A Design Method for Bistable Curve Fiber Laminates

Abstract

A design method for a bistable curve fiber laminate, including a bistable curve fiber laminate to be measured, the bistable curve fiber laminate having a curve fiber path, which is characterized by the following steps: determining the design parameters of the composite laminate, determining the angular parameters of the curve fiber path, establishing a steady-state analysis model of the composite laminate, establishing an Abaqus secondary development plug-in, and simulating and verifying the steady-state characteristics of the composite shell; compared with the prior art, by setting two design variables, namely the initial fiber angle and the terminal fiber angle, and designing a bistable variable-angle laminate with different curve paths according to the two design variables of the initial fiber angle and the terminal fiber angle, the flexibility of composite material design is enriched.

Description

Technical Field

[0001] The present invention relates to the field of composite material structure design, and particularly to a design method for a bistable curve fiber laminate. Background Art

[0002] Due to its advantages such as light weight and good mechanical properties, as well as its unique bistable behavior, bistable composite structures have been widely used in the fields of aerospace, energy harvesting, bionic structures, etc.

[0003] In actual deformation scenarios, bistable composite structures are usually realized by traditional straight fiber composite laminates, in which the fibers are laid in a straight line. Although the design process of straight fiber laying is simple and can meet general engineering requirements, it greatly limits the flexibility of composite material design and cannot make good use of the directional characteristics of composite materials. Summary of the Invention

[0004] The present invention is to overcome the above-mentioned defects in the prior art and provides a design method for a bistable curve fiber laminate with simulation verification and flexible design.

[0005] To achieve the above-mentioned invention purpose, the present invention adopts the following technical solutions: A design method for a bistable curve fiber laminate, including a bistable curve fiber laminate to be measured, the bistable curve fiber laminate having a curve fiber path, and is characterized by including the following steps:

[0006] Step A: Determine the design parameters of the composite laminate and determine the angular parameters of the curve fiber path: Wherein, T0 is located at the center of the composite laminate and is the initial angle of the fiber reference path, T1 is the flat edge angle at a / 2 away from the center of the composite laminate, d represents the distance from the center of the flat to the boundary, and X is the position of the curve path where the fiber laying angle linearly changes with the x-axis;

[0007] Step B: Establish a steady-state analysis model of the composite laminate, establish a steady-state analysis model of the composite laminate for the deterministic design parameters given in Step A, and use the classical laminate theory to solve the tensile stiffness, coupling stiffness, and bending stiffness matrices of the laminate;

[0008] For a variable angle laminate, the tensile stiffness, coupling stiffness, and bending stiffness matrices are functions of x and y. After setting appropriate mid-plane strain functions and out-of-plane displacement functions according to the Ritz method, the total potential energy of the laminate can be obtained. Then, according to the principle of minimum potential energy, the energy analysis of the composite laminate is carried out, the corresponding parameters are solved, and finally, the stability and the number of steady states of the solution are determined according to the positive definiteness of the Jacobian matrix of the component. The model is as follows:

[0009]

[0010] where represents the transformation matrix, which is related to material parameters and laying angles, and C i are the unknown parameters of the mid-surface strain energy and out-of-plane displacement, k represents the curvature, A is the tensile stiffness matrix, B is the coupling stiffness matrix, and C is the bending stiffness matrix;

[0011] Step C: Establish an Abaqus secondary development plug-in. Since the finite element software cannot directly model the curved fibers, the laminated plate needs to be discretized. The laminated plate is evenly divided into m small elements. The curved fibers are approximated as a linear piecewise function. For each element, the laying angle is a fixed constant, realizing "replacing the curve with a straight line";

[0012] Step D: Simulate and verify the steady-state characteristics of the composite shell. Use the finite element simulation software to create a variable-angle laminated plate according to the design parameters in Step A. Lay the curved fibers by means of the Abaqus secondary development plug-in. Simulate the actual curing process by fixing the center point and applying a temperature field. Finally, apply a displacement field at the four vertices of the laminated plate to make it transition to the second steady state, and output the steady-state curvature, and compare it with the analysis model to verify the error of the steady-state quantity and steady-state curvature.

[0013] As a preferred solution of the present invention, the design parameters of the composite laminated plate in Step A include the material parameters, lay-up conditions, overall dimensions, and curved fiber path of the composite laminated plate.

