CN108388763A - A kind of oriented fiber reinforced composite laminate structures reliability calculation method based on multiscale analysis - Google Patents

Abstract

The invention discloses a method for calculating the reliability of a laminated structure of directional fiber reinforced composite materials based on multi-scale analysis. Structural reliability is calculated by Monte Carlo sampling; coupled multi-scale analysis and finite element method are used to solve the static response of the structure, and the homogenization theory is used to transfer information from the mesoscale to the macroscale. The state is used as the cell boundary condition to realize the transmission of information from the macro scale to the micro scale; with the help of the ABAQUS\Pathon secondary development platform, the primary sampling calculation process and sampling process are realized in ABAQUS, achieving sampling, modeling, calculation and The effect of statistical process automation; the present invention has the advantages of more accurate structural reliability analysis and failure mode discrimination based on the traditional macro scale, and more accurate calculation results.

Description

A Multiscale Analysis-based Reliable Laminated Structure of Oriented Fiber Reinforced Composite sex calculation method

technical field

The invention belongs to the field of composite material structure design, relates to a multi-scale analysis technology and a reliability calculation method, in particular to a multi-scale analysis-based reliability analysis method for laminated structures of directional fiber reinforced composite materials.

Background technique

Composite materials refer to new materials that are composed of several different materials such as organic polymers, inorganic non-metals or metals through a composite process. The laminated structure is a structure widely used in composite material structures. It is composed of layers of fibers in different directions, and has a strong design. Traditional structural design and strength verification are based on deterministic design, that is, the design variables are all deterministic quantities. However, in composite material structures, there are uncertainties in load, structural size, and material properties, which make the results of deterministic design and actual conditions very different. deviation. Structural reliability design can make up for the deficiencies of traditional deterministic design, taking the uncertain factors in the structure into the design, and making a more reasonable judgment on the safety performance of the structure. On the other hand, compared with the macro-mechanics of composite materials, the meso-mechanics of composite materials has a more essential revelation of the elastic properties and failure laws of materials, and its mechanical model is more accurate. Based on the structural reliability of the latter, the discrimination of material failure modes is better. Specifically, the reliability calculation results are more accurate; if the analysis model of the composite structure is established completely from the mesoscopic scale, the calculation amount will be too large, and even the current calculation level may not be able to solve it. The multi-scale analysis method not only ensures the macro-scale The analysis efficiency can also analyze the important key parts of the structure on a mesoscopic scale. Among the existing studies on the reliability design of composite structures, studies based on macro-scale analysis account for the vast majority ^[1-11] . The disadvantage of this type of design is that the reliability design of the composite material structure stays at the macro scale, and its designability is limited to macro-scale variables such as ply angle design, ply thickness, etc. The characteristics are analyzed and designed; the macro-scale mechanical performance model and strength model of composite materials are often not as sufficient as the meso-mechanical model, especially the strength model. The former is not as accurate as the latter, so that the structural reliability cannot truly evaluate whether the structure is safe. For the existing studies on the reliability analysis of composite material structures based on multi-scale analysis ^[12-13] , the mesoscopic strength criterion was not considered, and only the potential of multi-scale analysis technology in the prediction of elastic properties was explored, while the reliability calculation The mesoscopic stress distribution and the prediction of mesoscopic failure behavior, which have a great influence on the results, have not been considered yet.

Contents of the invention

This method is a method for calculating the reliability of laminated structures of oriented fiber reinforced composite materials based on multi-scale analysis, which is divided into the following steps:

Step 1: The present invention accounts for stochastic uncertainties in the structure of oriented fiber composites. Specifically, the uncertainties of the following parameters are considered: elastic properties parameters of fibers and matrix, strength parameters of fibers and matrix, macroscopic loads and geometric parameters of macrostructures.

Step 2: The present invention adopts the Monte Carlo sampling method to calculate the structural reliability, and steps 3 to 14 are a sampling calculation process.

Step 3: Build a geometric model of the macrostructure.

Step 4: Discretize the geometric model of the macrostructure in step 3.

Step 5: Establish material cell model.

Step 6: Discretize the cell model in step 5.

Step 7: Define the material properties for the model in step 6, solve it with the finite element method, and calculate the equivalent constitutive matrix of the cell.

