CN110706759B - Method for predicting critical folding radius of foldable thin-wall composite pipe fitting - Google Patents

Method for predicting critical folding radius of foldable thin-wall composite pipe fitting Download PDF

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CN110706759B
CN110706759B CN201910762105.3A CN201910762105A CN110706759B CN 110706759 B CN110706759 B CN 110706759B CN 201910762105 A CN201910762105 A CN 201910762105A CN 110706759 B CN110706759 B CN 110706759B
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白江波
陈迪
熊峻江
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Abstract

A method for predicting the critical folding radius of a foldable thin-wall composite pipe fitting comprises three steps: step one, calculating a folding strain matrix of a foldable thin-wall composite pipe fitting; step two, calculating the stress of a main shaft of the foldable thin-wall composite pipe after being folded; and step three, establishing a theoretical model for calculating the critical folding radius of the foldable thin-wall composite pipe fitting. The method has the characteristics of simplicity, convenience, use and accuracy, can calculate the critical folding radius of the foldable thin-wall composite pipe fitting only by the geometric parameters and the basic mechanical property parameters of the open thin-wall circular pipe, and has important engineering application value and certain academic significance.

Description

Method for predicting critical folding radius of foldable thin-wall composite pipe fitting
Technical Field
The invention provides a theoretical method for predicting the critical folding radius of a foldable thin-wall composite pipe fitting, and belongs to the field of composite structure design and analysis.
Background
The foldable thin-wall composite pipe fitting can be used for gathering the large-scale aerospace structure into a small enough size for transportation and launching during launching, and unfolding the large-scale aerospace structure to form a large-scale structure after the spacecraft is in orbit to perform an aerospace task, so that the foldable thin-wall composite pipe fitting is widely applied to the aerospace field. A great deal of research is carried out on the mechanical properties of the alloy at home and abroad. Research shows that in the folding process of the foldable thin-wall composite pipe, the initial bending load is in direct proportion to the bending angle, when the bending load reaches a certain critical value (folding peak moment), a tiny moment is added, the structure is subjected to huge buckling deformation, and obvious geometric nonlinearity is presented. During the unfolding process of the foldable thin-wall composite pipe, the deformation and the load of the foldable thin-wall composite pipe show obvious nonlinear response. In order to explore the nonlinear performance of the foldable thin-wall composite pipe in the folding and unfolding processes, an analysis method based on an elastic shell theory, a buckling theory and an energy principle is developed at present. However, few researches relate to the critical folding radius of the foldable thin-wall composite pipe, the critical folding radius directly affects the volume of the foldable thin-wall composite pipe when the foldable thin-wall composite pipe is folded, the volume capacity of a spacecraft is wasted when the folding radius is too large, and the composite circular pipe fails when the folding radius is too small, so that a practical method for predicting the critical folding radius of the open composite circular pipe (the folding radius corresponding to the failure of the composite circular pipe) is urgently needed in engineering. Therefore, the theoretical method for predicting the critical folding radius of the foldable thin-wall composite pipe fitting is established, has the advantages of accuracy, practicability and simplicity, only needs the geometric parameters and basic mechanical properties of the foldable thin-wall composite pipe fitting as input values, and has important engineering application value and certain academic significance.
Disclosure of Invention
1. The purpose is as follows: the invention aims to provide a method for predicting the critical folding radius of a foldable thin-wall composite pipe fitting, which has the advantages of accuracy, practicability and simplicity and has guiding significance for the design and application of the foldable thin-wall composite pipe fitting.
2. The technical scheme is as follows: a method for predicting the critical radius of a foldable thin-wall composite pipe fitting comprises the following specific steps:
step one, calculating a folding strain matrix [ epsilon ] of a foldable thin-wall composite pipe fitting
The folding mode of the foldable thin-wall composite pipe is shown in figure 1, and the shape and the size of the foldable thin-wall composite pipe are shown in figure 2. The folding process is broken down into two steps: 1) flattening the circular tube along the transverse direction to change the circular tube into a flat plate; 2) the flat plate is folded and rolled up in the longitudinal direction.
During the process of transversely flattening the foldable thin-wall composite pipe fitting, each layer of the composite laminated plate is subjected to strain
Figure BDA0002170631020000021
Wherein i is the number of layers of the laminated sheet from top to bottom, r1The initial radius corresponding to the uppermost layer of the laminated plate, t is the single-layer thickness of the laminated plate, n is the number of laminated plate layers, the x axis is along the longitudinal direction of the circular tube, and y is the circumferential direction along the circumference of the cross section.
