Laminated truncated cone shell with pores and research method of thermoelastic buckling of laminated truncated cone shell

Abstract

The invention discloses a laminated truncated cone shell with pores and a research method of thermoelastic buckling of the laminated truncated cone shell. The shell comprises a ceramic heat insulation material layer, a graphene enhanced functionally graded material core layer and a piezoelectric layer. Wherein the ceramic heat insulation material layer and the piezoelectric layer are respectively an inner surface layer and an outer surface layer of the shell, and the graphene enhanced functionally graded material core layer is arranged in the middle of the laminated truncated cone shell. A heat conduction temperature field of the shell is solved according to a one-dimensional heat conduction equation, a control equation of the truncated cone shell in a thermal environment is established based on a Hamilton principle, and then an analytical solution of a buckling critical temperature is obtained by adopting a Galerkin integral method. The invention has the following advantages: 1, the heat-insulating material layer resists high temperature around the shell by utilizing the characteristics of heat-insulating materials such as ceramic with lower heat transfer coefficient; 2, the piezoelectric layer can slow down the vibration of the shell by pre-applying voltage according to the voltage-deformation conversion characteristic of a piezoelectric material; and thirdly, the buckling critical temperature of the shell in the thermal environment can be analyzed and calculated more accurately by adopting the method.

Description

[Technical Field]

[0001] This invention relates to the field of mechanical calculation, specifically to a method for studying the thermoelastic buckling of a porous laminated truncated cone shell. [Background Technology]

[0002] Nanocomposites possess excellent physical and mechanical properties such as lightweight and high strength, and have broad application prospects in engineering fields such as machinery, shipbuilding, and aerospace. Currently, the main engineering nanocomposites under research include carbon nanotube-reinforced composites (FG-CNTRC) and graphene-reinforced composites (FG-GPLRC). At present, nanocomposites have not yet been widely used in production. On the one hand, their preparation technology is quite difficult, and their performance and stability require further verification; on the other hand, their cost is relatively high.

[0003] When truncated conical shells operate in high-temperature environments, factors such as material thermal conductivity and the shell's mechanical properties must be considered. To ensure the structure functions properly in harsh environments, it is necessary to identify the critical buckling mode of the shell and calculate its critical buckling temperature before failure. Currently, research focuses on the thermal buckling of functionally graded truncated conical shells in a uniform temperature field, while studies on the effects of thermal conductivity on nanocomposite truncated conical shells are relatively limited. To obtain more accurate critical buckling temperatures for the shells, more scenarios need to be considered, further refining the theoretical calculations. [Summary of the Invention]

[0004] In summary, in view of the shortcomings of the existing technology, the technical problem to be solved by the present invention is to provide a research method for a porous laminated truncated cone shell and its thermoelastic buckling.

[0005] To solve the above technical problems, the present invention adopts the following technical solution:

[0006] A porous laminated truncated cone shell, characterized by comprising a ceramic or other insulating material layer, a graphene-reinforced functionally graded material core layer, and a piezoelectric layer. The ceramic or other insulating material layer and the piezoelectric layer are the inner and outer surfaces of the shell, respectively, while the graphene-reinforced functionally graded material core layer is located in the middle of the laminated truncated cone shell. The graphene-reinforced functionally graded material core layer is made of metallic materials and graphene, and the piezoelectric layer is mainly composed of piezoelectric materials such as zinc oxide and aluminum nitride.

[0007] A method for studying the thermoelastic buckling of a porous laminated truncated conical shell, characterized by the following steps:

[0008] Step 1: Establish the pore volume fraction model, graphene distribution model, and physical property model of the porous shell:

[0009] V P(z)=e1 cos(πz / 2h+π / 4)

[0010] V G (z)=v i [1-cos(πz / 2h+π / 4)]

[0011]

[0012] Among them, V P (z) and V G (z) represents the volume fraction of pores and the volume fraction of graphene, respectively; e1 represents the porosity coefficient; h represents the thickness of the shell; E M ρ M α M Let e ​​represent the Young's modulus, density, and coefficient of thermal expansion of a non-porous graphene-reinforced functional graded material. m V represents the mass density coefficient. i The maximum value representing the volume fraction of graphene is obtained by the following formula:

[0013]

[0014] in, The total volumetric composition of graphene in the truncated conical shell is calculated using the following formula:

[0015]

[0016] Among them, W GPL and ρ GPL ρ represents the total mass fraction and density of graphene, respectively. m This indicates the density of the matrix material.

