CN110096798B - Multi-state finite element model correction method - Google Patents
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Abstract
The invention discloses a method for correcting a multi-state finite element model, which comprises the following steps: (1) Determining finite element model materials and the like, and inputting an optimization initial value; (2) The MSC.Patran software is called to carry out modal analysis on the finite element models of all states; (3) Establishing mathematical optimization models of all states, and setting optimization step length and convergence accuracy value thereof; (4) Setting a similar constraint epsilon value according to the calculated frequency relative error; (5) Writing an MSC. Nastran optimization card, and extracting the iterated design variables and the iterated convergence values of the states of the design variables; (6) According to the target value of the iteration convergence of all states and the design variable value of each state, calculating the weight coefficient of each state, and calculating the initial value of the design variable of MSC. Nastran to be called next time; (7) setting a constraint range epsilon value, and re-writing an optimized card; (8) Repeating the fifth step, the sixth step and the seventh step until the vibration mode and the frequency of each state after iteration are approximately the same as the experimental vibration mode frequency. The method provides a reference for a multi-state finite element model correction method.
Description
Technical Field
The invention belongs to the technical field of engineering structural design, and particularly relates to a method for correcting a multi-state finite element model.
Background
At present, finite element tools are widely used for calculating various engineering structures, and for large complex structures such as rockets, missiles, airplanes and the like, finite element models are difficult to build, even if engineering technicians build the finite element models, the mechanical characteristics of actual structures cannot be accurately predicted due to large calculation errors, so that simulation and simulation work is greatly limited, and finally, the mechanical characteristics of the aircraft structures can be known only by physical prototype tests. The finite element correction technology is to utilize the advantages of both physical prototype test and finite element simulation, correct the finite element model with data obtained by a small amount of prototype test to obtain a relatively accurate finite element model, thereby being capable of replacing the manufacture of complex and costly physical prototypes, saving the cost and shortening the development period. The objective of the correction is to keep the calculation result of the finite element model consistent with the test result of the physical prototype, and establishing an accurate finite element model is an important current challenge.
In the field of aerospace, rocket attitude control is a difficult problem to be solved at present, along with rocket launching, rocket structure dynamics characteristics of different flight seconds are difficult to determine through experiments, and therefore modeling technology and dynamic characteristic numerical analysis technology of rockets and missiles are paid more attention to domestic and foreign students and engineers.
The finite element model correction of multiple states is carried out, namely, when a rocket or a missile is selected to launch at different times, modal analysis is carried out on the rocket or the missile, and due to different fuels at different times, the dynamics characteristics are different, and the finite element model correction is carried out according to the rocket model of the selected states, so that the dynamics characteristics of each state simulation are ensured to be close to the dynamics characteristics of an experiment, the accurate establishment of the rocket finite element model is achieved, and the finite element model has an important effect on the aerospace field.
Aiming at the problem that the dynamics characteristics of all states are inconsistent in the multi-state finite element model correction, the invention provides a method for correcting the multi-state finite element model. The method for correcting the multi-state finite element model combines a structural modal finite element analysis method, a reasonable constraint range is set by establishing a reasonable mathematical model, and MSC.Nastran optimization cards in all states are gradually called for iteration; calculating weight coefficients of all states by utilizing iteration convergence of all states, calculating initial values of design variables for calling MSC. Nastran next time, reducing frequency constraint range, writing optimization cards, and continuously calling the MSC. Nastran optimization cards of all states step by step for iteration; until the dynamics of the finite element of all the corrected states are consistent with the dynamics of the experimental model. The method for correcting the multi-state finite element model is beneficial to reducing the calculated amount and time in the operation process, and enables the dynamic characteristics of the finite element model in all states to be consistent with those of an experimental model to the greatest extent, so that the method has important significance in promoting the rapid development of important fields such as aerospace and the like.
