CN109472095B - Model shrinkage reducing method applied to automobile body part - Google Patents
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Abstract
The invention discloses a model shrinkage reducing method applied to an automobile body part, which aims at reducing the order of a finite element model of the automobile body part, firstly, acquiring the total mass and the total rigidity matrix of the model through commonly used finite element analysis software, and carrying out regular treatment on the total rigidity matrix; then dividing the total matrix into four matrices with different sizes, and automatically selecting the matrix at the upper left corner as a main matrix; then introducing a preprocessing method to improve matrix inversion operation in the model reduction process, and controlling the error of inversion operation; and finally substituting the accurate inversion operation result into a conversion matrix calculation formula to obtain a reduced model quality and rigidity matrix. The invention can automatically select the main degree of freedom matrix by the computer in the reduction process, thereby reducing the use difficulty of the model reduction method and improving the automation degree of the reduction process.
Description
Technical Field
The invention relates to the field of automobile bodies, in particular to a model shrinkage reducing method applied to automobile body parts.
Background
The modal analysis of the automobile body part is an effective means for identifying the dynamic performance of the automobile body, and the rationality of the automobile body structural design can be judged and the optimization opinion can be specifically proposed according to the result of the modal analysis of the automobile body part. However, the finite element model of an automobile body part, particularly a multi-part assembly, has a large number of degrees of freedom, and in order to effectively reduce the number of degrees of freedom of the model, a model reduction method is required. The existing model reduction methods such as an IRS method, an IIRS method, a high-precision iteration method and the like are mainly based on a Guyan method, and in order to ensure the precision of a model reduction result, a main degree of freedom needs to be accurately selected. The main degree of freedom selection work can be divided into two forms of manual selection and compiling selection programs, so that an operator is required to have certain model analysis experience, and proper values are selected one by one from the whole model total matrix to serve as main degree of freedom values, so that a large amount of labor and material costs are required.
Disclosure of Invention
The invention provides a method for reducing automobile body parts, which aims to overcome the defects of the prior art and can automatically select a main degree of freedom matrix by a computer in the reducing process, thereby reducing the use difficulty of a model reducing method and improving the automation degree of the reducing process.
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
the invention relates to a model shrinkage reducing method applied to automobile body parts, which is characterized by comprising the following steps:
step one: constructing an automobile body part model in finite element analysis software, and acquiring an n multiplied by n total mass matrix M and an n multiplied by n total rigidity matrix K of the automobile body part model;
step two: performing regular treatment on the total stiffness matrix K to obtain a symmetrical positive definite matrix;
step three: constructing a main degree of freedom matrix, and performing block processing on the total mass matrix M and the total stiffness matrix K by utilizing the main degree of freedom matrix to obtain a mass block matrix and a stiffness block matrix, wherein the mass block matrix comprises an M multiplied by M dimension mass main matrix M mm And an sxs-dimensional quality slave matrix M ss The method comprises the steps of carrying out a first treatment on the surface of the The rigidity block matrix comprises an m multiplied by m rigidity main matrix K mm And s x s dimensional stiffness slave matrix K ss And m+s=n;
step four: the sxs-dimensional stiffness slave matrix K using a basic sparse approximation inverse pretreatment method B-PSAI ss Preprocessing to obtain a preprocessing factor P:
step 4.1: converting the conversion matrix calculation formula corresponding to different model reduction methods into a generalized linear equation set form shown as a formula (1):
Ax＝b (1)
in the formula (1), A is a sparse matrix, and represents the s multiplied by s dimensional rigidity slave matrix K ss X represents the transformation matrix t, b represents the secondary matrix K excluding the transformation matrix t and s x s dimensions of stiffness in the transformation matrix calculation formula ss An external element;