[0014] As a preferred solution of the present invention, the lay-up conditions include the number of layers n and the laying method of the lay-up. The laying method includes symmetric laying, antisymmetric laying, and orthogonal laying.

[0015] As a preferred solution of the present invention, the overall dimensions are the length and width of the composite laminated plate.

[0016] As a preferred solution of the present invention, the parameters of the variable-angle laminated plate in Step A include the elastic modulus E1 in the fiber direction, the elastic modulus E2 in the fiber transverse direction, the in-plane Poisson's ratio v 12 , the in-plane shear modulus G 12 , the thickness t of a single ply s , the coefficient of thermal expansion α1 in the fiber direction, and the coefficient of thermal expansion α2 in the fiber transverse direction.

[0017] As a preferred solution of the present invention, Step C is completed by means of the Abaqus secondary development interface Python. Input fixed parameters such as the length and width of the laminated plate, the thickness of the laminated plate, the rotation angle, and the angle parameters to automatically establish the model.

[0018] As a preferred embodiment of the present invention, the laminated plate can maintain two stable configurations without the application of external forces.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows: By setting two design variables, namely the initial fiber angle and the terminal fiber angle, and designing a bistable variable-angle laminated plate with different curved paths according to these two design variables, the flexibility of composite material design is enriched. Description of the Drawings

[0020] Figure 1 is a schematic diagram of the curved fiber laminated plate of the present invention;

[0021] Figure 2 is the definition of the fiber angle of the present invention;

[0022] Figure 3 is the flow chart of the Abaqus secondary development plug-in of the present invention; Detailed Embodiments

[0023] The embodiments of the present invention will be described in detail below with reference to the drawings.

[0024] As shown in Figures 1 - 3 , a design method for a bistable curved fiber laminated plate includes a bistable curved fiber laminated plate to be measured. The bistable curved fiber laminated plate has a curved fiber path. The composite material laminated plate is composed of variable-angle laminated plates stacked together. The parameters of the variable-angle laminated plate include the fiber-direction elastic modulus E1, the fiber transverse elastic modulus E2, the in-plane Poisson's ratio v 12 , the in-plane shear modulus G 12 , the thickness t of a single layer plate s , the coefficient of thermal expansion α1 in the fiber direction and the coefficient of thermal expansion α2 in the fiber transverse direction.

[0025] It includes the following steps:

[0026] Step A: Determine the design parameters of the composite material laminated plate, including the material parameters, layup conditions, overall dimensions, and curved fiber path of the composite material laminated plate. The layup conditions include the number of layers n and the laying method of the layup. The laying method includes symmetric laying, antisymmetric laying, and orthogonal laying. The overall dimensions are the length and width of the composite material laminated plate. Determine the angle parameters of the curved fiber path: Among them, the angle parameters related to the linearly varying curved fiber mainly include T0 and T1. T0 is located at the center of the composite material laminated plate and is the initial angle of the fiber reference path, generally simply referred to as the initial angle. T1 is the flat plate edge angle at a / 2 away from the center of the composite material laminated plate and is called the terminal angle of the fiber reference path, generally simply referred to as the terminal angle. d represents the distance from the center of the flat plate to the boundary, and X is the position of the curved path where the fiber laying angle varies linearly with the x-axis.

[0027] A curvilinear fiber path refers to a curvilinear path where the fiber placement angle varies linearly with the x-axis. This linearly varying curve is more adaptable to manufacturing constraints and also helps to establish a simpler analytical model.

[0028] Step B: Establish a steady-state analysis model for the composite laminate. Based on the deterministic design parameters given in Step A, establish a steady-state analysis model for the composite laminate, and use the classical laminate theory to solve for the tensile stiffness, coupling stiffness, and bending stiffness matrices of the laminate.

[0029] For a variable-angle laminate, the tensile stiffness, coupling stiffness, and bending stiffness matrices are functions of x and y. After setting appropriate mid-plane strain functions and out-of-plane displacement functions according to the Ritz method, the total potential energy of the laminate can be obtained. Then, based on the principle of minimum potential energy, perform an energy analysis of the composite laminate, solve for the corresponding parameters, and finally determine the stability and the number of steady states according to the positive definiteness of the Jacobian matrix of the component. The model is as follows:

[0030]

[0031] where represents the transformation matrix, which is related to material parameters and laying angles. C i are the unknown parameters of the mid-plane strain energy and out-of-plane displacement, k represents the curvature, A is the tensile stiffness matrix, B is the coupling stiffness matrix, and C is the bending stiffness matrix.