During the process of folding and rolling up the flat plate along the longitudinal direction, the strain of each layer of the composite material laminated plate is
Figure BDA0002170631020000022
In the formula, r2The corresponding folding radius of the uppermost layer of the laminated plate.
During the integral folding process, the folding strain of each layer of the composite laminated board
Figure BDA0002170631020000023
In the formula, epsilonxAnd εyIs the tensile strain of the x-axis and y-axis, gammaxyIs the shear strain.
The main axis direction of each layer of the composite material is strained by
Figure BDA0002170631020000024
Wherein
Figure BDA0002170631020000025
In the formula, epsilon1And ε2Is 1-axis and 2-axis tensile strain, gamma12For shear strain, [ T ]]And theta is an included angle between the off-axis direction and the main axis direction.
Step two, calculating the stress of the main shaft after the foldable thin-wall composite pipe fitting is folded
According to the laminate theory and formula (4), the principal axis stress of each layer of the composite laminate is obtained as
Figure BDA0002170631020000031
Wherein
Figure BDA0002170631020000032
Figure BDA0002170631020000033
Figure BDA0002170631020000034
Q66＝G12 (10)
In the formula, σ1And σ2Is a 1-axis and 2-axis tensile stress, τ12For shear stress, Q11，Q12，Q22And Q66V is an engineering elastic constant12V and v21Poisson's ratio of single-layer plate, E1tIs a 1-axis tensile modulus of elasticity, E2tIs a 2-axis tensile modulus of elasticity, G12The shear modulus.
Step three, calculating the critical folding radius of the foldable thin-wall composite pipe fitting
The Chua Hill criterion is an important basis for judging the failure of the composite material and is written as
Figure BDA0002170631020000035
In the formula, X is the strength in the 1-axis direction, Y is the strength in the 2-axis direction, and S is the shear strength.
The main stress of each layer calculated in the step two is substituted into a formula (11), and r is solved 2The value is the critical folding radius.
Drawings
FIG. 1 is a schematic view of the folding process of the foldable thin-wall composite pipe.
Fig. 2 is a shape and size diagram of a foldable thin-wall composite pipe.
Fig. 3 is a block flow diagram of the method of the present invention.
The symbols in the figures are as follows:
in FIG. 2 r1To be at leastInitial radius, r, of folded thin-walled composite pipe2The folding radius of the foldable thin-wall composite pipe is shown, n is the total number of layers of the laminated plate, and t is the thickness of the laminated plate layer.
Detailed Description
Fig. 3 is a flow chart of the method of the present invention, which is implemented in three steps, specifically:
step one, calculating a folding strain matrix [ epsilon ] of a foldable thin-wall composite pipe fitting
The folding mode of the foldable thin-wall composite pipe is shown in figure 1, and the shape and the size of the foldable thin-wall composite pipe are shown in figure 2. The folding process is broken down into two steps: 1) flattening the circular tube along the transverse direction to change the circular tube into a flat plate; 2) the flat plate is folded and rolled up in the longitudinal direction.
During the process of transversely flattening the foldable thin-wall composite pipe fitting, each layer of the composite laminated plate is subjected to strain
Figure BDA0002170631020000041
Wherein i is the number of layers of the laminated sheet from top to bottom, r1The initial radius of the uppermost layer of the laminate, t is the thickness of a single layer of the laminate, and n is the number of layers of the laminate.
During the process of folding and rolling up the flat plate along the longitudinal direction, the strain of each layer of the composite material laminated plate is
Figure BDA0002170631020000042
In the formula, r2The corresponding fold radius for the uppermost layer of the laminate.
During the integral folding process, the folding strain of each layer of the composite laminated board
Figure BDA0002170631020000043
In the formula, epsilonxAnd εyIs the x axisAnd y-axis tensile strain, gammaxyIs the shear strain.
The main axis direction of each layer of the composite material is strained by
Figure BDA0002170631020000044
Wherein
Figure BDA0002170631020000051
In the formula, epsilon1And ε2Is 1-axis and 2-axis tensile strain, gamma12For shear strain, [ T ]]And theta is an included angle between the off-axis direction and the main axis direction.
Step two, calculating the stress of the main shaft after the foldable thin-wall composite pipe fitting is folded
According to the laminate theory and formula (4), the principal axis stress of each layer of the composite laminate is obtained as
Figure BDA0002170631020000052
Wherein
Figure BDA0002170631020000053
Figure BDA0002170631020000054
Figure BDA0002170631020000055
Q66＝G12 (10)
In the formula, σ1And σ2Is a 1-axis and 2-axis tensile stress, τ12For shear stress, Q11，Q12，Q22And Q66V is an engineering elastic constant12V and v21Poisson's ratio of single-layer plate, E1tIs a 1-axis tensile modulus of elasticity, E2tIs a 2-axis tensile modulus of elasticity, G12The shear modulus.
Step three, calculating the critical folding radius of the foldable thin-wall composite pipe fitting
The Chua Hill criterion is an important basis for judging the failure of the composite material and is written as
Figure BDA0002170631020000056
In the formula, X is the strength in the 1-axis direction, Y is the strength in the 2-axis direction, and S is the shear strength.
Substituting the main stress of each layer calculated in the step two into a formula (11), and solving the formula2The value is the critical folding radius.

