Material layout optimization method for vibrating laminates

Abstract

This invention relates to the field of vibrating laminated plate technology and discloses a method for optimizing the material layout of vibrating laminated plates, comprising the following steps: S1, dividing the laminated plate into an 80×80 grid, with five candidate materials provided on each grid; S2, the five candidate materials are 90° fiber material, ±45° fiber material, 0° fiber material, and a damping material; S3, using a discrete material optimization model and iterative optimization program, selecting the material with the best vibration reduction effect for the laminated plate on each grid; S4, after the optimization program iteration is completed, a material layout diagram on the laminated plate is provided. This method for optimizing the material layout of vibrating laminated plates applies a discrete material optimization model to the material layout optimization of vibrating laminated plates, establishing a material layout topology optimization model for vibrating laminated plates that considers material constraints, thereby helping structural engineers design more economical and reliable engineering structures.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of vibration laminated plate, in particular to a material layout optimization method of vibration laminated plate. BACKGROUND

[0002] Composite laminated plates are widely used in the structural design of aircraft fuselages, wings and other aircraft, and large areas of composite materials are used to process and form structural components such as aircraft wings and wall plates. In the process of high-speed flight of the aircraft, the structure of the aircraft wing and the wall plate will inevitably vibrate under the disturbance of the airflow. Once the wing aerodynamic structure of the aircraft resonates or loses stability, it will cause damage to the aircraft, resulting in incalculable losses. Therefore, these composite components should not only meet the lightweight structure, but also have good aerodynamic performance.

[0003] To meet the fierce international competition and resource shortage and other limitations, the optimization design of industrial equipment has posed a severe challenge. The traditional structural design method often relies on the experience of designers, and needs to be repeatedly tried and tested, which is time-consuming, inefficient, and the resulting structure is often only a feasible solution, not the optimal solution. China's manufacturing industry is facing the urgent need for self-design and innovative design, and there is an urgent need for efficient, economical and reliable structural design. Structural optimization design method has become a powerful theoretical tool and technical means to achieve the above goals. With the rapid development of computing hardware technology and the improvement of finite element method and mathematical programming theory, people not only have powerful structural analysis tools, but also have a systematic method to improve and optimize design. The field of structural optimization design has thus developed rapidly and become an important branch of computational mechanics. Structural optimization design is committed to improving structural design systematically and efficiently, so as to help engineering structural designers design more economical and reliable engineering structures. At present, due to the high stiffness-to-weight ratio and anisotropic characteristics of composite structures, their design has attracted the attention of many scholars, but there are few studies on applying discrete material optimization method to material layout design of composite structures to improve structural vibration performance. SUMMARY

[0004] (I) Technical problems solved

[0005] In view of the shortcomings of the prior art, the present application provides a material layout optimization method of vibration laminated plate, which has the advantages of helping engineering structural designers to design more economical and reliable engineering structures, and solves the problems of traditional structural design methods that often rely on the experience of designers, need to be repeatedly tried and tested, and have large design workload, long cycle and low efficiency, and the resulting structure is often only a feasible solution, not the optimal solution.

[0006] (II) Technical solutions

[0007] In order to achieve the above object, the present application provides the following technical scheme: a material layout optimization method of a vibration laminated plate, comprising the following steps:

[0008] S1, dividing the laminated plate into a 80x80 grid, and giving five kinds of alternative materials on each grid;

[0009] S2, the five kinds of alternative materials are 90° fiber material, ±45° fiber material, 0° fiber material, and a damping material;

[0010] S3, using a discrete material optimization model to iterate through an optimization program, and selecting one kind of material on each grid which is the best for the vibration reduction effect of the laminated plate;

[0011] S4, after the iteration of the optimization program is completed, a material layout diagram of the laminated plate is given, different colors represent different materials, so as to optimize the material layout of the laminated plate.

[0012] Preferably, the element constitutive matrix in the discrete material optimization model is:

[0013]

[0014]

[0015] wherein x i,j represents the artificial density, w i,j represents the weight function of the jth alternative material in the ith element, D j represents the elastic matrix of the jth alternative material, a represents the penalty index, and N can represents the number of alternative materials.

[0016] Preferably, the weight function interpolation scheme is:

[0017]

[0018]

[0019] Preferably, the convergence rate evaluation index in the discrete material optimization model is:

[0020]

[0021] The Heaviside function is:

[0022]

[0023]

[0024]

[0025] wherein β,η are penalty coefficients in the Heaviside projection function.