step 4.2: let the preprocessing factor be p= [ P ] 1 ,P 2 ,...,P k ,...,P s ]Wherein P is k Representing the kth column vector in the preprocessed factor P, let the kth column vector P k Marked as non-zero lines of (2)Then the kth column vector P k Is of the non-sparse form of
Let the sparse matrix be a= [ a ] 1 ,a 2 ,...,a k ,...,a s ]Wherein a is k Representing the kth column vector in the sparse matrix A, letThe non-zero row of the matrix for the column label is labeled +.>i represents the number of rows of matrix a, and i=1, 2, … s; the non-sparse form of the sparse matrix a is +.>
Let the kth column vector E of the identity matrix E k Is of the non-sparse form of
Step 4.3: initializing k=1;
step 4.4: setting the current cycle number as L, and initializing l=1; setting the maximum circulation times as L max The method comprises the steps of carrying out a first treatment on the surface of the Setting the control precision as epsilon; initializing under the L-th cycle
Step 4.5: solving the kth column vector P of the preprocessing factor P by using QR decomposition method under the L-th cycle k Is not sparse in form of (2)
Step 4.6: judgingIf so, outputting the kth column vector P in the L th cycle k Is>After that, step 4.9 is executed; otherwise, executing the step 4.7;
step 4.7: expanding the sparse structure of the pretreatment factor P by using a formula (2) to obtain a kth column vector in a sparse matrix A under the L+1th cycle
Step 4.8: after L+1 is assigned to L, judging that L is more than L max If so, executing the step 4.9, otherwise, returning to the step 4.5;
step 4.9: after k+1 is assigned to k, judging whether k > s is true, if so, obtaining an s multiplied by s dimension pretreatment factor P which is restored after being ordered according to the column standard; otherwise, returning to the step 4.4;
step five: the sxs-dimensional stiffness slave matrix K is determined by the pretreatment factor P ss Performing sparse matrix inversion calculation to obtain an inverse matrix of the sxs-dimensional stiffness slave matrix
Step six: dividing the mass and stiffness matrix into inverse of the sxs-dimensional stiffness matrixSubstituting the model into different conversion matrix calculation formulas, so as to solve the conversion matrix t in different model reduction methods;
step seven: and calculating a new total mass matrix and a new total stiffness matrix of the reduced automobile body part model by using the transformation matrix t, and solving modal characteristic values of the reduced automobile body part model.
Compared with the prior art, the invention has the beneficial effects that:
1. in order to simplify the model reduction flow and improve the automation degree of the reduction method, the main degree of freedom matrix is not accurately selected in the invention, so that the problem of inaccurate matrix inversion result can occur in the reduction process, and the error of preprocessing technology control matrix inversion calculation is introduced. The preprocessing technology is a method for ensuring iteration convergence and improving convergence speed when solving a large linear equation set, and can solve the problems in the model reduction process in a targeted manner.
2. The invention performs model reduction aiming at the finite element model of the automobile body part, can effectively reduce the number of degrees of freedom of the automobile body part model, realizes model reduction and improves the modal analysis efficiency of the automobile body part.
3. The invention uses the automatic dividing method when selecting the main degree of freedom, omits the complex main degree of freedom selecting work, reduces the application difficulty of the model reduction method and improves the automation level of the reduction process.
4. According to the invention, a small square matrix at the left upper corner of the total matrix of the model is automatically divided to serve as a main degree of freedom matrix for model reduction, and the accuracy of the inversion calculation result of the sparse matrix in the model reduction process is ensured by introducing an approximate inverse preprocessing technology, so that a simple high-automation model reduction flow is realized, and the high correspondence between the modal frequencies of each order of the reduced automobile body part model and the result of commercial finite element software modal analysis is ensured.
Drawings
FIG. 1 is a flow chart of the overall model reduction method of the present invention;
FIG. 2 is a finite element model diagram of an automobile bumper in an example of the invention;
FIG. 3 is a finite element model diagram of an automobile hood in an example of the invention;
FIG. 4 is a graph comparing the results of a conventional model reduction for an example of an automobile bumper of the present invention with the results of the method of the present invention;
FIG. 5 is a graph comparing the results of the traditional model reduction of an example of an automobile hood according to the present invention with the results of the method according to the present invention.
