Simulation method of quasi-zero stiffness composite material structure based on TPU material

Abstract

The application discloses a quasi-zero stiffness composite structure simulation method based on thermoplastic polyurethane (TPU) material and belongs to the field of composite structure design and simulation analog. In view of the problems that the traditional simulation method is difficult to accurately characterize the large deformation, super-elasticity and buckling negative stiffness characteristics of the TPU material, leads to inaccurate structure performance prediction and low design efficiency, a geometric model of a TPU core layer and a carbon fiber panel is established, a cell division grid suitable for large deformation is adopted, a super-elastic and orthogonal anisotropic material model is defined, constraints and loads are set and quasi-static compression simulation is carried out, a load-displacement curve is extracted and structure safety evaluation is completed. The method can accurately predict the static and dynamic characteristics of the quasi-zero stiffness composite structure, and provides reliable simulation support for the design and performance prediction of lightweight low-frequency vibration isolation structures in the fields of aerospace, precision instruments and the like.

Description

Technical Field

[0001] This invention relates to the field of composite material structure design and simulation, specifically to a simulation method for quasi-zero stiffness composite material structures based on thermoplastic polyurethane (TPU), applicable to the design and performance prediction of lightweight low-frequency vibration isolation structures in aerospace, precision instruments and other fields. Background Technology

[0002] With the rapid development of industries such as aerospace, high-speed trains, and precision instruments, higher demands are being placed on lightweight structures and the integration of load-bearing and vibration reduction. Quasi-zero stiffness vibration isolation technology, due to its characteristics of high static stiffness and low dynamic stiffness, can effectively solve the contradiction between the load-bearing capacity and low-frequency vibration isolation performance of traditional linear vibration isolation systems, and has become a research hotspot.

[0003] Currently, quasi-zero stiffness structure designs based on the principle of negative stiffness in buckling beams widely employ mechanical springs or metal buckling beams, which suffer from problems such as structural complexity, assembly difficulty, and heavy weight. In recent years, the development of additive manufacturing technology has made it possible to create integrated quasi-zero stiffness composite material structures based on flexible materials (such as TPU). TPU materials possess high elasticity and high toughness, enabling buckling behavior under large deformations; however, their nonlinear, hyperelastic, and large deformation characteristics pose challenges to traditional simulation methods based on metal materials. Existing simulation methods struggle to accurately simulate the buckling behavior, negative stiffness characteristics, and synergistic effect of TPU materials with carbon fiber panels in quasi-zero stiffness structures, leading to low structural design efficiency and inaccurate performance predictions. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, this invention provides a simulation method for quasi-zero stiffness composite material structures based on TPU material, aiming to accurately predict the static and dynamic properties of TPU benchmark zero stiffness sandwich structures and guide structural design.

[0005] To achieve the above objectives, the simulation method mentioned in this invention includes the following steps:

[0006] Step 1: Establish a three-dimensional geometric model of a quasi-zero stiffness composite material structure, which includes a core layer printed from thermoplastic polyurethane elastomer (TPU) material and a carbon fiber composite panel.

[0007] Step 2: Mesh the established geometric model. For the TPU core layer, use hybrid elements or hyperelastic elements to simulate its large deformation characteristics, and use continuous shell elements or hexahedral elements for the carbon fiber panel.

[0008] Step 3: Define the material model: Define a hyperelastic constitutive model for the TPU material, an orthotropic linear elastic constitutive model for the carbon fiber panel, and a linear elastic constitutive model for the rigid support part in the structure; the strain energy function of the hyperelastic constitutive model adopts the Mooney-Rivlin form or the Ogden form.

[0009]

[0010] in, For strain energy density, , For the first and second partial strain invariants, It is a volume ratio. , For material parameters, The compressibility parameter is used; the material parameters are obtained by fitting through uniaxial tensile tests, plane shear tests, and equal biaxial tensile tests; the orthotropic material parameters of the carbon fiber panel are obtained through composite material mechanical property tests.

[0011] Step 4: Set contact and boundary conditions, including defining the binding constraints between the carbon fiber panel and the TPU core, as well as the loads and boundary conditions for simulating quasi-static compression tests.