[0017] The physical properties of the aforementioned non-porous graphene-reinforced functional graded materials, such as Young's modulus, density, and coefficient of thermal expansion, can be expressed by the mixing ratio:

[0018] P M =P GPL V G (z)+P m [1-V G (z)]

[0019] Where P represents the shell's Young's modulus, density, coefficient of thermal expansion, and other physical properties.

[0020] Step 2: Solve for the thermal conduction temperature field of the shell using the one-dimensional heat conduction equation:

[0021]

[0022] Where T(z) represents the temperature field, which is expanded using a power series in the calculation; T0 and T1 represent the inner and outer surface temperatures of the shell, respectively; K h (z) represents the thermal conductivity of the graphene-enhanced functionally graded material, calculated using Taylor series expansion, K. h (z) Calculated using the following formula:

[0023]

[0024] Where U represents the aspect ratio of the graphene nanosheet, F(U) represents the dimensionless geometric parameter, δ represents the fitting parameter, and K GPL and K m These represent the thermal conductivity of graphene and the matrix material, respectively.

[0025] Step 3: Based on Hamilton's principle, establish the governing equations for the truncated conical shell under thermal conditions:

[0026]

[0027] Among them, U s W represents the total strain energy of the shell. a This indicates the work done by the temperature load.

[0028] Step 4: Obtain the analytical solution for the critical buckling temperature of the shell using the Galerkin integral method:

[0029]

[0030] T 1cr =ΔT cr +300(K)

[0031] Among them, L ij (i = 1 - 5, j = 1 - 6) are constant coefficients, d 1j (j=1-5) represents the process calculation parameters, ΔT cr T represents the buckling temperature difference between the inner and outer surfaces of the shell. 1cr Representing the temperature of the outer surface of the shell, U, V, W, X, and Y are all axially continuous smooth functions, and the following formula represents the three displacement functions u, v, and w, and the two directional rotation angles. and In Chinese expression:

[0032]

[0033] Where m and n represent the axial wave number and circumferential wave number of the shell, respectively, and L represents the length of the shell generatrix.

[0034] The beneficial effects of this invention compared to existing technologies are as follows:

[0035] (1) The present invention provides a porous laminated truncated cone shell, wherein the heat insulation material layer adopts the heat insulation material properties of ceramics and other materials with low heat transfer coefficient to resist the high temperature around the shell, the piezoelectric layer utilizes the voltage-deformation conversion characteristics of piezoelectric materials to reduce the vibration of the shell by pre-applying voltage, and the middle layer adds graphene reinforcing material to improve the strength of the shell.

[0036] (2) The present invention provides a method for studying the thermoelastic buckling of a porous laminated truncated conical shell. This method can accurately analyze and calculate the buckling critical temperature of the shell under thermal conditions. The calculated modes of the shell buckling critical temperature are approximately (5,7). The calculation results can provide theoretical basis and technical reference for the design of truncated conical shell structures. [Attached Image Description]

[0037] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the detailed embodiments of the invention to explain the invention, but do not constitute a limitation thereof. In the drawings:

[0038] Figure 1 This is a schematic diagram of the structure of the porous layered truncated conical shell provided by the present invention;

[0039] Figure 2 This is a cross-sectional view of the pore distribution in the shell core layer provided by the present invention;

[0040] Figure 3 This is a graphene distribution diagram of the shell core layer provided by the present invention;

[0041] Figure 4 and Figure 5 The buckling temperature ΔT of the shell are respectively 1cr Graph showing the relationship between axial wavenumber m and circumferential wavenumber n;

[0042] Figure 6 and Figure 7 The buckling temperature ΔT of the shell are respectively 1cr A graph showing the relationship between the length-to-diameter ratio L / R1 and the length-to-thickness ratio L / h of the shell.

[0043] In the diagram: 1. Insulation material layer such as ceramic; 2. Graphene-enhanced functional gradient material core layer; 3. Piezoelectric layer.

Detailed Implementation Methods

[0044] To better demonstrate the advantages and objectives of the present invention, the invention will be further described in detail below with reference to specific embodiments and the accompanying drawings. It should be emphasized that the following description is merely exemplary and not intended to limit the scope or application of the invention.

[0045] Example 1: As Figure 1-3As shown, the present invention discloses a porous laminated truncated conical shell, comprising:

[0046] The ceramic and other thermal insulation material layers and the piezoelectric layer are the inner and outer surfaces of the shell, respectively, while the graphene-reinforced functional gradient material core layer is located in the middle of the laminated truncated cone shell.

