CN111428411B - Method for removing node discrete errors in finite element simulation analysis result - Google Patents
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Abstract
The invention discloses a method for removing node discrete errors in finite element simulation analysis results, which relates to the field of finite element simulation, and aims to solve the problem that the discrete node errors can not be removed under the condition of large rigid body corner displacement by the conventional method, wherein the method mainly comprises the following steps: step 1, inputting information; step 2, establishing a mapping matrix; step 3, calculating a rigid body rotation matrix; and 4, removing the node discrete errors and outputting a finite element simulation analysis result without the node discrete errors. The method is used for removing the influence of node discrete errors in finite element simulation analysis results, and can improve the interpretation precision of post-processing programs on the simulation analysis results.
Description
Technical Field
The invention relates to the field of aviation and aerospace optical-mechanical structure simulation, in particular to a method for removing node discrete errors in finite element simulation analysis results, which is used for analyzing and removing the node discrete errors in the finite element simulation results to eliminate the influence of the errors on face analysis results, thereby providing pure data input for a finite element simulation analysis post-processing program, improving analysis precision and providing accurate and reliable data support for optical-mechanical structure design and optimization.
Background
The splicing type main mirror is the best technical means for realizing a very large caliber. The splicing type main mirror needs to be adjusted in an on-orbit common-phase mode to achieve the imaging capability of an equivalent design aperture, which is a very complex and very challenging task, and the surface shape parameters of the split mirror and the spatial position of the split mirror need to be actively adjusted. The surface shape parameter adjustment introduces parasitic deformation while changing the aspheric surface parameter of the split mirror; the posture adjustment of the split mirror can change the supporting state of the split mirror, so that the supporting force is changed, and the supporting deformation is introduced; in addition, the split mirrors are also affected by thermal loads and mounting stresses, resulting in surface shape changes.
The surface shape distortion analysis of the split mirror under the working conditions is generally carried out by using finite element simulation analysis. However, when the split mirror performs finite element mesh division, a node discrete error is introduced, which affects the precision of the split mirror shape analysis, and especially, when the high-precision calculation is performed, the node discrete error even submerges the effective analysis result, so that an erroneous conclusion is obtained, and the simulation analysis result is invalid. In xuguangzhou, the concept of discrete node errors is firstly proposed, and an approximate elimination method is provided, but the method is only suitable for the condition that the deformation of the rigid corner displacement of the reflector is very small, and for the analysis working condition of the unfolding and the common phase adjustment of the split mirror with large rigid displacement, the elimination effect of the discrete node errors is not obvious, and the correct result cannot be obtained.
Disclosure of Invention
In order to solve the problem that the existing method cannot solve the problem of removing the discrete node error under the condition of large rigid body corner displacement, the method for removing the node discrete error in the finite element simulation analysis result is provided.
A method for removing node discrete errors in finite element simulation analysis results comprises the following steps:
step one, information input;
the method for removing node discrete errors in the finite element simulation analysis result by substituting the finite element simulation result comprises the initial position vectors of all nodes (n in total) on the structural member to be solved
And a deformation position vector
Step two, establishing a mapping matrix;
inputting a mathematical expression of a surface to be analyzed:
in the formula,
is a surface theoretical parameter vector, j is an integer greater than 1 and less than m, a j J is a parameter of the surface shape to be analyzed, j is a jth theoretical parameter, m represents m theoretical parameters in total, and x, y and z are three-dimensional coordinate vectors respectively;
determining a mapping direction vector
And has:
in the formula,
a unit direction vector representing the mapping of the ith node to the surface to be analyzed, ix i ,iy i ,iz i Vector coordinates of the x axis, the y axis and the z axis after unitization are respectively;
using the initial position vector of node i
And mapping the direction vector
Establishing a straight line l i The equation:
simultaneous mathematical expression and straight line l of the surface to be analyzed i Equation, establishing equation system to solve straight line l i And wait to divideIntersection of the surfaces
The coordinates of (a):
in the formula, xn i ,yn i ,zn i Respectively mapping x, y and z axis position coordinate values of a point of the node i on the surface to be analyzed;
solving the mapping vector of node i
Synthesizing a mapping matrix P map ：
Step three, adopting a rigid body displacement solving algorithm to obtain a rigid body rotation matrix R;
step four, removing node discrete errors and outputting finite element simulation analysis results Pd without node discrete errors * ；
Pd * ＝Pd-R -1 P map
Where Pd is a matrix composed of vectors of deformation positions of all nodes, Pd * The position vector matrix is deformed for all nodes that do not contain node dispersion errors.
The invention has the beneficial effects that: the method can accurately analyze and separate the node discrete errors in the optical-mechanical simulation result, and provides pure and accurate data input for a simulation analysis post-processing program, so that a real surface shape distortion diagram can be obtained, is very important for the design of a support structure of a reflector, and is the most important basis for the structural design of an optical-mechanical of a space camera. Compared with the prior art, the method of the invention is not influenced by rigid body displacement and has wider application characteristics.
Drawings
FIG. 1 is a flow chart of a method for removing node dispersion errors from finite element simulation analysis results according to the present invention;
FIG. 2 is a deformation cloud of finite element simulation analysis results;
FIG. 3 is a diagram of the distortion effect of a mirror surface without removing the influence of discrete nodal errors, wherein FIG. 3a is a distortion diagram of a contour shape, and FIG. 3b is a distortion diagram of a three-dimensional shape;
FIG. 4 is a diagram of the mirror surface distortion effect of the method of the present invention for removing the effect of discrete nodal errors, wherein FIG. 4a is a diagram of equal height surface shape distortion and FIG. 4b is a diagram of three-dimensional surface shape distortion;
Detailed Description
First embodiment, a method for removing node dispersion errors in finite element simulation analysis results according to this embodiment is described with reference to fig. 1 to 4, which is a parametric analysis problem of finite element simulation results in which a certain mirror rotates 30 ° around the y-axis, and a deformed cloud diagram of the finite element analysis results is shown in fig. 2.