Disclosure of Invention
Aiming at the problems existing in the correction of the multi-state finite element model, a reasonable constraint range is set by establishing a reasonable mathematical model, and MSC.Nastran optimization cards in all states are gradually called for iteration; calculating weight coefficients of all states by utilizing iteration convergence of all states, calculating initial values of design variables for calling MSC. Nastran next time, reducing frequency constraint range, writing optimization cards, and continuously calling the MSC. Nastran optimization cards of all states step by step for iteration; and obtaining reasonable design variable values until the dynamic characteristics of the finite elements of all states are consistent with those of the experimental model. The method for correcting the multi-state finite element model is beneficial to shortening the structural design period, more accurately finding out the final optimal solution of all state model corrections, and has extremely strong practicability.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the technical scheme adopted by the invention is a method for correcting a multi-state finite element model, which comprises the following steps:
determining finite element model materials, structural dimension parameters and establishing finite element models of all states;
secondly, performing modal analysis on each state finite element model by using MSC.Patran software, wherein each state refers to a model of rocket launching along with fuel reduction, namely, a plurality of time points measured by each state experiment, setting a model result as vibration mode normalization processing, matching with an obtained vibration mode, finding out the modal order which is most matched with the actual vibration mode in the finite element model, and calculating the relative error of a simulation frequency value and an experimental frequency value after matching;
thirdly, establishing a mathematical optimization model of each state, and setting an optimization initial value, a step length and a convergence accuracy value of the mathematical optimization model;
setting a similar constraint epsilon value according to the calculated frequency relative error;
fifthly, compiling an MSC. Nastran optimization card, gradually submitting the compiled optimization card of each state to the MSC. Nastran, performing iterative calculation, and extracting the iterated design variables and the iterated convergence values of each state;
sixthly, calculating a weight coefficient of each state according to the target value of iteration convergence of all states and the design variable value of each state, and calculating an initial value of the design variable of MSC.Nastran to be called next time;
seventh, setting a constraint range epsilon value, and re-writing an optimized card;
and eighth step, repeating the fifth step, the sixth step and the seventh step until the vibration mode and the frequency of each state after iteration are approximately the same as the experimental vibration mode frequency.
Compared with the prior art, the invention has the advantages that:
based on the mechanical property analysis of the integral structure, according to iteration convergence values after each state model is called, the weight coefficient occupied by the state with smaller iteration convergence value is selected to be larger, the calculated optimal solution of all states is close to the optimal solution of the state with smaller iteration convergence value, the calculated optimal solution of all states is used as the initial value of the design variable of the MSC.Nastran to be called next time, the card of the MSC.Nastran is directly called for direct operation, the simulation frequency and the vibration mode are enabled to be more approximate to the experimental vibration mode and the frequency, the calculated amount can be reduced, the calculation time is reduced, finally, the design variable value which is similar to the actual one is obtained, the dynamic characteristic of the simulation model is enabled to be approximate to the experimental value, the multi-state model correction of the partial symmetrical structure can be solved, and the mode exchange does not occur in the correction process. A more accurate method of multi-state finite element model correction is provided for engineers.
In addition, compared with the multi-state model correction of the unconstrained optimization model, the correction result cannot be completely matched with the experimental result, and only the correction result and the experimental result can be gradually approximated, but the calculated amount is large when the correction result and the experimental result are very approximated, and the phenomena such as modal exchange and the like can also occur, so that the model correction method can be applied to model correction with errors set in a certain small range.
Drawings
Fig. 1 is a cross-sectional view of a three state variable cross-section beam model.
FIG. 2 is a target iteration curve of a state variable cross-section beamWhich designs a variable iteration curve. (a) is a target iteration history; (b) Is the section moment of inertia I 1 A directional iteration history; (c) Is the section moment of inertia I 2 The direction iteration history.
FIG. 3 is a target iteration curve of a two-state variable cross-section beam and its design variable iteration curve. (a) is a target iteration history; (b) Is the section moment of inertia I 1 A directional iteration history; (c) Is the section moment of inertia I 2 The direction iteration history.
Fig. 4 is a target iteration curve of a three-state variable cross-section beam and its design variable iteration curve. (a) is a target iteration history; (b) Is the section moment of inertia I 1 A directional iteration history; (c) Is the section moment of inertia I 2 The direction iteration history.
Fig. 5 is a mode shape diagram of a state-change cross-section beam experiment.
Fig. 6 is a mode shape diagram of a two-state variable cross-section beam experiment.
Fig. 7 is a mode shape plot of a three-state variable cross-section beam experiment.
FIG. 8 is a flow chart of a method of multi-state finite element model modification.