Detailed Description
In this embodiment, a model shrinkage reducing method applied to an automobile body part includes the steps of:
step one: and constructing an automobile body part model, such as an automobile bumper model shown in fig. 2 and an automobile engine cover model shown in fig. 3, in the Hypermesh of the finite element analysis software. An n×n-dimensional total mass matrix M and an n×n-dimensional total stiffness matrix K of the two models were obtained using Abaqus software, wherein the bumper model total matrix was a 6966×6966-dimensional square matrix and the hood model total matrix was a 10740 × 10740-dimensional square matrix.
Step two: and carrying out regular treatment on the total stiffness matrix K to obtain a symmetrical positive definite matrix, so that a singular matrix cannot appear in the matrix pretreatment process. The regularization method comprises the following steps:
K＝K-αM (1)
in the formula (1), α is a regular coefficient, and α=300000 is taken in the present invention. As shown in fig. 1, the model reduction preparation is completed, and the processed matrix may be substituted into the reduction main program.
Step three: constructing a main degree of freedom matrix, and performing blocking treatment on a total mass matrix M and a total stiffness matrix K by using the main degree of freedom matrix to obtain a mass blocking matrix and a stiffness blocking matrix, wherein the mass blocking matrix comprises an M multiplied by M dimensional mass main matrix M mm And an sxs-dimensional quality slave matrix M ss The method comprises the steps of carrying out a first treatment on the surface of the The rigidity block matrix comprises an m multiplied by m rigidity main matrix K mm And s x s dimensional stiffness slave matrix K ss And m+s=n, the specific block form is shown in formula (2):
taking m as 10% -15% of s generally, wherein too small m may cause insufficient model information contained in the main matrix to cause shrinkage failure; if m is too large, the model reduction can not be achieved, because the reduced model matrix is an m×m-dimensional square matrix with the same size as the main matrix.
Step four: using a basic sparse approximation inverse pretreatment method B-PSAI vs. sxs dimensional stiffness slave matrix K ss And (5) preprocessing to obtain a preprocessing factor P. The B-PSAI method has good parallelism naturally, can fully utilize a plurality of processors of the multi-core computer to calculate the large matrix according to columns, and can effectively reduce the time cost of calculation. As shown in FIG. 1, the preprocessing program is independently written as a subprogram in Matlab, and the rigidity slave matrix K is obtained in the main program ss And then called. Stiffness slave matrix K ss And the interface between the main program and the subprogram is also used for preprocessing the subprogram to obtain the preprocessing factor P by calculation and then outputting the preprocessing factor P to the reduction main program.
Step 4.1: converting the conversion matrix calculation formulas (8), formula (9) and formula (10) corresponding to different model reduction methods into a generalized linear equation set form shown as formula (3):
Ax＝b (3)
in the formula (3), A is a sparse matrix, and represents an sxs-dimensional rigidity slave matrix K ss X represents the transformation matrix t, b represents the transformation matrix calculated formulas (8), (9), (10) except the transformation matrix t and s×s dimensionsDegree slave matrix K ss External elements. The preprocessing technique is introduced by calculating a preprocessing factor P and converting equation (3) into:
APy＝b，x＝Py (4)
in the formula (4), the preprocessing factor P is an s×s dimensional square matrix, the array vector group y is a new unknown number, and the AP needs to be as close to the unit matrix as possible.
Step 4.2: let the preprocessing factor be p= [ P ] 1 ,P 2 ,...,P k ,...,P s ]Wherein P is k Representing the kth column vector in the preprocessed factor P, let the kth column vector P k Marked as non-zero lines of (2)Then the kth column vector P k Is of the non-sparse form of
Let the sparse matrix be a= [ a ] 1 ,a 2 ,...,a k ,...,a s ]Wherein a is k Representing the kth column vector in sparse matrix A, letThe non-zero row of the matrix for the column label is labeled +.>i represents the number of rows of matrix a, and i=1, 2, … s; the non-sparse form of the sparse matrix a is +.>
Let the kth column vector E of the identity matrix E k Is of the non-sparse form of
The sparse matrix and the vector are processed into a non-sparse form, so that the requirement on the memory of a computer can be effectively reduced, and therefore, some large-sized vehicle body models can also be calculated by using the method.