Step 8: Assign the equivalent constitutive matrix in step 7 to the macroscopic discrete structure in step 4 to obtain the macrostructure finite element model.

Step 9: Solve the macrostructure finite element in step 8.

Step 10: Obtain the strain states of all integration points of the macroscopic model in 9.

Step 11: Take the strain state of the integration point in step 10 as the boundary condition of the microscopic cell model in step 7, and each integration point corresponds to the microscopic finite element model.

Step 12: Solve all the mesoscopic finite element models in step 11.

Step 13: Obtain the solution results of the mesoscopic stress field and strain field in step 12.

Step 14: Input the mesoscopic strength parameters, and for the mesoscopic stress field and strain field in step 13, use the mesoscopic strength criterion to judge whether mesoscopic failure occurs. If none of the integration points fails, the structure is safe; if at least one integration point fails, the structure fails.

The advantages of a multi-scale analysis-based reliability calculation method for laminated structures of directional fiber reinforced composite materials in the present invention are:

(1) The present invention considers multi-scale analysis in the structural reliability design of directional composite materials, that is, compared with the traditional macro-scale structural analysis, it also considers the mesoscopic characteristics of materials, so that the structural mechanics model has multiple scales at the same time information, the model is more accurate.

(2) In the reliability design of the directional composite material structure, the present invention judges whether the material fails according to the cell mesoscopic stress field corresponding to the integration point, the strain field, and the mesoscopic failure criterion, compared with the roughly judged macroscopic failure criterion , the judging method of the present invention is more accurate; in addition, it is difficult to discriminate the failure mode by the macroscopic failure criterion, and the present invention can clearly judge which failure mode of the material occurs, such as fiber fracture and matrix failure, by using the mesoscopic failure criterion.

Description of drawings

Fig. 1 is a flow chart of the arrangement steps of a multi-scale analysis-based reliability calculation method for laminated structures of oriented fiber reinforced composite materials in the present invention, the Monte Carlo sampling process is omitted in the flow chart, and the flow chart expresses a sampling calculation process (Steps 3-14 in "Contents of the Invention");

Fig. 2 is the modeling in ABAQUS of macrostructure (taking flat plate as example);

Figure 3 is the cell model of oriented fiber reinforced composite material established in ABAQUS;

Fig. 4 is the finite element model of cell;

Figure 5 is the finite element model of the macrostructure.

Detailed ways

The invention aims to provide a multi-scale analysis-based method for calculating the reliability of laminated structures of directional fiber reinforced composite materials.

The Monte Carlo method is used to sample and calculate the structural reliability, and the coupled multi-scale analysis technology is used to calculate the static response of the structure. The coupled multi-scale analysis is based on the finite element numerical algorithm, and the information transfer from the meso scale to the macro scale is realized through homogenization. The strain state on the integral point of the macro-scale structural unit is used as the boundary condition of the cell to realize the transmission of information from the macro-scale to the micro-scale; through the secondary development platform of ABAQUS\Pathon, the entire calculation process is realized in ABAQUS, achieving sampling, construction Modeling, calculation and statistical automation; the present invention has the advantages of more accurate structural reliability analysis and failure mode discrimination based on the traditional macro scale, and more accurate calculation results.

This method is divided into the following steps:

Step 1: Generate several groups of random numbers in MATLAB according to the given parameter distribution law, where each group of random numbers contains all uncertain parameters in a sampling calculation (elastic performance parameters of fibers and matrix, strength parameters of fibers and matrix , the macro load and the geometric parameters of the macro structure), which are saved in the sample.txt file for sampling.

Step 2: Using the secondary development function of the Python level in ABAQUS finite element software, write a Python program, read a set of random numbers in the sample.txt file for one sampling calculation, and write a loop statement to realize multiple sampling calculations, so as to count failure events Frequency of occurrence, estimated probability of failure. Using this method to pre-generate random numbers and save them in the file, the entire sampling calculation can be automatically completed in the finite element software (using its secondary development function), without the need for users to manually operate during the sampling calculation process. The following steps 3 to 14 introduce the implementation of a sampling calculation. The programming language of the entire calculation process is based on ABAQUS\Python.