[0012] Step 5: Establish an explicit dynamic analysis step or use the improved Riks method to perform quasi-static compression simulation, solve and extract the load-displacement curves of the structure, and verify the characteristics of the quasi-zero stiffness plateau segment of the structure; wherein, the quasi-zero stiffness plateau segment satisfies the stiffness requirement. The condition, stiffness is defined as ;

[0013] Step 6: Extract the stress-strain cloud map of the structure during the compression process based on the simulation results, and evaluate the structural safety.

[0014] Optionally, in step 1, the core layer of the quasi-zero stiffness composite material structure includes at least one unit cell, each unit cell including: a pair of orthogonally arranged Euler buckling beams, a semi-circular arc positive stiffness structure located below the buckling beams, and a fixed support for constraining the ends of the buckling beams; the buckling beams and the semi-circular arc structure are integrally printed from TPU material, and the fixed support is printed from polylactic acid (PLA) material.

[0015] Optionally, in step 2, the specific method of mesh generation is as follows: use C3D8RH or C3D10H hybrid units for the TPU core layer in Hypermesh or Abaqus / CAE, and use SC8R continuous shell units or C3D8R hexahedral units for the carbon fiber panel.

[0016] Optionally, in step 3, the hyperelastic constitutive model of the TPU material adopts the Mooney-Rivlin model, and its strain energy function is:

[0017]

[0018] in, For strain energy density, , For the first and second partial strain invariants, It is a volume ratio. , For material parameters, The compressibility parameter is used; the material parameters are obtained by fitting through uniaxial tensile tests, plane shear tests, and equal biaxial tensile tests; the orthotropic material parameters of the carbon fiber panel are obtained through composite material mechanical property tests.

[0019] Optionally, in step 4, the binding constraint is a Tie connection, used to simulate epoxy resin curing connection; the boundary conditions of the quasi-static compression test are set as follows: the lower end support clamp is completely fixed, the upper end indenter moves downward at a constant speed, and load and displacement data are collected by force sensor and displacement sensor.

[0020] Optionally, in step 5, the governing equations for the explicit dynamic analysis step are solved using the central difference method:

[0021]

[0022]

[0023]

[0024] in, For the quality matrix, For external force vectors, For internal force vectors, For displacement, For speed, For acceleration, The time step is set to a value; to ensure quasi-static conditions, the mass scaling factor is set to no more than 10, and the time step satisfies the Courant-Friedrichs-Lewy stability condition.

[0025]

[0026] in, For the smallest unit size, The material wave velocity; or the Riks method in Abaqus / Standard can be used to track the negative stiffness response of the structure after buckling.

[0027] Optionally, in step 5, the criterion for determining the quasi-zero stiffness characteristic is: near the static equilibrium position, the structural stiffness... satisfy ,in This represents the maximum stiffness of the linear segment; at this point, the structure's natural frequency... Approaching zero:

[0028]

[0029] For effective quality.

[0030] Optionally, in step 6, the assessment criterion for structural safety is: extract the maximum Mises stress of the TPU core layer and PLA support, and determine whether it is less than the yield strength of the corresponding material; the formula for calculating the Mises equivalent stress is:

[0031]

[0032] in , , Principal stress, The Mises equivalent stress was used. Simultaneously, repeated loading-unloading simulations were conducted to verify whether the structure could still recover its original shape after multiple bucklings, thus assessing its reliability.

[0033] Optionally, the method further includes step 7: performing batch simulations of quasi-zero stiffness structures under different unit cell array arrangements, analyzing the influence of the number of horizontal arrays on the effective load value, and the influence of the number of vertical array layers on the length of the quasi-zero stiffness platform segment, so as to realize programmable design of structural performance.

[0034] Compared with the prior art, the beneficial effects of the present invention are:

[0035] This invention provides a simulation method for quasi-zero stiffness composite material structures based on TPU material. Targeting the large deformation and hyperelastic properties of TPU flexible material, it employs a hyperelastic constitutive model and hybrid element technology to accurately simulate the negative stiffness behavior of buckling beams and their coupling with positive stiffness structures. This method can effectively predict the load-displacement curve, effective load range, and structural safety of quasi-zero stiffness plateau segments, providing a reliable and efficient simulation tool for the design and optimization of lightweight, load-bearing-vibration-isolation integrated composite material structures. It overcomes the shortcomings of traditional linear simulation methods that cannot accurately capture the buckling behavior of TPU materials, and has the advantages of high computational accuracy and strong applicability. Attached Figure Description