Detailed Description
As shown in fig. 1, the present invention provides a method for correcting a multi-state finite element model, and the specific solution is as follows:
the method comprises the steps of firstly, determining finite element model materials and structural parameters thereof, and establishing finite element models of all states;
first, based on the msc. Patran software platform, a finite element model of each state is built. Dividing a finite element grid, defining materials, structural parameters and designing initial values of variables.
Secondly, carrying out modal analysis on each state finite element model by using MSC.Patran software, setting a modal result as a vibration mode normalization process, matching the modal vibration mode obtained by finite elements with the experimentally obtained vibration mode according to a modal confidence criterion MAC, finding out the modal order which is most matched with the actual vibration mode in the finite element model, and calculating the relative error of the matched simulation frequency value and the experimental frequency value;
according to a mode confidence criterion MAC, the finite element model is matched with the mode shape obtained through experiments, the mode order which is most matched with the actual mode shape in the finite element model is found out, and the relative error between the simulation frequency value and the experimental frequency value after matching is calculated;
in the formula ,φi and φi t Respectively representing the simulation value and the test mode shape vector corresponding to the ith-order mode of each state,
and />
Respectively represent the vector phi i Sum vector phi i t Is a transposed matrix of (a). The MAC value is always 0,1]Closer to 1 indicates better correlation.
Thirdly, establishing a mathematical optimization model of each state, and setting an optimization initial value, a step length and a convergence accuracy value of the mathematical optimization model;
and inputting parameters such as step length, initial value, convergence accuracy and the like according to the experimental value measured by the structure in an optimization card window of the MSC. Nastran software platform. Establishing a mathematical optimization model taking frequency as constraint and the minimum sum of squares of residual errors of feature vectors as an optimization target, wherein the mathematical optimization model of each state is as follows:
wherein: x is a design variable to be corrected, F (x) represents a single state model correction overall objective function, m represents the total number of experimental points of a single experimental order mode of a single state, I represents the total number of experimental order modes of the single state, and u ij Is an imitation value in a finite element model corresponding to a jth test point in an ith order mode of a single state, u ij t Is the experimental value f of the jth test point under the ith order mode of a single state i (x) Representing the corresponding simulation frequency f under the ith-order mode of a single state i t Representing the corresponding experimental frequency in the i-th order mode of the single state, epsilon represents the allowable maximum value of the frequency residual error.
Setting a similar epsilon value according to the calculated frequency relative error;
a reasonable value is set according to the relative frequency value of the simulation and experiment calculated in the second step, and epsilon can be selected from 0.2, 0.1 and 0.03 according to the situation.
Fifthly, compiling an MSC. Nastran optimization card, gradually submitting the compiled optimization card of each state to the MSC. Nastran, performing iterative calculation, and extracting the iterated design variables and the iterated convergence values of each state;
and step six, calculating the weight coefficient of each state according to the design variables extracted and iterated in all states and the iteration convergence values of each state, and calculating the initial value of the design variable of the MSC.
According to the iteration convergence value of each state extracted in the fifth step, calculating each state weight coefficient w h 。
Wherein S represents the number of states contained in the model,
an objective function convergence value representing the h-th state of the model.
The smaller the objective function convergence value is, the larger the weight coefficient corresponding to the state is.
And (3) calculating the initial value of the next iteration according to the iterated design variables of each state extracted in the sixth step and the weight coefficient of each state of the model.
wherein ,
and (3) representing the optimal solution of the design variable after the h state iteration, wherein x represents the overall optimal solution calculated according to the optimal solution of all states, namely the initial value of the design variable serving as the next call of MSC.
And seventhly, setting a constraint range epsilon value and re-writing the optimized card.
Resetting the value of the constraint range, reducing the epsilon value, enabling the simulation frequency to gradually approach the experimental frequency, and re-writing the optimized card.
ε k+1 ＝ε k /2
And eighth step, repeating the fifth step, the sixth step and the seventh step until the vibration mode and the frequency of each state after iteration are approximately the same as the experimental vibration mode frequency.
