable thickness cylinder of the present invention.
Detailed Description
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
In the description of the present invention, it is to be understood that the terms "central," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like are used in relative terms of orientation or position to facilitate describing the invention and to simplify the description, but do not indicate or imply that the referenced device or element must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be considered limiting of the invention. Furthermore, the terms "first", "second", etc. are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first," "second," etc. may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless otherwise specified.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art through specific situations.
The following is a detailed description of specific embodiments of the invention.
As shown in fig. 1 to 3, the method for calculating the shift amount of the center of mass of the variable thickness shell unit based on finite element analysis comprises the following steps,
s1, establishing a shell section with variable thickness properties, wherein the thickness of the shell section is 0 as a function f (x, y, z) of a space coordinate, distributing the variable thickness section properties to a geometric model with the shell properties, dividing a grid based on the geometric model, setting boundary conditions and submitting calculation;
s2, establishing a secondary development program, extracting mesh nodes before deformation, and dispersing quadrilateral units into triangular units;
s3, establishing a local coordinate system O ' X ' Y ' Z ', taking the long edge of the triangle as the X ' axis of the local coordinate system, taking the axis where the height of the long edge is as the Y ' axis of the local coordinate system, and determining the Z ' axis according to the right-hand rule;
s4, establishing a coordinate transformation matrix M1 of a local coordinate system and a whole coordinate system, and acquiring a function g (x ', y ', z ',) -0 of the thickness of the shell section of the local coordinate system changing along with the space coordinate;
s5, integrating the triangular units under a local coordinate system to obtain the volumes of the triangular units, obtaining the mass of the triangular units and the mass center position under the local coordinate system by combining the material density, obtaining the mass center position of the triangular units under the global coordinate system according to the coordinate conversion matrix, and calculating the overall mass center of the structure before deformation by using a mass center formula;
s6, dispersing the deformed quadrilateral units into triangular units according to the method in the step 2, and determining the local coordinate system O 'X' Y 'Z' of the deformed triangular units according to the method in the step 3;
and S7, calculating the mass center drift amount before and after deformation by applying a space distance formula.
Further, in step S4, the coordinate conversion matrix is expressed as follows:
and replacing x, y and z parameters in f (x, y, z ') -0 with x ', y ' and z ' through a coordinate transformation matrix to obtain a shell thickness spatial distribution function g (x ', y ', z ') -0 in a local coordinate system.
Further, in step S5, the local coordinate system volume and centroid formula is as follows:
further, in step S6, when the cell feature size is not greater than the structural feature size 1/50, the deformation of the size of a single triangle cell is a high-order small quantity compared with the overall displacement of the triangle cell, the mass and the position of the centroid of the triangle cell in the local coordinate system after deformation are considered to be the same as those before deformation, the coordinate of the centroid position of the triangle cell before deformation determined in step S5 is used as the coordinate of the centroid of the triangle cell in the local coordinate system after deformation, the mass of the triangle cell before deformation determined in step S5 is used as the mass of the triangle cell after deformation, the position of the centroid of the triangle cell after deformation in the overall coordinate system is calculated according to the coordinate transformation matrix M2 of the local coordinate system of the triangle cell after deformation and the overall coordinate system, and the overall centroid position of the centroid of the.
Further, the coordinate transformation matrix is expressed as follows,
the centroid formula is as follows,
where p represents density, xUnit cell、yUnit cell、zUnit cellRepresenting the coordinates of the center of mass of the cell, VUnit cellRepresents the volume of the cell, xCenter of mass、yCenter of mass、zCenter of massRepresenting the coordinates of the mass center of the structure as a whole.
Example (b): the central bearing cylinder of the triaxial air bearing table is a conical cylinder, a conical cylinder model is shown in figure 2, the loading mode is that the upper end is fixed, and the Z-direction loading is 10 g.
Firstly, the accuracy of the calculation method is verified, and since the abaqus finite element software can only calculate the quality attribute of the shell element with the same thickness, the wall thickness is 10mm on the assumption of the wall thickness of the conical cylinder shown in fig. 2. The results of the calculation by using abaqus finite element software and the calculation method are shown in table 1, and it can be seen that the mass center drift error of the abaqus finite element software and the abaqus finite element software is less than 2e-7 mm.