[0026] Preferably, the finite element analysis in the discrete material optimization model comprises displacement and strain fields of the plate, stress-strain relationship of the plate, element stiffness matrix and non-proportional damping vibration solution method.

[0027] wherein the displacement and strain fields of the plate are:

[0028] u(x,y,z) = u0(x,y) - zθ x (x,y)

[0029] v(x,y,z) = v0(x,y) - zθ y (x,y)

[0030] w(x,y,z) = w0(x,y);

[0031] ε = Bu e ;

[0032] the stress-strain relationship of the plate is:

[0033]

[0034] σ = Dε;

[0035] wherein E is the elastic modulus and v is the Poisson's ratio.

[0036] Preferably, the element stiffness matrix is:

[0037] D α = TD0T T ;

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] Where K, M, and C are the overall structural stiffness matrix, overall mass matrix, and overall damping matrix, respectively; B is the geometric matrix; and T is the coordinate transformation matrix.

[0048] Preferably, the non-proportional damped vibration solution method adopts the complex modal superposition method, specifically as follows:

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] v k =a k e iθt ;

[0058]

[0059] Preferably, the laminate has the property of E. h =69GPa, v h =0.33, ρ = 2700 kg / m 3 The fiber material has the property of E. x =54 GPa, E y =E z =18GPa, ρ1=1900kg / m 3 α1 = 5 × 10 -3 β1=5×10 -3 G xy =G yz =G xz =9 GPa, v xy =0.3, α1=5×10 -3 β1=5×10 -3 The damping material has the following properties: E = 1.25 GPa, v = 0.3, ρ = 100 kg / m. 3 α2=0.5,β2=1.

[0060] (III) Beneficial Effects

[0061] Compared with the prior art, the present invention provides a method for optimizing the material layout of vibrating laminates, which has the following beneficial effects:

[0062] This material layout optimization method for vibrating laminates applies a discrete material optimization model to the material layout optimization of vibrating laminates, and establishes a material layout topology optimization model for vibrating laminates that considers material constraints, thereby helping engineering structural designers to design more economical and reliable engineering structures. Attached Figure Description

[0063] Figure 1 This is a structural diagram of the laminate in this invention;

[0064] Figure 2 This is a diagram of the four-corner fixed square plate in this invention;

[0065] Figure 3 This is an iteration history diagram in this invention;

[0066] Figure 4 This is a diagram showing the optimization results in this invention;

[0067] Figure 5 This is a diagram showing the amplitude variation in this invention;

[0068] Figure 6 This is an optimized flowchart of the present invention. Detailed Implementation

[0069] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0070] Please see Figures 1-6 The material layout optimization method for the vibrating laminate in this embodiment includes the following steps:

[0071] S1. Divide the laminate into an 80×80 grid, with five alternative materials provided for each grid;

[0072] S2. The five alternative materials are 90° fiber material, ±45° fiber material, 0° fiber material, and a damping material.

[0073] S3. Using a discrete material optimization model, the optimization program iterates through each grid to select the material that has the best vibration reduction effect for the laminate.

[0074] S4. After the optimization process is completed, a material layout diagram of the laminate is given. Different colors represent different materials, thereby optimizing the material layout of the laminate.

[0075] Wherein, the element constitutive matrix in the discrete material optimization model is:

[0076]

[0077]

[0078] Where, x i,j w represents artificial density. i,j D represents the weight function corresponding to the j-th candidate material in the i-th unit. j Let N represent the elasticity matrix of the j-th candidate material, a represent the penalty index, and N represent the elasticity matrix of the j-th candidate material. can Indicates the quantity of alternative materials.

[0079] Meanwhile, the weight function interpolation scheme is as follows:

[0080]

[0081]

[0082] In addition, the convergence rate evaluation index in the discrete material optimization model is:

[0083]

[0084] The Heaviside function is:

[0085]

[0086]

[0087]

[0088] Where β,η are the penalty coefficients in the Heaviside projection function.

[0089] Furthermore, the finite element analysis in the discrete material optimization model includes the displacement field and strain field of the plate, the stress-strain relationship of the plate, the element stiffness matrix, and the solution method for non-proportional damped vibration.

[0090] The displacement field and strain field of the plate are as follows:

[0091] u(x,y,z)=u0(x,y)-zθ x (x,y)

[0092] v(x,y,z)=v0(x,y)-zθ y (x,y)

[0093] w(x,y,z)=w0(x,y);

[0094] ε = Bue;

[0095] The stress-strain relationship of the plate is as follows:

[0096]

[0097] σ=Dε;

[0098] Where E is the elastic modulus and v is Poisson's ratio.