Step 4.3: initializing k=1;
step 4.4: setting the current cycle number as L, and initializing l=1; setting the maximum circulation times as L max The method comprises the steps of carrying out a first treatment on the surface of the Setting the control precision as epsilon; initializing under the L-th cycleIn the invention take L max When the maximum number of cycles is too large or the control accuracy is set too small, =6, ε=0.3, the number of cycles increases greatly.
Step 4.5: solving the kth column vector P of the preprocessing factor P by using QR decomposition method under the L-th cycle k Is not sparse in form of (2)The specific calculation formula is as follows:
step 4.6: judgingIf so, outputting the kth column vector P in the L th cycle k Is>After that, step 4.9 is executed; otherwise, executing the step 4.7;
step 4.7: expanding the sparse structure of the pretreatment factor P by using a formula (7) to obtain a kth column vector in the sparse matrix A under the L+1th cycle
The purpose of the extended sparse structure is to increase the number of non-zero numbers in the column vector, so that the column vector contains more information, and the extended calculation result is ensured to meet the requirement of control precision more easily.
Step 4.8: after L+1 is assigned to L, judging that L is more than L max If so, executing the step 4.9, otherwise, returning to the step 4.5;
step 4.9: after k+1 is assigned to k, judging whether k > s is true, if so, obtaining an s multiplied by s dimension pretreatment factor P which is restored after being ordered according to the column standard; otherwise, returning to the step 4.4;
step five: from matrix K using pretreatment factor P for s x s dimensional stiffness ss Performing sparse matrix inversion calculation to obtain an inverse matrix of the sxs-dimensional stiffness slave matrixThe stable bi-conjugate gradient algorithm in the Krylov subspace method is selected as a sparse matrix inversion algorithm, and the bicgstab function is called in Matlab to use the algorithm. The positional relationship of the matrices in the formulas (3) and (4) is strictly observed during calculation, and the left and right order of matrix multiplication cannot be arbitrarily changed.
Step six: dividing the mass and stiffness block matrices and the inverse of the s x s dimensional stiffness slave matrixSubstituting the model into different conversion matrix calculation formulas, so as to solve the conversion matrix t in different model reduction methods. The conversion matrix calculation formula used in the invention is as follows:
IRS method formula:
ITE method formula:
wherein t is G Is a transformation matrix in Guyan method, M G And K G Is a mass and stiffness matrix after Guyan reduction. The Guyan method is the basis of various model reduction methods, but its own reduction accuracy is low and therefore is not used as a separate method.
Step seven: and calculating a new total mass matrix and a new total stiffness matrix of the reduced automobile body part model by using the transformation matrix t, wherein the reduced model total matrix is an m multiplied by m dimensional square matrix, and solving modal characteristic values of the reduced automobile body part model.
When the automobile bumper model and the engine cover model are reduced, m is 11% of n, namely the main matrix of the bumper model is 766 multiplied by 766 dimensional square matrix; the principal matrix of the hood model is a 1181 x 1181 dimensional square. Program compiling is carried out in Matlab software according to a flow chart 1, and formulas of an IRS method and an ITE method in the step six are respectively used for calculating the two models. The model reduction method of the present invention combines B-PSAI pretreatment techniques, so to distinguish from conventional methods, it is named the B-IRS method and the B-ITE method, respectively. The results of the free vibration mode analysis of the Abaqus software are taken as theoretical values (the data name is recorded as ABA), the reduction results are compared, and the comparison results are shown in fig. 4 and 5.
It can be found from the graph that, in the case of obtaining the master matrix and the slave matrix of the model by using the matrix partitioning method shown in the third step, the reduction results of the conventional IRS method and ITE method are far greater than the theoretical values, which indicates that the two methods are completely ineffective. Substituting the same master matrix and slave matrix into the calculation step of the invention, the obtained reduction result is good in correspondence with the theoretical value, which indicates that the invention has good reduction effect on automobile body parts.