Claims (1)

1. A method for predicting the critical folding radius of a foldable thin-wall composite pipe fitting has the advantages of accuracy, practicability and simplicity, and comprises the following specific steps:
step one, calculating a folding strain matrix [ epsilon ] of the foldable thin-wall composite pipe fitting
The folding process of the foldable thin-wall composite pipe fitting is decomposed into two steps: 1) flattening the circular tube along the transverse direction to change the circular tube into a flat plate; 2) folding and rolling the flat plate along the longitudinal direction;
during the process of transversely flattening the foldable thin-wall composite pipe fitting, each layer of the composite laminated plate is subjected to strain
Figure FDA0003581500540000011
Wherein i is the number of layers of the laminated sheet from top to bottom, r1The initial radius corresponding to the uppermost layer of the laminated plate, t is the single-layer thickness of the laminated plate, n is the number of laminated plate layers, the x axis is along the longitudinal direction of the circular tube, and the y axis is along the circumferential direction of the circumference of the cross section;
during the process of folding and rolling up the flat plate along the longitudinal direction, the strain of each layer of the composite material laminated plate is
Figure FDA0003581500540000012
In the formula, r2The folding radius corresponding to the uppermost layer of the laminated plate;
during the integral folding process, the folding strain of each layer of the composite laminated board
Figure FDA0003581500540000013
In the formula, epsilonxAnd εyIs the tensile strain of the x-axis and y-axis, gamma xyIs shear strain;
the main axis direction of each layer of the composite material is strained by
Figure FDA0003581500540000014
Wherein
Figure FDA0003581500540000021
In the formula, epsilon1And ε2Is 1-axis and 2-axis tensile strain, gamma12For shear strain, [ T ]]Is a coordinate transformation matrix, and theta is an included angle between the off-axis direction and the main axis direction;
step two, calculating the stress of the main shaft after the foldable thin-wall composite pipe fitting is folded
According to the laminate theory and formula (4), the principal axis stress of each layer of the composite laminate is obtained as
Figure FDA0003581500540000022
Wherein
Figure FDA0003581500540000023
Figure FDA0003581500540000024
Figure FDA0003581500540000025
Q66＝G12 (10)
In the formula, σ1And σ2Is a 1-axis and 2-axis tensile stress, τ12For shear stress, Q11，Q12，Q22And Q66Is an engineering elastic constant, v12V and v21Poisson's ratio of single-layer plate, E1tIs a 1-axis tensile modulus of elasticity, E2tIs a 2-axis tensile modulus of elasticity, G12Is the shear modulus;
step three, calculating the critical folding radius of the foldable thin-wall composite pipe fitting
The Chua Hill criterion is an important basis for judging the failure of the composite material and is written as
Figure FDA0003581500540000026
Wherein X is the strength in the 1-axis direction, Y is the strength in the 2-axis direction, and S is the shear strength;
the main stress of each layer calculated in the step two is substituted into a formula (11), and r is solved2The value is the critical folding radius.
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