CN114398798B - Method for predicting position of neutral section of stretching deformation of foldable composite material bean pod rod - Google Patents
Method for predicting position of neutral section of stretching deformation of foldable composite material bean pod rod Download PDFInfo
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Abstract
A method for predicting the position of a neutral section of stretching deformation of a foldable composite material pod rod simplifies a three-dimensional foldable composite material pod rod structure into a two-dimensional spring system and a rigid rod which are continuously distributed in parallel along the length direction, and the position of the neutral section of the stretching deformation of the foldable composite material pod rod can be determined by simultaneously solving an equation set through a balance equation and a geometric relation. The method is convenient and efficient, and the position of the neutral section of the stretching deformation of the folding composite material bean pod rod can be conveniently and quickly predicted only by determining the performance parameters and the geometric parameters of the component materials.
Description
Technical Field
The invention provides a method for predicting the position of a neutral section of a pod rod in a foldable composite material in tensile deformation, and belongs to the field of manned spaceflight.
Background
The foldable composite material bean pod rod has the characteristics of light weight, high rigidity, high folding efficiency, reliable unfolding process and the like, is widely concerned and researched in the field of aerospace, and has a good application prospect. The foldable composite material pod rod is usually made of carbon fiber resin matrix composite materials, and is a thin-wall tubular rod structure capable of realizing folding and unfolding functions. When the folding machine is folded, the foldable composite material bean pod rods are rolled up at the neutral section positions where the two ends of the reel are stretched and deformed to form a folded state; and when the foldable composite material bean pod rod is unfolded, the foldable composite material bean pod rod can be restored to an unfolded state from a folded state by means of elastic strain energy of the foldable composite material bean pod rod. The pod rod made of the foldable composite material is complicated to deform in the folding process, and the pod rod made of the foldable composite material is changed into a flat shape from a pod shape when viewed from the cross section direction of the pod rod made of the foldable composite material; when viewed axially, the foldable composite pod rod needs to be curled from a long strip shape and folded into the spacecraft, and the whole process needs to be finished by designing a proper folding mechanism. The neutral section position of the collapsible composite pod rod in the collapsed deformation is very important for the fine design of the folding mechanism and the precise control of folding and unfolding, so that it is necessary to analyze the neutral section position of the collapsible composite pod rod in the collapsed deformation. The experiment means directly measures the neutral section position of the collapsible composite material bean pod rod pulling deformation, the cost is high, and the test process is easily influenced by many accidental factors. The numerical simulation method needs to establish a complex finite element model, and has complex calculation, low calculation efficiency and difficult guarantee of calculation precision. A method for efficiently predicting the location of the neutral cross-section of a collapsible composite pod rod in tensile deformation is established herein. The method can quickly and accurately predict the position of the stretching deformation neutral section of the foldable composite material bean pod rod only by a small amount of component material performance parameters and geometric parameters, and has important academic value and wide engineering application prospect.
Disclosure of Invention
The invention establishes a method for predicting the position of a neutral section of stretching deformation of a foldable composite material bean pod rod, and the method has the advantages of simple and convenient calculation, high precision and the like, and the technical scheme is as follows:
the foldable composite material bean pod rod can realize the folding and unfolding functions through the elastic strain stored in the foldable composite material bean pod rod in the deformation process, one end of the foldable composite material bean pod rod is stretched and deformed in the first step, the folding or unfolding process is completed through a winding drum in the second step, and the schematic diagram of the whole deformation process is shown in figure 1. The cross-sectional geometry of the collapsible composite pod rod is shown in fig. 2 and consists of a circular arc portion and a glue joint edge. During the first step of stretching deformation, the cross section shapes of the foldable composite material bean pod rods are changed at other positions along the length direction except for the constant cross section shape of the neutral cross section, the cross section from the neutral cross section to the stretching end is elongated in the width direction, and particularly the cross section from the neutral cross section to the free end is shortened.
Foldable composite pod rod under transverse tension F 1 In action (as shown in figure 3), the loaded end is gradually pulled flat. The foldable composite pod rod model under transverse tension is simplified into a spring system (shown in figure 4) which is continuously distributed in parallel along the length direction, the rigidity of a circular arc part (a spring part) per unit length is k, and a cementing edge AB is similar to a rigid rod. When one end is connectedWhen a transverse pulling force is applied, there is a center of rotation O (as shown in fig. 4 and 5) where the "spring" remains in an initial unstressed state (i.e., the "spring" remains as long), while the "springs" at the two ends of the center are subjected to compression (OB end) and tension (OA end), respectively, corresponding to q1 and q2, respectively.