[0032] Step C: Establish an Abaqus secondary development plug-in. Since the finite element software cannot directly model the curvilinear fiber, it is necessary to discretize the laminate. Divide the laminate into m small elements evenly. The curvilinear fiber is approximated as a linear piecewise function. For each element, the laying angle is a fixed constant, achieving "replacing the curve with a straight line". This is completed with the help of the Abaqus secondary development interface Python. Input fixed parameters such as the length and width of the laminate, the thickness of the laminate, the rotation angle, and the angle parameter to automatically establish the model.

[0033] Step D: Simulate and verify the steady-state characteristics of the composite shell. Use the finite element simulation software to create a variable-angle laminate according to the design parameters in Step A. Lay the curvilinear fiber through the Abaqus secondary development plug-in, simulate the actual curing process by fixing the center point and applying a temperature field, and finally apply a displacement field at the four vertices of the laminate to make it transition to the second steady state, and output the steady-state curvature. Compare it with the analysis model to verify the error of the number of steady states and the steady-state curvature.

[0034] Without external force, the laminate can maintain two steady-state configurations.

[0035] During the actual use process, determine the parameters of the variable-angle laminated plate, including the material parameters of the composite laminated plate, the layup situation, the overall dimensions, and the angle parameters of the curved fiber path. For example, the elastic modulus in the fiber direction E1 = 138 GPa, the elastic modulus transverse to the fiber E2 = 8.36 GPa, the in-plane Poisson's ratio v12 = 0.27, the in-plane shear modulus G12 = 4.51 GPa, the coefficient of thermal expansion in the fiber direction α1 = -0.000000106 / °C, the coefficient of thermal expansion transverse to the fiber α2 = 0.0000256 / °C, and the thickness t of a single ply s = 0.45 mm, the total number of plies is 2, the layup method is orthogonal layup similar to [0 / 90], the shape of the laminated plate is square, and the side length is 150 mm. The angle parameters of the curved fiber path are T0 = -T1, and T0 takes 5°, 10°, 15°, and 20° respectively.

[0036] According to the classical laminated plate theory, using the material parameters and angle functions determined in step A, obtain the tensile stiffness, coupling stiffness, and bending stiffness matrices of the composite laminated plate. Subsequently, after determining the appropriate out-of-plane displacement function and mid-plane strain function, according to the formula in step A Integrate over the entire laminated plate to obtain the total potential energy of the entire laminated plate. The potential energy can be expressed by 14 unknown parameters. Finally, solve according to the principle of minimum potential energy to conduct the energy analysis of the composite laminated plate and solve the corresponding parameters.

[0037] Finally, determine the stability and the number of steady states of the solution according to the positive definiteness of the constructed Jacobian matrix. With the help of Mathematica software, two steady-state solutions are obtained, which are respectively:

[0038] K1 = [0.00670977]

[0039] K2 = [0.00680981].

[0040] Establish a secondary development plug-in for Abaqus. Since the finite element software cannot directly model the curved fiber, it is necessary to discretize the laminated plate. Divide the laminated plate into m tiny elements on average. The curved fiber is approximated as a linear piecewise function. For each element, the laying angle is a fixed constant, "replacing the curve with a straight line". If manually assign values to each element, the workload is very large. Therefore, it is necessary to complete it with the help of the Abaqus secondary development interface Python. Just input fixed parameters such as: the length and width of the laminated plate; the thickness of the laminated plate; the angle parameters and the number of meshes, etc., and the model can be automatically established and the job can be submitted.

[0041] Verify the steady-state characteristics of the composite shell through simulation. Use the finite element simulation software to draw the structure of the composite laminated plate according to the design parameters in step 1, and lay the curved fiber by means of the secondary development plug-in of Abaqus.

[0042] The actual curing process is simulated by fixing through the center point and applying a temperature field. Finally, a displacement field is applied to the four vertices of the laminate to make it transform to the second steady state, and the curvature of the steady state is output, resulting in:

[0043] K1 = [0.00663994]

[0044] K2 = [0.00667558].