The invention discloses a method for correcting a multi-state finite element model, which comprises the following steps: (1) Determining finite element model materials, structural dimension parameters and establishing finite element models of all states; (2) The MSC.Patran software is called to conduct modal analysis on the finite element models of all states, modal results are set to be vibration mode normalization processing, the vibration modes are paired with vibration modes obtained through experiments, modal orders which are most matched with actual vibration modes in the finite element models are found out, and relative errors of simulation frequency values and experimental frequency values after matching are calculated; (3) Establishing a mathematical optimization model of each state, and setting an optimization initial value, a step length and a convergence accuracy value thereof; (4) Setting a similar constraint epsilon value according to the calculated frequency relative error; (5) Writing an MSC. Nastran optimization card, gradually submitting the written optimization cards of all states to the MSC. Nastran, performing iterative calculation, and extracting the iterative convergence values of the design variables and all the states after iteration; (6) According to the iteration convergence values of all states and the design variable values when all states converge, calculating the weight coefficient of each state, and calculating the initial value of the design variable of MSC. Nastran to be called next time; (7) setting a constraint range epsilon value, and re-writing an optimized card; (8) Repeating the fifth step and the sixth step until the vibration mode and the frequency of each state after iteration are approximately the same as the experimental vibration mode and the frequency.
According to the method for correcting the multi-state finite element model, a reasonable mathematical model is established, a reasonable constraint range is set, and MSC.Nastran optimization cards in all states are gradually called for iteration; calculating weight coefficients of all states by utilizing iteration convergence of all states, calculating initial values of design variables for calling MSC. Nastran next time, reducing frequency constraint range, writing optimization cards, and continuously calling the MSC. Nastran optimization cards of all states step by step for iteration; and obtaining reasonable design variable values until the dynamic characteristics of all states and finite elements are consistent with those of the experimental model. The method for correcting the multi-state finite element model is beneficial to shortening the structural design period, provides more detailed guidance for the detailed design of the structure, ensures that the dynamic characteristics of the finite element model in all states are consistent with those of an experimental model to the maximum extent, and has extremely strong practicability.
Example:
the specific implementation steps of the present invention will be described in detail below with reference to three different states of a rocket model (variable cross-section beams of five beam sections with different mass concentration points added at both ends of each beam section, with the cross-sectional moments of inertia of the five beam sections of the variable cross-section beam as design variables).
Firstly, respectively building variable-section beams with the dimensions shown in figure 1 and comprising five beam sections based on MSC.Patran, wherein the whole structure adopts aluminum materials, the elastic modulus is 70GPa, the Poisson ratio is 0.3, and the density is 2700kg/m 3 The structure was divided into 45 beam units, each unit length being 1.333m, each beam section comprising 9 adjacent units, each unit section parameter, each node mass, beam Duan Biaohao as shown in fig. 1, the section moment of inertia as shown in table 1 being experimental values, the initial values of the set model and their values after iteration as shown in table 2, the mass concentration point masses for each state as shown in table 3.
Secondly, free modal analysis is carried out on the finite element models in three states by calling MSC.Patran software, experimental values and simulation values in the three states are matched by using a modal confidence criterion, modal orders which are most matched with actual vibration modes in the finite element models in all states are found out, vibration mode normalization processing is carried out on the experimental values and the simulation values, and the relative errors of the matched simulation frequency values and the experimental frequency values are calculated;
thirdly, establishing a mathematical optimization model of each state, setting an optimization initial value, a step length and a convergence accuracy value thereof, wherein the step length is set to be 0.01;
setting a similar constraint epsilon value according to the calculated frequency relative error, wherein epsilon is 0.03;
fifthly, compiling an MSC. Nastran optimization card, gradually submitting the compiled optimization card of each state to the MSC. Nastran, performing iterative calculation, and extracting the iterated design variables and the iterated convergence values of each state;
sixth, calculating weight coefficients w of the three states according to the target values of all states in iteration convergence and the design variable values of all states in convergence 1 ，w 2 ，w 3 The initial value of the next invocation msc. Nastran design variable is calculated.
Seventh, setting a constraint range epsilon k+1 ＝ε k And (2) re-writing the optimized card.
And eighth, repeating the fifth and sixth steps until the vibration mode and frequency of each state after iteration are approximately the same as the experimental vibration mode and frequency.
The weight coefficients of the three states and the values of the constraint range epsilon of the weight coefficients are shown in table 7, and the values of the weight coefficients can be shown in tables 4, 5 and 6, so that the correction frequencies of the three states of the model are basically identical to the experimental frequency, the relative errors of the correction frequencies of the three states and the original frequency are basically identical, the experimental values in table 1 and the iterative values are compared, the dynamics characteristics of the three states are close to the experimental values, and the optimal solutions of all the states are calculated through the iterative convergence values of all the states; the feasibility of the multi-state model correction method is proved by gradually approaching the simulation dynamics characteristic to the true value gradually through gradually approaching the frequency constraint range.
