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

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

A Modeling Method for Composite Laminates Based on Split Isometric Recombination Curves

technical field

The invention relates to the technical field of composite material modeling, in particular to a modeling method for composite material laminates based on split equidistant recombination curves.

Background technique

At present, the finite element model of composite laminates includes constant stiffness finite element model and variable stiffness finite element model. When generating a variable stiffness finite element model, in order to save modeling time, an ideal laminate structure is often used instead, but the ideal type There are still differences between the laminate structure and the real laminate structure; the selection of the variable stiffness laminate structure with the tow width will cause defects such as overlap and gap between the tows, which will make the modeling steps more complicated; When the trajectory of the displacement angle is changed, the traditional method uses the existing curve to define the initial trajectory of the target laminate, but this method limits the design idea to a certain extent; and in the process of finite element model analysis, the user needs to model by himself. , after the modeling is completed, the analysis is submitted by oneself, and the user needs to retrieve the target data one by one in the results after the results come out, resulting in low work efficiency.

SUMMARY OF THE INVENTION

The present invention discloses a modeling method for composite material laminates based on split equidistant recombination curves, which solves the problems of complex modeling steps, easy overlap and gaps between tows, and work problems existing in the existing composite material laminates modeling methods. For the problem of low efficiency, the user can obtain the finite element model of the composite constant/variable stiffness laminate with tow width simply by inputting parameters. The modeling method is simple and the tows will not produce overlap and gaps.

In order to achieve the above object, the technical scheme of the present invention is specifically realized in this way:

The invention discloses a modeling method for a composite material laminate based on a split equidistant recombination curve, comprising the following steps:

Input the dimensional parameters of the laminate, the layer structure, the definition curve function, the hole diameter and the position information of the holes;

Scatter the reference trajectory;

Fit the trajectory points and reorganize the bump function equidistantly;

Output isometric curve coordinates and function expression parameters;

Generate a variable stiffness laminate model.

Further, the specific steps of performing scatter processing on the reference trajectory include:

Define the variable angle trajectory;

Generate a variable angle reference trajectory;

Input the generated variable angle trajectory data into the program;

Find the split point on the reference trajectory where the second derivative is 0;

Offset the split curves equally in the direction of decreasing curvature;

Perform translational reorganization of the offset trajectory;

Solve the solution of the functional equation.

Further, the distance at which the division curves are equidistantly offset along the direction of decreasing curvature is equal to the product of the offset distance and the number of offsets.

Further, the described program function equation is:

where the reference curve Γ propagates over the entire planar domain Ω, each point on the curve has a constant velocity orthogonal to the curve, and 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 from x to Γ.

Further, a machine learning method is used to fit the trajectory points.

Beneficial technical effects:

The invention discloses a modeling method for composite material laminates based on split equidistant recombination curves. Scattering processing; fitting the trajectory points and equidistantly recombining the concave and convex functions; outputting the equidistant curve coordinates and function expression parameters; The method has the problems of complex modeling steps, easy overlap and gap between tows, and low work efficiency. The user can obtain the finite element model of composite constant/variable stiffness laminate with tow width by simply inputting parameters. The method is simple and there is no overlap or gap between the tows.

Description of drawings

In order to illustrate the technical solutions of the present invention more clearly, the following briefly introduces the accompanying drawings used in the description of the embodiments.

1 is a flow chart of the steps of a method for modeling a composite material laminate based on a split equidistant recombination curve according to the present invention;

Fig. 2 is a logic flow chart of a method for modeling a composite material laminate based on a split equidistant recombination curve according to the present invention;

FIG. 3 is a schematic diagram of a trajectory division point of a method for modeling a composite material laminate based on a split equidistant recombination curve according to the present invention;

4 is a schematic diagram of trajectory offset of a method for modeling composite laminates based on split equidistant recombination curves according to the present invention;

5 is a schematic diagram of the trajectory reorganization of a method for modeling a composite laminate based on a split equidistant reorganization curve according to the present invention;

Fig. 6 is the propagation path diagram of the function equation of the modeling method of the composite material laminate based on the split equidistant recombination curve according to the present invention;

7 is a schematic diagram of fiber laying with width of a modeling method of a composite material laminate based on a split equidistant recombination curve according to the present invention;

Fig. 8 is a machine learning fitting curve data diagram of a method for modeling a composite material laminate based on a split equidistant recombination curve according to the present invention;

FIG. 9 is a schematic diagram of generating a variable stiffness laminate with a width by a modeling method for a composite laminate based on a split equidistant recombination curve according to the present invention.