[0099] The element stiffness matrix is:

[0100] D α =TD0T T ;

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110] Where K, M, and C are the overall structural stiffness matrix, overall mass matrix, and overall damping matrix, respectively; B is the geometric matrix; and T is the coordinate transformation matrix.

[0111] The non-proportional damped vibration solution method adopts the complex modal superposition method, specifically as follows:

[0112]

[0113]

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120] v k =a k e iθt ;

[0121]

[0122] The laminate has property E. h =69GPa, v h =0.33, ρ = 2700 kg / m 3 The fiber material has the property of E. x =54 GPa, E y =E z =18GPa, ρ1=1900kg / m 3 α1 = 5 × 10 -3 β1=5×10 -3 G xy =G yz =G xz =9 GPa, v xy =0.3, α1=5×10 -3 β1=5×10 -3 The damping material has the following properties: E = 1.25 GPa, v = 0.3, ρ = 100 kg / m. 3 α2=0.5,β2=1.

[0123] It is understandable that the formulation of the optimization problem in the discrete material optimization model includes:

[0124] Find X = {x i，j} i∈N e , j∈N can

[0125]

[0126] st(-θ 2 M+iθC+K)Y=F

[0127] In dynamic optimization, dynamic compliance is considered an effective method for measuring the degree of structural vibration and can be used to evaluate the response of a structure at a given frequency.

[0128] Sensitivity analysis in discrete material optimization models includes:

[0129]

[0130] W = -θ 2 M+iθC+K;

[0131]

[0132]

[0133]

[0134]

[0135] It should be noted that the solutions obtained by discrete material optimization methods are generally local optima. This phenomenon is also common in structural topology optimization, especially for structural dynamics optimization, which is itself a highly non-convex problem. At the same time, the material layout we obtain is also relatively complex and not very regular, which will bring certain difficulties to the manufacturing process. However, these local optima still have very important guiding significance in the conceptual design stage of considering structural dynamic performance and have great potential in practical applications.

[0136] The beneficial effects of this invention are:

[0137] By applying discrete material optimization models to the material layout optimization of vibrating laminates, a material layout topology optimization model for vibrating laminates considering material constraints is established, thereby helping engineering structural designers to design more economical and reliable engineering structures.

[0138] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method of material layout optimization of a vibratory laminate, characterized by, The method comprises the following steps: S1, dividing the laminated plate into a 80*80 grid, and giving five kinds of alternative materials on each grid; S2, the five kinds of alternative materials are 90° fiber material, ±45° fiber material, 0° fiber material, and a damping material; S3, selecting one kind of material with the best damping effect on the laminated plate on each grid by using a discrete material optimization model through an optimization program iteration; The unit constitutive matrix in the discrete material optimization model is: wherein, denotes the artificial density, denotes the weight function corresponding to the jth alternative material in the ith cell, denotes the elastic matrix of the jth alternative material, denotes the penalty index, denotes the number of alternative materials; The weight function interpolation scheme is: ； The convergence rate evaluation index in the discrete material optimization model is: The Heaviside function is: wherein, is a penalty coefficient in the Heaviside projection function; S4, after the optimization program iteration is completed, a material layout diagram of the laminated plate is given, different colors represent different materials, and thus the material layout of the laminated plate is optimized.

2. The material layout optimization method of a vibratory laminate according to claim 1, wherein, The finite element analysis in the discrete material optimization model comprises displacement field and strain field of the plate, stress-strain relationship of the plate, element stiffness matrix and non-proportional damping vibration solving method; The displacement field and strain field of the plate are: ； ； The stress-strain relationship of the plate is: ； ； Wherein, E is the elastic modulus, and v is the Poisson's ratio.

3. The material layout optimization method of a vibratory laminate according to claim 2, wherein, The element stiffness matrix is: ； ； ； ； ； ； Wherein, K, M, C are the structure overall stiffness matrix, overall mass matrix and overall damping matrix respectively, B is the geometric matrix, and T is the coordinate conversion matrix.

4. The material layout optimization method of a vibratory laminate according to claim 2, wherein, The non-proportional damping vibration solving method adopts the complex modal superposition method, and specifically is: ； ； ； ； ； 、 ； ； ； 。 5. The material layout optimization method of a vibratory laminate according to claim 1, wherein, The laminate properties are , , The fiber material properties are , , The damping material properties are , .

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