CN114692455A - Modeling method of composite material laminated plate based on segmented equidistant recombination curve - Google Patents

Modeling method of composite material laminated plate based on segmented equidistant recombination curve Download PDF

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CN114692455A
CN114692455A CN202210311102.XA CN202210311102A CN114692455A CN 114692455 A CN114692455 A CN 114692455A CN 202210311102 A CN202210311102 A CN 202210311102A CN 114692455 A CN114692455 A CN 114692455A
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equidistant
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曹忠亮
董明军
赵佳
徐铀
刘凯磊
韩振华
范广宏
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Abstract

The invention provides a modeling method of a composite material laminated plate based on a segmented equidistant recombination curve, which comprises the following steps: inputting the size parameters of the laminated plate, the laminated structure, a defined curve function, the aperture and the position information of the hole; performing scatter processing on the reference track; fitting the track points and performing equidistant recombination on the concave-convex functions respectively; outputting equidistant curve coordinates and function expression parameters; the variable-rigidity laminated plate model is generated, the problems that the modeling steps are complex, overlapping and gaps are prone to occur among tows, and the working efficiency is low in the existing composite laminated plate modeling method are solved, a user can obtain a finite element model of the width of the tows of the composite constant/variable-rigidity laminated plate strip simply by inputting parameters, the modeling method is simple, and overlapping and gaps cannot occur among the tows.