10 is an airfoil curve of a certain aircraft based on a modeling method of a composite material laminate based on a split equidistant recombination curve according to the present invention;

11 is a schematic diagram of the conversion from two-dimensional coordinates to three-dimensional coordinates of a method for modeling a composite material laminate based on a split equidistant recombination curve according to the present invention;

12 is a schematic diagram of the laying angle of the airfoil surface of a modeling method for a composite material laminate based on a split equidistant recombination curve according to the present invention;

FIG. 13 is a schematic diagram of laying fibers on the airfoil of a modeling method for a composite material laminate based on a split equidistant recombination curve according to the present invention.

Detailed ways

The following describes in detail the embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary, only used to explain the present invention, and should not be construed as a limitation of the present invention.

The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

The present invention discloses a modeling method for a composite material laminate based on a split equidistant recombination curve, referring to FIG. 1 , which specifically includes the following steps:

S1: Input the size parameters of the laminate, the layer structure, the definition curve function, the hole diameter and the position information of the holes;

Specifically, the types of composite laminates include constant-stiffness laminates and variable-stiffness laminates, and the pre-model is pre-generated according to the input size parameters of the laminate, hole information, etc., so that the model can be modified and saved later.

S2: Scattering the reference trajectory and equidistantly reorganizing the concave-convex function;

After the trajectories are scattered, the concave and convex functions are recombined equidistantly to obtain the recombination curve, which specifically includes the following steps:

S21: Define the variable angle track;

S22: Generate a variable-angle reference trajectory;

The linear variable angle method in the variable angle trajectory definition is:

Among them, θ _x (x) represents the angle of the laminate fiber at the coordinate x, T ₀ is the starting angle of the fiber, T ₁ is the ending angle of the fiber, and a is the characteristic length;

The flow field function method in the variable angle trajectory definition is:

Among them, ψ is the iso-streamline, and x, y are the point coordinates of the streamline cluster layup;

The Bezier curve method in the variable angle trajectory definition is:

Among them, β ₁ is the position parameter of the control point P ₁ ; β ₂ is the position parameter of the control point P ₂ in the x-axis direction; h is the distance between the control points P ₁ and P ₂ in the x-axis direction. When β ₁ and β ₂ are determined, h can determine the position of the control points P ₂ and P ₃ in the y-axis direction, Ni _,j is the basis function of the cubic NURBS curve, and w is the weight factor;

S23: Input the generated variable-angle trajectory data into the program;

S24: Find the segmentation point where the second derivative is 0 on the reference trajectory;

Specifically, find the division point where the second derivative of the reference trajectory is 0, that is, f″(x)=0, see FIG. 3 ;

S25: Perform equidistant offset on the segmentation curve along the direction of decreasing curvature;

Specifically, referring to Fig. 4, taking the normal at the dividing point as a boundary, the curve is regarded as several parts, and the concave and convex curve parts are respectively offset along the curvature decreasing direction equidistantly, that is, the concave function is biased downward, and the convex function is offset downward. Offset upward, the offset distance is equal to the product of the offset distance and the offset number;

S26: Perform translational reorganization on the offset trajectory;

Recombining the offset trajectories of each part into a new trajectory, it can be understood that the curve obtained at this time as shown in Figure 5 does not have a translation or parallel line relationship with the given reference trajectory, that is, there is no Overlaps and gaps between tows;

S27: Solve the solution of the function equation.