[0036] Figure 1 This is a flowchart of a simulation method for quasi-zero stiffness composite material structures based on TPU material according to an embodiment of the present invention;

[0037] Figure 2 This is a schematic diagram of the geometric model of the quasi-zero stiffness unit cell structure in an embodiment of the present invention;

[0038] Figure 3 This is a schematic diagram of finite element mesh generation in an embodiment of the present invention;

[0039] Figure 4 This is a comparison chart of the load-displacement curves obtained from simulation and the experimental results in an embodiment of the present invention;

[0040] Figure 5 This is a simulation diagram of compressive stress obtained in an embodiment of the present invention. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to examples and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0042] Figure 1 This is a flowchart of the simulation method for quasi-zero stiffness composite material structures based on TPU material according to an embodiment of the present invention. See also Figure 1 The specific steps of this simulation method are as follows:

[0043] Step 1: Establish a geometric model.

[0044] In this embodiment, the quasi-zero stiffness composite material structure is Arrayed single-layer sandwich panels. The core layer unit cell structure is as follows: Figure 2 As shown, it includes: a pair of orthogonally arranged Euler buckling beams, a semi-circular arc normal stiffness structure located below the buckling beams, and fixed supports located around the perimeter and bottom. The buckling beams and semi-circular arc structure are printed from TPU material, while the fixed supports are printed from PLA material. The dimensions of the upper and lower carbon fiber panels are... The layup sequence is Each panel has 8 layers.

[0045] Step 2: Grid generation.

[0046] Mesh the model in Hypermesh. For example... Figure 3 As shown, the TPU core layer uses C3D10MH hybrid tetrahedral units, with a unit size of [missing information]. The PLA support was modeled using C3D8R hexahedral elements; the carbon fiber panel was modeled using SC8R continuous shell elements, with one layer of elements in the thickness direction. The total number of meshes was approximately 150,000.

[0047] Step 3: Define the material model.

[0048] The TPU material is modeled using the Mooney-Rivlin two-parameter hyperelasticity model, and the strain energy function is:

[0049]

[0050] in, , , First partial strain invariant Second partial strain invariant Calculated from the deformation tensor:

[0051]

[0052] , , Main elongation ratio. Material density. .

[0053] PLA material adopts a linear elastic model, elastic modulus Poisson's ratio ,density Its stress-strain relationship satisfies the generalized Hooke's law:

[0054]

[0055] in, It is a fourth-order elastic tensor.

[0056] The carbon fiber panel adopts an orthotropic linear elastic model, and its constitutive equation is:

[0057]

[0058] Longitudinal tensile modulus Transverse tensile modulus In-plane shear modulus Poisson's ratio , .

[0059] Step 4: Set contact and boundary conditions.

[0060] In Abaqus / Explicit, the contact relationship between the upper and lower carbon fiber panels and the top platform and bottom support of the TPU core layer is set to Tie bonding to simulate epoxy resin curing. The boundary conditions are set as follows: the lower support clamp is fully fixed. ), upper pressure head The speed moves downwards. The applied load is displacement controlled, and the total compressive displacement is... .

[0061] Step 5: Quasi-static compression simulation and result extraction.

[0062] The Abaqus / Explicit explicit dynamics solver was used. The explicit dynamics solution employed the central difference method, with the time integration scheme as follows:

[0063]

[0064]

[0065]

[0066] To ensure quasi-static conditions, the quality scaling factor is set to 5. The critical time step is determined by the Courant condition:

[0067]

[0068] in, For TPU material, the longitudinal wave velocity is... , This is the secant modulus.

[0069] Set the analysis step time to After solving, extract the head reaction force and displacement data, and plot the load-displacement curve. Overall structural stiffness. Defined as load For displacement The derivative:

[0070]

[0071] The criterion for determining a quasi-zero stiffness platform segment is: within the displacement range Inside, In this embodiment, as Figure 4 As shown, in displacement Within the range, the average stiffness is approximately The maximum stiffness of the linear segment This satisfies the quasi-zero stiffness condition. At this point, the effective load is approximately... (correspond (Preload), the natural frequency of the structure is:

[0072]

[0073] It achieves low-frequency vibration isolation at frequencies far below the natural frequency of traditional vibration isolators.

[0074] Step 6: Structural safety assessment.