TABLE 1 comparison of the results of the abaqus and the present calculation method
The abaqus can not calculate the mass center drift amount of the variable-thickness shell unit, the mass center drift amount of the variable-thickness conical cylinder after being loaded is calculated by using the method, the section of the conical cylinder is shown in figure 3, the loading mode is that the upper end is fixed, 10g is loaded in the Z direction, and the calculation result is shown in table 2.
TABLE 2 Mass center drift after loading of variable thickness cone model
The calculation result shows that the variable-thickness central bearing cylinder is adopted, the transverse rigidity of the bearing cylinder is enhanced, and the reduction of the interference torque of the air bearing table is facilitated.
While one embodiment of the present invention has been described in detail, the description is only a preferred embodiment of the present invention and should not be taken as limiting the scope of the invention. All equivalent changes and modifications made within the scope of the present invention shall fall within the scope of the present invention.
Claims (6)
1. Finite element analysis based variable thickness shell unit mass center drift amount calculation method is characterized in that: comprises the following steps of (a) carrying out,
s1, establishing a shell section with variable thickness properties, wherein the thickness of the shell section is 0 as a function f (x, y, z) of a space coordinate, distributing the variable thickness section properties to a geometric model with the shell properties, dividing a grid based on the geometric model, setting boundary conditions and submitting calculation;
s2, establishing a secondary development program, extracting mesh nodes before deformation, and dispersing quadrilateral units into triangular units;
s3, establishing a local coordinate system O ' X ' Y ' Z ', taking the long edge of the triangle as the X ' axis of the local coordinate system, taking the axis where the height of the long edge is as the Y ' axis of the local coordinate system, and determining the Z ' axis according to the right-hand rule;
s4, establishing a coordinate transformation matrix M1 of a local coordinate system and a whole coordinate system, and acquiring a function g (x ', y ', z ',) -0 of the thickness of the shell section of the local coordinate system changing along with the space coordinate;
s5, integrating the triangular units under a local coordinate system to obtain the volumes of the triangular units, obtaining the mass of the triangular units and the mass center position under the local coordinate system by combining the material density, obtaining the mass center position of the triangular units under the global coordinate system according to the coordinate conversion matrix, and calculating the overall mass center of the structure before deformation by using a mass center formula;
s6, dispersing the deformed quadrilateral units into triangular units according to the method in the step 2, and determining the local coordinate system O 'X' Y 'Z' of the deformed triangular units according to the method in the step 3;
and S7, calculating the mass center drift amount before and after deformation by applying a space distance formula.
2. The finite element analysis-based method for calculating the mass center drift amount of the variable-thickness shell unit according to claim 1, wherein: in step S4, the coordinate conversion matrix is expressed as follows:
and replacing x, y and z parameters in f (x, y, z ') -0 with x ', y ' and z ' through a coordinate transformation matrix to obtain a shell thickness spatial distribution function g (x ', y ', z ') -0 in a local coordinate system.
3. The finite element analysis-based method for calculating the mass center drift amount of the variable-thickness shell unit according to claim 1, wherein: in step S5, the local coordinate system volume and centroid formulas are as follows:
4. the finite element analysis-based method for calculating the mass center drift amount of the variable-thickness shell unit according to claim 1, wherein: in step S6, when the cell feature size is not greater than the structural feature size 1/50, the deformation of the size of a single triangle cell is a high-order small quantity compared with the displacement of the entire triangle cell, the mass and the position of the centroid of the triangle cell in the local coordinate system after deformation are considered to be the same as those before deformation, the coordinate of the centroid of the triangle cell before deformation determined in step S5 is used as the coordinate of the centroid of the triangle cell in the local coordinate system after deformation, the mass of the triangle cell before deformation determined in step S5 is used as the mass of the triangle cell after deformation, the position of the centroid of the triangle cell after deformation in the entire coordinate system is calculated according to the coordinate transformation matrix M2 of the local coordinate system of the triangle cell after deformation and the entire coordinate system, and the position of the centroid of the entire.
5. The finite element analysis-based method for calculating the center-of-mass drift of variable-thickness shell units according to claim 4, wherein the method comprises the following steps: the coordinate transformation matrix is expressed as follows,
6. the finite element analysis-based method for calculating the center-of-mass drift of variable-thickness shell units according to claim 4, wherein the method comprises the following steps: the centroid formula is as follows,
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