Specifically, the program function equation can be:

where the reference curve Γ propagates over the entire planar domain Ω, each point on the curve has a constant velocity orthogonal to the curve, and 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 from x to Γ.

曲线L距离为常数D的等距曲线L_d的点应满足如下参数方程：Specifically, referring to Fig. 6, generating a set of equidistant curves can be divided into the following steps: 1) defining the reference curve Γ on the grid to construct the initial conditions in the above equation; 2) solving T in the above equation at the grid nodes 3) Calculate T from the constant value direction of each grid cell. In order to better describe the algorithm of the equidistant curve, the parametric equation expression of the equidistant curve is also given in this paper. Let the rectangular coordinate equation of the smooth curve L in the plane be y=f(x), and the equation of the normal L _f passing through any point p(x, y) on the curve L is:

The points of the equidistant curve L _d whose distance from the curve L is a constant D should satisfy the following parametric equation:

or

S3: Fit the trajectory points;

In order to obtain the trajectory curve after fitting the trajectory points, the machine learning method is used to fit the trajectory points. Since the trajectory points are a collection of discrete points, if the trajectory points are directly connected, the curve trajectory will become a polyline segment, so it is necessary to Fitting the trajectory points, it can be known from Taylor's formula that for any smooth curve, a polynomial function can be constructed to approximate the expression curve. In order to conveniently obtain the polynomial coefficients, a high-order polynomial is used in the present invention to represent, and the constructed function is:

f(x)≈p _n (x)=a ₀ +a ₁ (xx ₀ )+a ₂ (xx ₀ ) ² +…+a _n (xx ₀ ) ⁿ +R _n (x);

Among them, R _n (x) is the nth-order Taylor remainder;

However, there is still an error between the fitted curve and the target curve. In order to judge the quality of the curve fitting, the least squares method is used as the loss function to represent the error relationship between f(x) and the curve to be fitted, namely:

Let x ₀ =0 get

In order to make the objective function optimal, the partial derivative a _k1 of each Loss to the coefficient is 0, namely:

...

According to the above formula, all the coefficients a _k are calculated by the gradient descent method, and the iterative method is used to approximate the optimal solution, which can avoid finding the optimal solution of k equations in one step. First, enter the number of iterations and the learning rate learn_rate, after initializing k coefficient values, start the iteration, update the coefficient _ak obtained in each iteration, the corresponding Loss value is constantly decreasing, and the iteration is stopped after the number of iterations is reached.

更新系数a_k为a_k＝a_k+learn_rate*gradient_ak，最后将得到的训练结果保存在本地以便后续调用。The gradient value corresponding to the coefficient a _k is

The update coefficient _ak is _ak = _ak +learn_rate*gradient_ak, and finally the obtained training result is saved locally for subsequent calls.

S4: output isometric curve coordinates and function expression parameters;

时，曲线拟合是欠拟合的，而当

时，曲线是过拟合的，得到其训练结果均方误差meansquare error＝0.101后，将此均方误差作为边界值训练其余轨迹曲线，得到如图6所示带宽度铺放曲线；Specifically, referring to Figures 7-8, a trajectory point in Figure 4 is taken as a reference point, the highest order is set to 10, the number of iterations is 5000, and the learning rate is learn _rate = 1e-3. After machine learning, the shown 10 is obtained. a fitting curve. It can be seen that when the polynomial fitting order is 7, its mean square error reaches the minimum value, which also means that when the polynomial fitting order is 7

, the curve fit is underfit, and when

When , the curve is over-fitted, and after the mean square error of the training result is obtained as meansquare error=0.101, the mean square error is used as the boundary value to train the rest of the trajectory curves, and the width placement curve shown in Figure 6 is obtained;

S5: Generate a variable stiffness laminate model.

Specifically, referring to Fig. 9, when the laminate parameters are given, if the fiber angle change of the laying path in the laminate plane is to be equal to the fiber angle change of the reference path, the laying path of the laminate needs to be designed according to the laying angle of the reference path , the fiber angle in the laminate is <0|45>, which meets the design requirements.