TABLE 1 experimental values for section moment of inertia
Table 2 initial values of section moment of inertia settings and values after iteration thereof
TABLE 3 mass at mass concentration points for three states
TABLE 4 one State experiment frequency and post-iteration frequency
TABLE 5 two-state experiment frequency and post-iteration frequency
TABLE 6 three-state experiment frequency and post-iteration frequency
Table 7 weight coefficient values for each iteration
Claims (4)
1. A method for correcting a multi-state finite element model, characterized by: the method comprises the steps of,
determining finite element model materials, structural dimension parameters and establishing finite element models of all states;
secondly, performing modal analysis on each state finite element model by using MSC.Patran software, wherein each state refers to a model of rocket launching along with fuel reduction, namely, a plurality of time points measured by each state experiment, setting a model result as vibration mode normalization processing, matching with an obtained vibration mode, finding out the modal order which is most matched with the actual vibration mode in the finite element model, and calculating the relative error of a simulation frequency value and an experimental frequency value after matching;
thirdly, establishing a mathematical optimization model of each state, and setting an optimization initial value, a step length and a convergence accuracy value of the mathematical optimization model; establishing a mathematical optimization model taking frequency as constraint and the minimum sum of squares of residual errors of feature vectors as an optimization target, wherein the mathematical optimization model of each state is as follows:
wherein: x is a design variable to be corrected, F (x) represents a single state model correction overall objective function, m represents the total number of experimental points of a single experimental order mode of a single state, I represents the total number of experimental order modes of the single state, and u ij Is an imitation value in a finite element model corresponding to a jth test point in an ith order mode of a single state, u ij t Is the experimental value f of the jth test point under the ith order mode of a single state i (x) Representing the corresponding simulation frequency f under the ith-order mode of a single state i t Representing the corresponding experimental frequency under the ith-order mode of a single state, wherein epsilon represents the allowable maximum value of the frequency residual error;
setting a similar constraint epsilon value according to the calculated frequency relative error;
fifthly, compiling an MSC. Nastran optimization card, gradually submitting the compiled optimization card of each state to the MSC. Nastran, performing iterative calculation, and extracting the iterated design variables and the iterated convergence values of each state;
sixthly, calculating a weight coefficient of each state according to the target value of iteration convergence of all states and the design variable value of each state, and calculating an initial value of the design variable of MSC.Nastran to be called next time;
seventh, setting a constraint range epsilon value, and re-writing an optimized card;
and eighth step, repeating the fifth step, the sixth step and the seventh step until the vibration mode and the frequency of each state after iteration are approximately the same as the experimental vibration mode frequency.
2. A method of multi-state finite element model modification according to claim 1, wherein: according to a mode confidence criterion MAC, the finite element model is matched with the mode shape obtained through experiments, the mode order which is most matched with the actual mode shape in the finite element model is found out, and the relative error between the simulation frequency value and the experimental frequency value after matching is calculated;
in the formula ,φi and φi t Respectively representing the simulation value and the test mode shape vector corresponding to the ith-order mode of each state,
and
respectively represent the vector phi i Sum vector phi i t Is a transposed matrix of (a); the MAC value is always 0,1]Closer to 1 indicates better correlation.
3. A method of multi-state finite element model modification according to claim 1, wherein:
according to the iteration convergence value of each state extracted in the fifth step, calculating each state weight coefficient w h ；
Wherein S represents the number of states contained in the model,
an objective function convergence value representing an h state of the model;
the smaller the objective function iteration convergence value of all states is, the larger the weight coefficient corresponding to the state is;
calculating the initial value of the next iteration according to the iterated design variables of each state extracted in the sixth step and the weight coefficients of each state of the model;
wherein ,
and (3) representing the optimal solution of the design variable after the h state iteration, wherein x represents the overall optimal solution calculated according to the optimal solution of all states, namely the initial value of the design variable serving as the next call of MSC.
4. A method of multi-state finite element model modification according to claim 1, wherein:
resetting the value of the constraint range, reducing the epsilon value, enabling the simulation frequency to gradually approach to the experimental frequency, and re-writing the optimized card;
ε k+1 ＝ε k /2。
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