Description

Modeling method of composite material laminated plate based on segmented equidistant recombination curve
Technical Field
The invention relates to the technical field of composite material modeling, in particular to a modeling method of a composite material laminated plate based on a segmented equidistant recombination curve.
Background
At present, a finite element model of a composite material laminated plate comprises a constant-rigidity finite element model and a variable-rigidity finite element model, and when the variable-rigidity finite element model is generated, an ideal laminated plate structure is often selected to replace the model in order to save the modeling time, but the ideal laminated plate structure is still different from a real laminated plate structure; the variable-rigidity laminated plate structure with the width of the tows is selected, so that the defects of overlapping, gaps and the like of the tows can be caused, and the defects can make the modeling step more complicated; when the limiting variable-angle track is defined, the traditional method adopts the existing curve to define the initial track of the target laminated plate, however, the design thought is limited to a certain extent by the method; in the finite element model analysis process, a user needs to model by himself, submit the model to be analyzed after the model is built, and retrieve target data in the result one by one after the result is obtained, so that the working efficiency is low.
Disclosure of Invention
The invention discloses a modeling method of a composite material laminated plate based on a segmented equidistant recombination curve, which solves the problems of complex modeling steps, easy overlapping and clearance among tows and low working efficiency of the traditional composite material laminated plate modeling method.
In order to achieve the purpose, the technical scheme of the invention is realized as follows:
the invention discloses a modeling method of a composite material laminated plate based on a segmented equidistant recombination curve, which comprises the following steps:
inputting the size parameters of the laminated plate, the laminated structure, a defined curve function, the aperture and the position information of the hole;
performing scatter processing on the reference track;
fitting the track points and performing equidistant recombination on the concave-convex functions respectively;
outputting equidistant curve coordinates and function expression parameters;
a variable stiffness laminate model is generated.
Further, the concrete step of performing scatter processing on the reference trajectory includes:
defining a variable angle track;
generating a variable angle reference track;
inputting the generated variable-angle track data into a program;
finding a dividing point with a second derivative of 0 on the reference track;
equidistantly biasing the segmentation curve along the direction of curvature reduction;
carrying out translation recombination on the deflected track;
and solving the solution of the equation function.
Further, the distance by which the division curves are equidistantly offset in the direction of decreasing curvature is equal to the product of the offset distance and the offset number.
Further, the equation of the equation function is:
Figure BDA0003567153600000021
wherein a reference curve Γ propagates over the entire plane domain Ω, each point on the curve having a constant velocity orthogonal to the curve, t (x) is the time required for the curve Γ to reach point x with a velocity equal to 1/f, t (x) is proportional to the distance x to Γ.
And further, fitting the track points by adopting a machine learning method.
The beneficial technical effects are as follows:
the invention discloses a modeling method of a composite material laminated plate based on a segmented equidistant recombination curve, which comprises the following steps: inputting the size parameters of the laminated plate, the laminated structure, a defined curve function, the aperture and the position information of the hole; performing scatter processing on the reference track; fitting the track points and performing equidistant recombination on the concave-convex functions respectively; outputting equidistant curve coordinates and function expression parameters; the variable-rigidity laminated plate model is generated, the problems that the modeling steps are complex, overlapping and gaps are prone to occur among tows, and the working efficiency is low in the existing composite laminated plate modeling method are solved, a user can obtain a finite element model of the width of the tows of the composite constant/variable-rigidity laminated plate strip simply by inputting parameters, the modeling method is simple, and overlapping and gaps cannot occur among the tows.
Drawings
In order to more clearly illustrate the technical solution of the present invention, the drawings used in the description of the embodiments will be briefly described below.
FIG. 1 is a flow chart of the steps of a method of modeling a composite laminate based on segmented equidistant recombination curves according to the invention;
FIG. 2 is a logic flow diagram of a method of modeling a composite laminate based on segmented equidistant reforming curves in accordance with the present invention;
FIG. 3 is a schematic diagram of the trajectory of a modeling method for segmenting equidistant rebinning curves based on a composite laminate according to the present invention;
FIG. 4 is a schematic diagram of a trajectory offset for a modeling method for a composite laminate based on segmented equidistant rebinning curves according to the present invention;
FIG. 5 is a schematic trace regrouping diagram of a modeling method for a composite laminate based on a segmented equidistant regrouping curve according to the present invention;
FIG. 6 is a graph of the path of propagation of the engineering function equation of a modeling method for a composite laminate based on segmented equidistant recombination curves according to the present invention;
FIG. 7 is a schematic illustration of fiber placement over tape width for a modeling method for segmenting equidistant recombination curves based on a composite laminate according to the present invention;
FIG. 8 is a graph of machine learning fitted curve data for a modeling method for a composite laminate based on segmented equidistant rebinning curves in accordance with the present invention;
fig. 9 is a schematic diagram of a variable stiffness laminate generated with a width based on a modeling method for segmenting equidistant recombination curves of the present invention.
FIG. 10 is an airfoil profile for an aircraft based on a modeling method for segmenting equidistant recombination profiles for composite laminates in accordance with the present invention;
FIG. 11 is a schematic representation of a two-dimensional to three-dimensional coordinate transformation of a modeling method for a composite laminate based on segmented equidistant rebinning curves in accordance with the present invention;
FIG. 12 is a schematic illustration of airfoil surface lay-up angles for a modeling method for a composite laminate based on segmenting equidistant rebinning curves in accordance with the present invention;
FIG. 13 is a schematic illustration of airfoil surface fiber placement for a modeling method for composite laminates based on segmenting equidistant recombination curves in accordance with the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
The invention discloses a modeling method of a composite material laminated plate based on a segmented equidistant recombination curve, which specifically comprises the following steps of:
s1: inputting the size parameters of the laminated plate, the laminated structure, a defined curve function, the aperture and the position information of the hole;
specifically, the types of composite laminates include normal-stiffness laminates and variable-stiffness laminates, and the pre-model is pre-generated according to inputted laminate dimensional parameters, hole information, and the like, so that the model can be modified and saved later.
S2: performing scatter processing on the reference track and performing equidistant recombination on the concave-convex functions respectively;
after the tracks are scattered, equidistant recombination is carried out on the concave-convex functions respectively to obtain a recombination curve, and the method specifically comprises the following steps:
s21: defining a variable angle track;
s22: generating a variable angle reference track;
the linear angle change method in the definition of the angle change track is as follows:
Figure BDA0003567153600000041
wherein, thetax(x) Representing the angle, T, of the laminate fibers at coordinate x0Is the initial angle of the fibre, T1Is the fiber termination angle, a is the characteristic length;
the flow field function method in the variable angle trajectory definition is as follows:
Figure BDA0003567153600000042
wherein psi is an equal streamline, and x and y are point coordinates of streamline cluster laying;
the Bezier curve method in the variable angle trajectory definition comprises the following steps:
Figure BDA0003567153600000051
wherein, beta1Is a control point P1A location parameter of (a); beta is a2To a control point P2A position parameter in the x-axis direction; h is a control point P1、P2In the x-axis direction. At beta1And beta2In the definite case h can decide the control point P2And P3Position in the y-axis direction, Ni,jIs a basis function of a cubic NURBS curve, and w is a weight factor;
s23: inputting the generated variable-angle track data into a program;
s24: finding a dividing point with a second derivative of 0 on the reference track;
specifically, find the division point where the second derivative of the reference trajectory is 0, i.e. f "(x) is 0, see fig. 3;
s25: equidistantly biasing the segmentation curve along the direction of curvature reduction;
specifically, referring to fig. 4, with the normal line at the dividing point as a boundary, regarding the curve as several parts, respectively performing equidistant bias on the concave-convex curve part along the curvature decreasing direction, that is, the concave function is biased downward, and the convex function is biased upward, and the offset distance is equal to the product of the bias distance and the offset number;
s26: carrying out translation recombination on the deflected track;
recombining the tracks with each offset into a new track, it can be understood that the curve obtained in fig. 5 and the given reference track do not have a line position relationship in translation or in parallel, i.e., there is no overlap or gap between the tows;
s27: and solving the solution of the equation function.
Specifically, the equation of the equation function may be:
Figure BDA0003567153600000052
wherein a reference curve Γ propagates over the entire plane domain Ω, each point on the curve having a constant velocity orthogonal to the curve, t (x) is the time required for the curve Γ to reach point x with a velocity equal to 1/f, t (x) is proportional to the distance x to Γ.
Specifically, referring to fig. 6, generating a set of equidistant curves can be divided into the following steps: 1) defining a reference curve Γ on the grid to construct the initial conditions in the above equation; 2) solving the value of T in the equation at the grid node; 3) t is calculated from the direction of the constant value of each grid cell. In order to better express the algorithm of the equidistant curve, the parameter equation expression of the equidistant curve is also given. Let y be f (x) as the rectangular coordinate equation of the smooth curve L in the plane, and pass through the normal of any point p (x, y) on the curve LLfThe equation is
Figure BDA0003567153600000061
Equidistant curve L with constant D of distance of curve LdShould satisfy the following parametric equation:
Figure BDA0003567153600000062
or
Figure BDA0003567153600000063
S3: fitting the track points;
in order to obtain a track curve after track point fitting, a machine learning method is adopted to fit track points, the track points are a set of discrete points, if the track points are directly connected, a curve track is changed into a broken line segment, so that the track points need to be fitted, a Taylor formula can know that for any smooth curve, a polynomial function can be constructed to approximate an expression curve, and in order to conveniently calculate a polynomial coefficient, the polynomial function is expressed, and the function is constructed as follows:
f(x)≈pn(x)＝a0+a1(x-x0)+a2(x-x0)2+…+an(x-x0)n+Rn(x)；
wherein R isn(x) Is an n-th order Theilerler remainder;
however, the fitted curve has an error with the target curve, and in order to judge whether the curve is fit, the error relationship between f (x) and the curve to be fitted is expressed by using a least square method as a loss function, namely:
Figure BDA0003567153600000064
let x00 is got
Figure BDA0003567153600000065
To optimize the objective function, each Loss is given a coefficient partial derivative ak1Is 0, namely:
Figure BDA0003567153600000071
Figure BDA0003567153600000072
……
Figure BDA0003567153600000073
calculating all coefficients a by gradient descent method according to the formulakAnd an iterative method is adopted to approximate the optimal solution, so that the optimal solution of k equations can be avoided being solved in one step. Firstly, inputting iteration times and a learning rate learn _ rate, starting iteration after initializing k coefficient values, and updating a coefficient a iterated each timekAnd the corresponding Loss value is continuously reduced, and the iteration is stopped after the iteration times are reached.
Wherein the coefficient akCorresponding gradient value of
Figure BDA0003567153600000074
Figure BDA0003567153600000075
Updating the coefficient akIs ak＝ak+ spare _ rate _ gradient _ ak, and finally saving the obtained training result locally for subsequent calling.
S4: outputting equidistant curve coordinates and function expression parameters;
specifically, referring to fig. 7-8, a trace point in fig. 4 is taken as a reference point, the highest order is set to be 10, the iteration number is 5000, and the learning rate lea is setrnrateAfter 1e-3, the 10 fitted curves shown were obtained by machine learning. It can be seen that when the polynomial fitting order is 7, the mean square error reaches a minimum value, which also means when
Figure BDA0003567153600000076
When the curve fit is under-fitted, and when
Figure BDA0003567153600000077
Then, after the curve is over-fitted and the mean square error of the training result is obtained and is equal to 0.101, the mean square error is used as a boundary value to train the rest trajectory curves to obtain the belt width laying curve shown in fig. 6;
s5: a variable stiffness laminate model is generated.
Specifically, referring to fig. 9, for a given laminate parameter, if the fiber angle variation of the in-plane laying path of the laminate is equal to the fiber angle variation of the reference path, the laminate laying path needs to be designed according to the reference path laying angle, and the fiber angle in the laminate is <0|45>, which meets the design requirement.
The method disclosed by the invention is utilized to lay the composite material fibers of the airplane wings in a variable angle manner, the upper half curve of the airfoil profile curve of a certain airplane wing is taken as a prototype surface to generate a laying curved surface, and the airfoil profile curve is shown in figure 10.
Using an algorithm for segmenting equidistant rebinning curves, an in-plane fiber placement trajectory is generated, wherein the curve coordinates are no longer (x, y), but instead (x, y, z) when transitioning from two-dimensional planar to three-dimensional curved surface placement. If the plane track is laid on a curved surface, the coordinate transformation is needed. Assuming that there is a plane Ω 1 and 6 feature points in the plane coordinate system, as shown in fig. 11 below, the feature point of Ω 1 becomes (x, y,0) in the rectangular spatial coordinate system, Ω 1 changes from a plane to a curved surface when Ω 1 changes to Ω 2, Ω 1 is called a projection plane of Ω 2 in the xy plane, at this time, the x and y coordinates of the feature point of Ω 2 are unchanged, the projection feature point coordinates of Ω 2 in the xz plane are (x, z), and z (x) is a function of the section curve. So when the planar trajectory coordinates (x, y) and the section curve coordinates (x, z) are known, the two-dimensional coordinates to three-dimensional coordinates are converted to:
Figure BDA0003567153600000081
let the trajectory line coordinate be (x)1,y1) The wing curve is (x)2,y2) Obtaining the trajectory coordinates of the three-dimensional curved surface, the trajectory coordinates (x, y, z) obtained by equation 9 are (x, y, z)1,y1,y2) In the case where the fibers meet no more than maximum geodetic curvature, a simple two-to-three-dimensional transition is achieved, resulting in an upper airfoil surface lay as shown in FIGS. 12 and 13 below.
According to the modeling method for the composite material laminated plate based on the segmented equidistant recombination curve, the processes of generating the track curve, the equidistant track curve, fitting the track curve, generating the laminated plate model and the like are simplified to be obtained only by inputting relevant parameters, so that the modeling step is simple and convenient, and the analysis efficiency is effectively improved.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The above examples are only for describing the preferred embodiments of the present invention, and are not intended to limit the scope of the present invention, and various modifications and improvements made to the technical solution of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims (5)