The method disclosed in the present invention is used to lay the composite fiber of the aircraft wing at variable angles, and the upper half curve of the airfoil curve of an aircraft wing is used as the prototype surface to generate the laying surface. The airfoil curve is shown in Figure 10.

Using the algorithm of dividing the equidistant recombination curve, the in-plane fiber laying trajectory is generated. When the two-dimensional plane is converted to the three-dimensional surface laying, the curve coordinates are no longer (x, y), but become (x , y, z). When the plane track is laid on the surface, it needs to be coordinate transformed. Assuming that there is a plane Ω1 in the plane coordinate system, there are 6 feature points, as shown in Figure 11 below, the feature point of Ω1 becomes (x, y, 0) in the space rectangular coordinate system, when Ω1 transforms to Ω2 , Ω1 is transformed from a plane to a curved surface, and Ω1 is called the projection surface of Ω2 under the xy plane. At this time, the x and y coordinates of the feature points of Ω2 remain unchanged, and the coordinates of the projected feature points of Ω2 under the xz plane are (x, z ), z(x) is a function of the profile curve. Therefore, when the coordinates of the plane track line (x, y) and the coordinates of the profile curve (x, z) are known, the two-dimensional coordinates are converted to the three-dimensional coordinates as:

Assuming that the coordinates of the trajectory line are (x ₁ , y ₁ ), and the wing curve is (x ₂ , y ₂ ), the trajectory coordinates of the three-dimensional surface are obtained by formula 9. The trajectory coordinates (x, y, z) = (x ₁ , y ₁ , y ₂ ), under the condition that the fibers satisfy the maximum geodesic curvature, a simple transformation from two-dimensional to three-dimensional is achieved, and the upper airfoil surface placement shown in Figure 12 and Figure 13 is obtained.

The invention discloses a modeling method for composite material laminates based on splitting and equidistant recombination curves, which simplifies the processes of generating trajectory curves, equidistant trajectory curves, fitting trajectory curves, and generating laminate models to only need to input relevant parameters can be obtained, which makes the modeling steps simple and effectively improves the analysis efficiency.

In the description of this specification, description with reference to the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples", etc., mean specific features described in connection with the embodiment or example , structure, material or feature is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms 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 embodiments are only to describe the preferred embodiments of the present invention, and do not limit the scope of the present invention. Variations and improvements should fall within the protection scope determined by the claims of the present invention.

Claims (5)

1. a modeling method based on the composite material laminate of the split isometric recombination curve, is characterized in that, comprises the following steps: Input the dimensional parameters of the laminate, the layer structure, the definition curve function, the hole diameter and the position information of the holes; Scattering the reference trajectory and equidistantly reorganizing the concave and convex functions respectively; Fit the track points; Output isometric curve coordinates and function expression parameters; Generate a variable stiffness laminate model. 2. The modeling method of a composite material laminate based on a split equidistant recombination curve according to claim 1, wherein the specific steps of performing scatter processing on the reference track include: Define the variable angle trajectory; Generate a variable angle reference trajectory; Input the generated variable angle trajectory data into the program; Find the split point on the reference trajectory where the second derivative is 0; Offset the split curves equally in the direction of decreasing curvature; Perform translational reorganization of the offset trajectory; Solve the solution of the functional equation. 3. A method for modeling composite material laminates based on splitting equidistant recombination curves according to claim 2, wherein the distance of performing equidistant offsets on the splitting curves along the direction in which the curvature decreases is equal to the offset. The product of the offset distance and the offset amount. 4. a kind of modeling method based on the composite material laminate of splitting equidistant recombination curve according to claim 2, is characterized in that, described program function equation is:

where the reference curve Γ propagates over the entire planar domain Ω, each point on the curve has a constant velocity orthogonal to the curve, and 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 from x to Γ. 5 . The modeling method of a composite material laminate based on a split equidistant recombination curve according to claim 1 , wherein a machine learning method is used to fit the trajectory points. 6 .

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