Step 3: Use the secondary development function of the Python level in the ABAQUS finite element software, and use the geometric parameters of the macrostructure in the random numbers read in step 2 to establish a geometric model of the macrostructure. Take the flat structure as an example, as shown in Figure 2. All modeling processes of the present invention use Python language to control the scripting language in ABAQUS to model, so that it is convenient to realize sampling calculation without user operation, and the data reading and calculation of the present invention are all based on the secondary development function of ABAQUS\Python Implemented in ABAQUS.

Step 4: Write a Python program, and establish the cell model of the directional fiber reinforced composite material in ABAQUS, as shown in Figure 3. The invention establishes a three-dimensional cell model, so the three-dimensional stress state can be analyzed, but compared with the two-dimensional cell model, the number of units and the number of nodes increase, and the calculation amount increases when solving the finite element equation.

Step 5: Use the material parameters in the random numbers read in step 2 to assign material properties (fibers, matrix constitutive relations) to the cells. After completion, write a program to discretize the structure to obtain the cell finite element model as shown in Figure 4.

Step 6: Predict equivalent three-dimensional elastic properties for the discrete cell model in step 5. Predict macroscopically equivalent properties based on homogenization theory, whose equivalent elasticity matrix in is the average stress of the cell body, and its magnitude is equal to the average of the cell volume integral of the cell stress field, similarly, is the average cell strain.

Step 7: Assign the equivalent elastic properties predicted in step 6 to the macrostructure model established in step 3 by defining material properties, and discretize the structure after completion, as shown in Figure 5. Add the structural load, whose load size is derived from the macro load random number read in step 2.

Step 8: Calculate the finite element model of the macrostructure in step 7.

Step 9: Read the strain information of all integration points in the solution result ODB file in step 8.

Step 10: Apply the strain information in step 9 as the boundary condition of the cell to the boundary of the cell finite element model in step 5, and finally make each integration point correspond to the microscopic finite element model.

Step 11: Calculate the mesoscopic finite element model in step 10.

Step 12: Read the ODB file of the calculation results in step 11, and store the calculation results of the mesoscopic stress field and strain field.

Step 13: Read the random number of the mesoscopic strength parameter in step 3, and use the mesoscopic strength criterion to judge whether mesoscopic failure occurs for the mesoscopic stress field and strain field in step 12. If none of the integration points fails, the structure is safe; if at least one integration point fails, the structure fails.

Step 14: Read the next set of random numbers, return to step 3 to start the next sampling calculation, until all sets of random numbers are calculated.

Step 15: Use the program to record the frequency of failures. If a total of n samples are taken (n is large enough), and m failures occur, the structural failure probability is Structural safety probability R=1-P _f .

references

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Claims (5)

1. a kind of oriented fiber reinforced composite laminate structures reliability calculation method based on multiscale analysis, feature exist In：Use Monte Carlo method sample calculation structural reliability, coupling multiscale analysis technical computing structure statics response, coupling Numerical algorithm of the multiscale analysis based on finite element is closed, realizes that meso-scale is transmitted to macro-scale information by homogenization, leads to It crosses and realizes that macro-scale sees ruler to thin using strain regime on macro-scale structures element integral point as thin cell element boundary condition of seeing Spend the transmission of information；By ABAQUS Pathon secondary developing platforms, so that entire calculating process is realized in ABAQUS, reach The effect of sampling, modeling and calculating process automation.

2. a kind of oriented fiber reinforced composite laminate structures reliability meter based on multiscale analysis as described in claim 1 Calculation method, it is characterised in that：Calculating process be based on ABAQUS Pathon secondary developing platforms, so that entire calculating process is existed Realized in ABAQUS, sample, model and calculating process automation.

3. the as described in claim a kind of oriented fiber reinforced composite laminate structures Calculation of Reliability based on multiscale analysis Method, it is characterised in that：Cell element model boundary condition is seen using strain regime at point as thin, solves micro-stress, strain .

4. the as described in claim a kind of oriented fiber reinforced composite laminate structures Calculation of Reliability based on multiscale analysis Method, it is characterised in that：It is as structural response judge structure using cell element micro-stress, strain field at meso-scale upper integral point No failure.

5. the as described in claim a kind of oriented fiber reinforced composite laminate structures Calculation of Reliability based on multiscale analysis Method, it is characterised in that：Differentiated respectively to whether fiber and matrix fail with thin failure criteria of seeing.