[0045] Through finite element verification, the accuracy of the theoretical model is verified. Both are bistable, and the error of the curvature results is not significant.

[0046] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features disclosed herein.

[0047] Although terms such as reference numerals in the drawings are used more frequently herein, the possibility of using other terms is not excluded. These terms are used only to more conveniently describe and explain the essence of the present invention; interpreting them as any additional limitation is contrary to the spirit of the present invention.

Claims

1. A design method for a bistable curve fiber laminate, including a bistable curve fiber laminate to be measured, the bistable curve fiber laminate having a curve fiber path, characterized in that, It includes the following steps: Step A: Determine the design parameters of the composite laminate and the angular parameters of the curved fiber path: Among them, T0 is located at the center of the composite laminate and is the initial angle of the fiber reference path. T1 is the flat plate edge angle at a distance of a / 2 from the center of the composite laminate. d represents the distance from the center of the flat plate to the boundary. X is the position of the curved path where the fiber placement angle changes linearly with the x-axis. Step B: Establish a steady-state analysis model of the composite laminate. For the deterministic design parameters given in Step A, establish a steady-state analysis model of the composite laminate, and use the classical laminate theory to solve the tensile stiffness, coupling stiffness, and bending stiffness matrices of the laminate; For a variable-angle laminate, the tensile stiffness, coupling stiffness, and bending stiffness matrices are functions of x and y. After setting appropriate mid-plane strain functions and out-of-plane displacement functions according to the Ritz method, the total potential energy of the laminate can be obtained. Then, according to the principle of minimum potential energy, perform energy analysis of the composite laminate, solve the corresponding parameters, and finally determine the stability and the number of steady states based on the positive definiteness of the Jacobian matrix of the component. The model is as follows: Among them represents the transformation matrix, which is related to material parameters and laying angles, C i are the unknown parameters of in-plane strain energy and out-of-plane displacement, k represents curvature, A is the tensile stiffness matrix, B is the coupling stiffness matrix, and C is the bending stiffness matrix; Step C: Establish an Abaqus secondary development plug-in. Since the finite element software cannot directly model the curved fibers, the laminate needs to be discretized. The laminate is evenly divided into m small elements, and the curved fibers are approximated as linear piecewise functions. For each element, the laying angle is a fixed constant, realizing "replacing the curve with a straight line"; Step D: Simulate and verify the steady-state characteristics of the composite shell. Use the finite element simulation software to create a variable-angle laminate according to the design parameters in Step A. Lay the curved fibers by means of the Abaqus secondary development plug-in, simulate the actual curing process by fixing the center point and applying a temperature field, and finally apply a displacement field at the four vertices of the laminate to make it transition to the second steady state, and output the curvature of the steady state, and compare it with the analysis model to verify the error of the number of steady states and the steady-state curvature.

2. The design method of a bistable curve fiber laminate according to claim 1, characterized in that The design parameters of the composite laminate in Step A include the material parameters, lay-up conditions, overall dimensions, and curved fiber path of the composite laminate.

3. The design method of a bistable curve fiber laminated plate according to claim 2, characterized in that, The lay-up conditions include the number of lay-up layers n and the laying method. The laying methods include symmetric laying, anti-symmetric laying, and orthogonal laying.

4. The design method of a bistable curve fiber laminate according to claim 2, characterized in that The overall dimensions are the length and width of the composite laminate.

5. The design method of a bistable curve fiber laminated plate according to claim 1, wherein The parameters of the variable-angle laminated plate in step A include the fiber-direction elastic modulus E1, the fiber-transverse elastic modulus E2, the in-plane Poisson's ratio v 12 , the in-plane shear modulus G 12 , the thickness t of the single layer plate s , the coefficient of thermal expansion α1 in the fiber direction and the coefficient of thermal expansion α2 in the fiber transverse direction.

6. The design method of a bistable curve fiber laminated plate according to claim 1, characterized in that, Step C is completed by means of the Abaqus secondary development interface Python. Input fixed parameters such as the length and width of the laminate, the thickness of the laminate, the rotation angle, and the angular parameters to automatically establish the model.

7. The design method of a bistable curve fiber laminate according to claim 1, characterized in that, Without external force, the laminate can maintain two steady-state configurations.

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