The equilibrium equations for the system forces and moments shown in FIG. 6 are respectively
∑F y ＝0 (1)
∑M o ＝0 (2)
May particularly be represented as
In the formula, F 1 The pod rods made of foldable composite materials are subjected to transverse concentrated tensile load; alpha is the corner of the glued edge; s is 1 And s 2 Respectively the length variable along two directions of the rotation center of the gluing edge; a is the total length of the "spring" portion under the tensile load; b is the total length of the "spring" section under compressive load; q. q of 1 And q is 2 The "springs" are respectively loaded by compression (OB end) and tension (OA end), and can be specifically
q 1 ＝ks 2 sinα (5)
q 2 ＝ks 1 sinα (6)
Where k is the stiffness per unit length of the simplified model "spring" section.
By substituting (5) and (6) into (3) and (4)
By integrating the equations (7) and (8), the product can be obtained
By substituting formula (9) for formula (10)
a and b are the lengths of OA and OB, respectively, and the total length of the foldable composite pod rod is l
a+b＝l (12)
Combining equations (11) and (12) into a system of equations for a and b:
by solving the equation set of equation (13), the
By substituting formula (14) into formulae (9) and (10)
In the formula,. DELTA. Ay Is the lateral (Y-direction) displacement of the a-end.
As can be seen from equations (14) and (15), the center of rotation is 2/3 of the length of the bar, i.e., the neutral cross-sectional position of the collapsible composite pod bar during tensile deformation is 2/3 of the length.
The invention relates to a method for predicting the position of a neutral section of a stretching deformation of a foldable composite material bean pod rod, which is characterized in that the position of the neutral section of the stretching deformation of the foldable composite material bean pod rod can be conveniently and quickly predicted according to the performance parameters and the geometric parameters of component materials of the foldable composite material bean pod rod.
FIG. 1 is a schematic view of a process for folding and deforming a pod rod made of a foldable composite material.
FIG. 2 is a schematic cross-sectional view of a collapsible composite pod rod.
FIG. 3 is a schematic drawing of a collapsible composite pod rod in a stretched configuration.
FIG. 4 is a schematic view of a simplified model of a collapsible composite pod rod in an initial state of tension.
FIG. 5 is a schematic view of a simplified model of a collapsible composite pod rod in a state of tensile force deformation.
FIG. 6 is a schematic drawing of a simplified model of a collapsible composite pod rod under tension.
The symbols in the figures are as follows:
in fig. 1: 1. foldable composite pod rods, 2. Reels.
In fig. 2: theta is the central angle of the tangent concave-convex circular arc, c is the width of the adhesive joint edge, R is the curvature radius of the concave-convex circular arc, 1 is the circular arc part, and 2 is the adhesive joint edge.
In fig. 3: f 1 The pod rods are subjected to a laterally concentrated tensile load for the collapsible composite material.
In fig. 4: a and B are the two end points of the spring system before deformation, and O is the neutral section position.
In fig. 5: a 'and B' are two end points of the deformed spring system respectively, X and Y are coordinate axes of a rectangular coordinate system, alpha is a corner of the glued edge, and s 1 And s 2 The length variables along the two directions of the center of rotation of the glued edge, a and b are the lengths of OA and OB, respectively, and l is the total length of the foldable composite pod rod.
In fig. 6: q. q.s 1 And q is 2 The "springs" are loaded in compression (OB end) and tension (OA end), respectively.
The specific implementation mode is as follows:
the foldable composite material bean pod rod can realize the folding and unfolding functions through the elastic strain stored in the foldable composite material bean pod rod in the deformation process, one end of the foldable composite material bean pod rod is stretched and deformed in the first step, the folding or unfolding process is completed through a winding drum in the second step, and the schematic diagram of the whole deformation process is shown in figure 1. The cross-sectional geometry of the collapsible composite pod rod is shown in fig. 2 and consists of a circular arc portion and a glue joint edge. During the first step of stretching deformation, the cross section shapes of the foldable composite material bean pod rods are changed at other positions along the length direction except for the constant cross section shape of the neutral cross section, the cross section from the neutral cross section to the stretching end is elongated in the width direction, and particularly the cross section from the neutral cross section to the free end is shortened.
The pod rods of the foldable composite material are transversely pulled and loaded F 1 In action (as shown in figure 3), the loaded end is gradually pulled flat. The foldable composite pod rod model under transverse tension is simplified into a spring system (shown in figure 4) which is continuously distributed in parallel along the length direction, the rigidity of a circular arc part (a spring part) per unit length is k, and a cementing edge AB is similar to a rigid rod. When a lateral pulling force is applied at one end, there is a center of rotation O (as shown in fig. 4 and 5) where the "spring" remains in an initial unstressed state (i.e., the "spring" remains in its original length), while the "springs" at the two ends of the center are subjected to compression (OB end) and tension (OA end), respectively, corresponding to q1 and q2, respectively.