The object to be solved is determined first, and in practical engineering application, the deformation state of the optical surface of the reflector is most concerned, so the optical surface of the reflector is taken as a main research object in the embodiment.
Extracting initial coordinate vectors of all nodes on the mirror optical surface
Nodal deformation vector
And importing the node deformation as an input condition into a solving program:
inputting a mathematical expression of a surface to be analyzed:
in the formula, a 1 ＝c＝1/10m；a 2 ＝k＝-0.9
Determining a mapping direction vector
Solving along direction
And pass through the node
Straight line l of i ：
x＝xo i ；y＝yo i ；z＝zo i +t i (4)
The straight line l can be obtained by combining the vertical type (2) and the formula (4) i Point of intersection with surface to be analyzed
The coordinates of (a):
solving the mapping vector of node i
Synthesizing a mapping matrix P map ：
Step 3, calculating a rigid body rotation matrix:
calculating a rigid body rotation matrix R of the analysis surface by using a rigid body displacement solving algorithm;
step 4, removing node discrete errors and outputting finite element simulation analysis results Pd without node discrete errors * ：
Pd * ＝Pd-R -1 P map (9)
Where Pd is a matrix composed of deformation position vectors of all nodes, Pd * Deforming the position vector matrix for all nodes without node discrete errors, and having:
wherein,
the deformed position vector of the node i without the node dispersion error is obtained.
Pd is added * Performing surface shape distortion extraction as original data to obtain a surface shape distortion diagram shown in FIG. 4; a surface shape distortion cloud chart obtained by performing surface shape distortion extraction on data which is not processed by the method for removing node dispersion errors in finite element simulation analysis results according to the embodiment is shown in fig. 3, and it can be known from a comparison chart that discrete nodesThe point error can reduce the surface shape distortion extraction precision, and is not beneficial to the design optimization of the reflector supporting structure.
In this embodiment, the node dispersion error removing method in step 4 may be further expressed as:
Pd # ＝R·Pd * ＝R·Pd-P map (12)
wherein,
the deformation position vector matrix of all nodes after the node discrete error is not contained and the rigid body displacement is removed, and the deformation position vector matrix comprises the following components:
wherein,
and a deformation position vector which does not contain node discrete errors and rigid body displacement is taken as the node i.
Claims (4)
1. A method for removing node discrete errors in finite element simulation analysis results is characterized in that: the method accurately analyzes the node discrete errors in the simulation result of the optical-mechanical device, separates the node discrete errors, provides data input for a simulation analysis post-processing program and obtains a real surface shape distortion diagram; the method comprises the following steps:
step one, information input;
the method for eliminating node discrete errors in finite element simulation analysis results by substituting finite element simulation results comprises the initial position vectors of all nodes on the structural member to be solved
And a deformation position vector
Step two, establishing a mapping matrix;
inputting a mathematical expression of a surface to be analyzed:
in the formula,
is a surface theoretical parameter vector, j is an integer greater than 1 and less than m, a j J is a parameter of the surface shape to be analyzed, j is a jth theoretical parameter, m represents m theoretical parameters in total, and x, y and z are three-dimensional coordinate vectors respectively;
determining a mapping direction vector
And has:
in the formula,
a unit direction vector representing the mapping of the ith node to the surface to be analyzed, ix i ,iy i ,iz i Vector coordinates of the x axis, the y axis and the z axis after unitization are respectively;
using the initial position vector of node i
And mapping the direction vector
Establishing a straight line l i The equation:
mathematical expression and straight line l for simultaneous surfaces to be analyzed i Equation, establishing equation set to solve straight line l i Point of intersection with surface to be analyzed
The coordinates of (a):
in the formula, xn i ,yn i ,zn i Respectively mapping x, y and z axis position coordinate values of a point of the node i on the surface to be analyzed;
solving the mapping vector of node i
Synthesizing a mapping matrix P map ：
Step three, adopting a rigid body displacement solving algorithm to obtain a rigid body rotation matrix R;
step four, removing node discrete errors and outputting finite element simulation analysis results Pd without node discrete errors * And analyzing the result Pd of the finite element simulation without the node dispersion error * Performing surface shape distortion extraction as original data to obtain a surface shape distortion diagram;
Pd * ＝Pd-R -1 P map
where Pd is a matrix composed of vectors of deformation positions of all nodes, Pd * To not contain node separationAnd deforming all nodes with scattered errors to form a position vector matrix.
2. The method of claim 1, wherein the method comprises the steps of: in step one, the initial position vector
And a deformation position vector
Are respectively formulated as:
wherein i is an integer of more than 1 and less than n, xo i ,yo i ,zo i X, y and z-axis initial position coordinate values, xd, of node i, respectively i ,yd i ,zd i The x, y and z axis deformation position coordinate values of node i, respectively.
3. The method of claim 1, wherein the method comprises the steps of: in step four, the matrix Pd composed of the deformed position vectors of all nodes and the deformed position vector matrix Pd of all nodes without node dispersion errors * Respectively expressed as:
in the formula,
the deformed position vector of the node i without the node dispersion error is obtained.
4. The method of claim 1, wherein the method comprises the steps of: the node discrete error removing mode of the step four is expressed as follows:
Pd # ＝R·Pd * ＝R·Pd-P map
in the formula,
the deformed position vector matrix of all nodes after removing rigid body displacement and not containing node discrete error has the following components:
in the formula,
and a deformation position vector which does not contain node discrete errors and rigid body displacement is taken as the node i.
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