Claims (1)
1. A method of model reduction for automotive body parts, comprising the steps of:
step one: constructing an automobile body part model in finite element analysis software, and acquiring an n multiplied by n total mass matrix M and an n multiplied by n total rigidity matrix K of the automobile body part model;
step two: performing regular treatment on the total stiffness matrix K to obtain a symmetrical positive definite matrix;
step three: constructing a main degree of freedom matrix, and performing block processing on the total mass matrix M and the total stiffness matrix K by utilizing the main degree of freedom matrix to obtain a mass block matrix and a stiffness block matrix, wherein the mass block matrix comprises an M multiplied by M dimension mass main matrix M mm And an sxs-dimensional quality slave matrix M ss The method comprises the steps of carrying out a first treatment on the surface of the The rigidity block matrix comprises an m multiplied by m rigidity main matrix K mm And s x s dimensional stiffness slave matrix K ss And m+s=n;
step four: the sxs-dimensional stiffness slave matrix K using a basic sparse approximation inverse pretreatment method B-PSAI ss Preprocessing to obtain a preprocessing factor P:
step 4.1: converting the conversion matrix calculation formula corresponding to different model reduction methods into a generalized linear equation set form shown as a formula (1):
Ax＝b (1)
in the formula (1), A is a sparse matrix, and represents the s multiplied by s dimensional rigidity slave matrix K ss X represents the transformation matrix t, b represents the secondary matrix K excluding the transformation matrix t and s x s dimensions of stiffness in the transformation matrix calculation formula ss An external element;
step 4.2: let the preprocessing factor be p= [ P ] 1 ,P 2 ,...,P k ,...,P s ]Wherein P is k Representing the kth column vector in the preprocessed factor P, let the kth column vector P k Marked as non-zero lines of (2)Then the kth column vector P k Is of the non-sparse form ofk＝1,2,…s；
Let the sparse matrix be a= [ a ] 1 ,a 2 ,...,a k ,...,a s ]Wherein a is k Representing the kth column vector in the sparse matrix A, letThe non-zero row of the matrix for the column label is labeled +.>i represents the number of rows of matrix a, and i=1, 2, … s; the non-sparse form of the sparse matrix a is +.>
Let the kth column vector E of the identity matrix E k Is of the non-sparse form of
Step 4.3: initializing k=1;
step 4.4: setting the current cycle number as L, and initializing l=1; setting the maximum circulation times as L max The method comprises the steps of carrying out a first treatment on the surface of the Setting the control precision as epsilon; initializing under the L-th cycle
Step 4.5: solving the kth column vector P of the preprocessing factor P by using QR decomposition method under the L-th cycle k Is not sparse in form of (2)
Step 4.6: judgingIf so, outputting the kth column vector P in the L th cycle k Is>After that, step 4.9 is executed; otherwise, executing the step 4.7;
step 4.7: expanding the sparse structure of the pretreatment factor P by using a formula (2) to obtain a kth column vector in a sparse matrix A under the L+1th cycle
Step 4.8: after L+1 is assigned to L, judging that L is more than L max If so, executing the step 4.9, otherwise, returning to the step 4.5;
step 4.9: after k+1 is assigned to k, judging whether k > s is true, if so, obtaining an s multiplied by s dimension pretreatment factor P which is restored after being ordered according to the column standard; otherwise, returning to the step 4.4;
step five: the sxs-dimensional stiffness slave matrix K is determined by the pretreatment factor P ss Performing sparse matrix inversion calculation to obtain an inverse matrix of the sxs-dimensional stiffness slave matrix
Step six: dividing the mass and stiffness matrix into inverse of the sxs-dimensional stiffness matrixSubstituted into different conversion matrix calculation formulas, fromSolving a conversion matrix t in different model reduction methods;
step seven: and calculating a new total mass matrix and a new total stiffness matrix of the reduced automobile body part model by using the transformation matrix t, and solving modal characteristic values of the reduced automobile body part model.
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