The equilibrium equations for the system forces and moments shown in FIG. 6 are respectively
∑F y ＝0 (1)
∑M o ＝0 (2)
May particularly be expressed as
In the formula, F 1 The pod rod made of the foldable composite material is subjected to transverse concentrated tensile load; alpha is the corner of the glue joint edge; s 1 And s 2 Respectively the length variable along two directions of the rotation center of the gluing edge; a is the total length of the "spring" portion under the tensile load; b is the total length of the "spring" section under compressive load; q. q.s 1 And q is 2 The "spring" is respectively loaded by compression (OB end) and extension (OA end), and can be specifically
q 1 ＝ks 2 sinα (5)
q 2 ＝ks 1 sinα (6)
Where k is the stiffness per unit length of the simplified model "spring" section.
By substituting (5) and (6) into (3) and (4)
By integrating the equations (7) and (8), the product can be obtained
By substituting formula (9) for formula (10)
a and b are the lengths of OA and OB, respectively, and the total length of the foldable composite pod rod is l can be expressed as
a+b＝l (12)
Combining equations (11) and (12) into a system of equations for a and b:
by solving the equation set of equation (13), it is possible to obtain
By substituting formula (14) into formula (9) and formula (10), the compound can be obtained
In the formula,. DELTA. Ay Is the lateral (Y-direction) displacement of the a-end.
As can be seen from equations (14) and (15), the center of rotation is 2/3 of the length of the rod, i.e., the neutral cross-sectional position of the collapsible composite pod rod during tensile deformation is 2/3 of the length.
The invention relates to a method for predicting the position of a neutral section of a stretching deformation of a foldable composite material bean pod rod, which is characterized in that the position of the neutral section of the stretching deformation of the foldable composite material bean pod rod can be conveniently and quickly predicted according to the performance parameters and the geometric parameters of component materials of the foldable composite material bean pod rod.
Claims (1)
1. A method of predicting the location of a neutral section of a tensile deformation of a collapsible composite pod rod, comprising: the method comprises the following specific steps:
the foldable composite material bean pod rod can realize folding and unfolding functions through elastic strain stored in the foldable composite material bean pod rod in the deformation process, one end of the foldable composite material bean pod rod is stretched and deformed in the first step, the folding or unfolding process is completed through a winding drum in the second step, and the foldable composite material bean pod rod consists of an arc part and a glue joint edge; in the first step of stretching deformation process of the foldable composite material bean pod rod, the cross section shapes of other positions along the length direction are changed except that the cross section shape of the neutral cross section is unchanged, the cross section from the neutral cross section to the stretching end is stretched in the width direction, and particularly the cross section from the neutral cross section to the free end is shortened;
foldable composite pod rod under transverse tension F 1 Acting, the loaded end is gradually pulled flat; simplifying a foldable composite material pod rod model subjected to transverse pulling load into a 'spring system' continuously distributed in parallel along the length direction, wherein the rigidity of the unit length of an arc part (a 'spring' part) is k, and a cementing edge AB is similar to a rigid rod; when a lateral pulling force is applied at one end, there is a center of rotation O where the "spring" is kept in an initial unstressed state (i.e., the "spring" is kept as long), while the "springs" at both ends of the center are subjected to a compression action (OB end) and a tension action (OA end), respectively, corresponding to q1 and q2;
the balance equations of the system force and moment are respectively sigma F y ＝0 (1)
∑M o ＝0 (2)
May particularly be expressed as
In the formula, F 1 The pod rods made of foldable composite materials are subjected to transverse concentrated tensile load; alpha is the corner of the glue joint edge; s 1 And s 2 Respectively two at the center of rotation along the bonding edgeA length variation of the direction; a is the total length of the "spring" portion under the tensile load; b is the total length of the "spring" section under compressive load; q. q.s 1 And q is 2 The "spring" is respectively loaded by compression (OB end) and extension (OA end), and can be specifically
q 1 ＝ks 2 sinα (5)
q 2 ＝ks 1 sinα (6)
In the formula, k is the stiffness of the simplified model 'spring' part per unit length;
by substituting (5) and (6) into (3) and (4)
By integrating the equations (7) and (8), the product can be obtained
By substituting formula (9) for formula (10)
a and b are the lengths of OA and OB, respectively, and the total length of the foldable composite pod rod is l can be expressed as
a+b＝l (12)
Combining equations (11) and (12) into a system of equations for a and b:
by solving the equation set of equation (13), the
By substituting formula (14) into formula (9) and formula (10), the compound can be obtained
In the formula,. DELTA. Ay Is the transverse (Y direction) displacement of the A end;
as can be seen from equations (14) and (15), the center of rotation is 2/3 of the length of the rod, i.e., the neutral cross-sectional position of the collapsible composite pod rod during tensile deformation is 2/3 of the length.
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