[0047] The method for studying the thermoelastic buckling of a truncated conical shell according to the present invention mainly includes the following steps:

[0048] Step 1: Establish the pore volume fraction model, graphene distribution model, and physical property parameter model of the porous shell;

[0049] Step 2: Solve for the thermal conduction temperature field of the shell using the one-dimensional heat conduction equation;

[0050] Step 3: Based on Hamilton's principle, establish the governing equations for the truncated conical shell under thermal conditions;

[0051] Step 4: Use the Galerkin integral method to obtain the analytical solution for the critical buckling temperature of the shell.

[0052] This specific embodiment is merely an explanation of the present invention and is not intended to limit the invention. Those skilled in the art can make modifications to this embodiment without contributing any inventive element after reading this specification, but such modifications are protected by patent law as long as they are within the scope of the claims of the present invention.

Claims

1. A method for studying the thermoelastic buckling of a porous laminated truncated conical shell, characterized in that: It includes a ceramic or other thermal insulation material layer (1), a graphene-enhanced functional gradient material core layer (2), and a piezoelectric layer (3).

2. The porous laminated truncated conical shell according to claim 1, characterized in that: The piezoelectric layer (3) and the ceramic or other heat-insulating material layer (1) are respectively distributed on the inner and outer surfaces of the shell, and the graphene-enhanced functional gradient material core layer (2) is located between them.

3. The method for studying the thermoelastic buckling of a porous laminated truncated conical shell according to claim 1, characterized in that, Includes the following steps: Step 1: Establish the pore volume fraction model, graphene distribution model, and physical property parameter model of the porous shell; The pore volume fraction model and graphene distribution model are in the following forms: V P (z)=e1cos(πz / 2h+π / 4) (1) V G (z)=v i [1-cos(πz / 2h+π / 4)] (2) Among them, V P (z) and V G (z) represents the volume fraction of pores and the volume fraction of graphene, respectively; e1 represents the porosity coefficient; h represents the thickness of the shell; v i This represents the maximum value of the graphene volume fraction. The physical property parameter model of the porous shell is in the following form: Among them, E M ρ M α M Let e ​​represent the Young's modulus, density, and coefficient of thermal expansion of a non-porous graphene-reinforced functional graded material. m This represents the mass density coefficient. Step 2: Solve for the thermal conduction temperature field of the shell according to the one-dimensional heat conduction equation; Among them, K h (z) represents the thermal conductivity of the graphene-enhanced functionally graded material, T(z) represents the temperature field, and T0 and T1 represent the inner and outer surface temperatures of the shell, respectively. Step 3: Based on Hamilton's principle, establish the governing equations for the truncated conical shell under thermal conditions; Among them, U s W represents the total strain energy of the shell. a This indicates the work done by the temperature load. Step 4: The analytical solution for the critical buckling temperature of the shell is obtained using the Galerkin integral method; Among them, L ij (i = 1-5, j = 1-6) are constant coefficients, U, V, W, X, and Y are all axially continuous smooth functions, and ΔT cr T represents the buckling temperature difference between the inner and outer layers of the shell. 1cr d represents the temperature of the outer surface of the shell. 1j (j=1-5) represents the process calculation parameters.

4. The method for studying the thermoelastic buckling of porous laminated truncated conical shells according to claim 1, characterized in that: v in equation (2) i Expressed by the following formula: in, The total volumetric composition of graphene in the truncated conical shell is calculated using the following formula: Among them, W GPL and ρ GPL ρ represents the total mass fraction and density of graphene, respectively. m This indicates the density of the matrix material.

5. The method for studying the thermoelastic buckling of porous laminated truncated conical shells according to claim 1, characterized in that: The relevant physical properties of the non-porous graphene-enhanced functional graded material in equation (3) are expressed by the following formula: P M =P GPL In G (w)+P m [1-V G (with)] (9) Where P represents the shell's Young's modulus, density, coefficient of thermal expansion, and other physical properties.

6. The method for studying the thermoelastic buckling of porous laminated truncated conical shells according to claim 1, characterized in that: The thermal conductivity K of the graphene-enhanced functional graded material in equation (4) h The temperature field T(z) and the temperature field T(z) are expressed by the following equation: Where U represents the aspect ratio of the graphene nanosheet, F(U) represents the dimensionless geometric parameter, δ represents the fitting parameter, and K GPL and K m Let {a} represent the thermal conductivity of graphene and the matrix material, respectively, and let {a} represent the undetermined coefficients {a1, a2, ..., a}. N }, the vector {Y} represents {y,y 2 ,…,y N } 7. The method for studying the thermoelastic buckling of porous laminated truncated conical shells according to claim 1, characterized in that: Three displacement functions (u, v, w) and two directional rotation angles. and Expressed by the following formula: Where m and n represent the axial wave number and circumferential wave number of the shell, respectively, and L represents the length of the shell generatrix.

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