1. A modeling method of a composite material laminated plate based on a segmented equidistant recombination curve is characterized by comprising the following steps of:
inputting the size parameters of the laminated plate, the laminated structure, a defined curve function, the aperture and the position information of the hole;
performing scatter processing on the reference track and performing equidistant recombination on the concave-convex functions respectively;
fitting the track points;
outputting equidistant curve coordinates and function expression parameters;
a variable stiffness laminate model is generated.
2. The modeling method for the composite material laminated plate based on the segmented equidistant recombination curve according to claim 1, wherein the step of performing the scattering processing on the reference track comprises:
defining a variable angle track;
generating a variable angle reference track;
inputting the generated variable-angle track data into a program;
finding a dividing point with a second derivative of 0 on the reference track;
equidistantly biasing the segmentation curve along the direction of curvature reduction;
carrying out translation recombination on the deflected track;
and solving the solution of the equation function.
3. The method of modeling a composite laminate based on segmented equidistant rebinning curves according to claim 2 wherein the distance that the segmented curves are equidistantly offset in the direction of decreasing curvature is equal to the product of the offset distance and the offset number.
4. The modeling method for segmenting equidistant recombination curves based on composite laminates according to claim 2 wherein said equation of function is:
Figure FDA0003567153590000011
wherein a reference curve Γ propagates over the entire plane field Ω, each point on the curve having a constant velocity orthogonal to the curve, t (x) is the time it takes for the curve Γ to reach point x with a velocity equal to 1/f, t (x) is proportional to the distance x to Γ.
5. The modeling method for the composite material laminated plate based on the segmented equidistant recombination curve according to claim 1, characterized in that the tracing points are fitted by a machine learning method.
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Cited By (1)

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Publication number Priority date Publication date Assignee Title
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CN113191048A (en) * 2021-04-27 2021-07-30 华中科技大学 Optimal design method of equidistant curve fiber reinforced structure
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CN112507587A (en) * 2020-12-04 2021-03-16 中国航空工业集团公司成都飞机设计研究所 Variable-stiffness composite material structure optimization design method oriented to compression stability
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