[0075] Extract the stress cloud diagram of the structure during compression, such as Figure 5 As shown. The formula for calculating Mises equivalent stress is:

[0076]

[0077] in , , There are three principal stresses. The maximum Mises stress of the TPU core layer is calculated to be... Less than TPU strength The maximum Mises stress of the PLA support is Less than PLA strength The maximum stress of the carbon fiber panel is The stress was far below its strength limit. Furthermore, through repeated loading-unloading simulations (a total of 3 cycles), the structure was able to recover to its initial configuration after each unloading, without any plastic deformation or damage accumulation, thus verifying the safety of the structure.

[0078] Step 7: Batch simulation of different layout methods.

[0079] Establish single cells separately Single-layer array Array double layer, Array of four layers and Simulations were performed using four models for a single-layer array. Load-displacement curve analysis showed that the number of horizontal array elements was... At that time, the effective payload Satisfies a linear relationship:

[0080]

[0081] in The effective payload of a single cell (approximately) ), platform segment length The number of vertical array layers remains unchanged. At that time, the effective load remains unchanged, and the platform segment length satisfies:

[0082]

[0083] in The length of a single-layer platform segment (approximately) This method can be used to guide the programmable design of structures.

[0084] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A simulation method for quasi-zero stiffness composite material structures based on TPU material, characterized in that, Includes the following steps: Step 1: Establish a three-dimensional geometric model of a quasi-zero stiffness composite material structure, which includes a core layer printed from thermoplastic polyurethane elastomer (TPU) material and a carbon fiber composite panel. Step 2: Mesh the established geometric model. Use hybrid or hyperelastic elements for the TPU core layer and continuous shell or hexahedral elements for the carbon fiber panel. Step 3: Define the material models: Define a hyperelastic constitutive model for the TPU material, an orthotropic linear elastic constitutive model for the carbon fiber panel, and a linear elastic constitutive model for the rigid support portion of the structure; the strain energy function of the hyperelastic constitutive model adopts the Mooney-Rivlin form. ， in, For strain energy density, , For the first and second partial strain invariants, It is a volume ratio. , For material parameters, The compressibility parameter is used; the material parameters are obtained by fitting through uniaxial tensile tests, plane shear tests, and equal biaxial tensile tests; the orthotropic material parameters of the carbon fiber panel are obtained through composite material mechanical property tests. Step 4: Set contact and boundary conditions, including defining the binding constraints between the carbon fiber panel and the TPU core, as well as the loads and boundary conditions for simulating quasi-static compression tests. Step 5: Establish an explicit dynamic analysis step or use the improved Riks method to perform quasi-static compression simulation, solve and extract the load-displacement curves of the structure, and verify the characteristics of the quasi-zero stiffness plateau segment of the structure; wherein, the quasi-zero stiffness plateau segment satisfies the stiffness requirement. conditions; Step 6: Extract the stress-strain cloud map of the structure during the compression process based on the simulation results, and evaluate the structural safety.

2. The simulation method for quasi-zero stiffness composite material structures based on TPU material according to claim 1, characterized in that, In step 1, the core layer of the quasi-zero stiffness composite material structure includes at least one unit cell, each unit cell including: a pair of orthogonally arranged Euler buckling beams, a semi-circular arc positive stiffness structure located below the buckling beams, and a fixed support for constraining the ends of the buckling beams; the buckling beams and the semi-circular arc structure are integrally printed from TPU material, and the fixed support is printed from polylactic acid (PLA) material.

3. The simulation method for quasi-zero stiffness composite material structures based on TPU material according to claim 1, characterized in that, In step 2, the specific method of mesh generation is as follows: in Hypermesh or Abaqus / CAE, C3D8RH or C3D10H hybrid units are used for the TPU core layer, and SC8R continuous shell units or C3D8R hexahedral units are used for the carbon fiber panel.

4. The simulation method for quasi-zero stiffness composite material structures based on TPU material according to claim 1, characterized in that, In step 3, the hyperelastic constitutive model of the TPU material adopts the Mooney-Rivlin model or the Ogden model, and its material parameters are obtained by fitting through uniaxial tensile tests, plane shear tests and equal biaxial tensile tests; the orthotropic material parameters of the carbon fiber panel are obtained through composite material mechanical property tests.

5. The simulation method for quasi-zero stiffness composite material structures based on TPU material according to claim 1, characterized in that, In step 4, the binding constraint is a Tie connection, used to simulate epoxy resin curing connection; the boundary conditions of the quasi-static compression test are set as follows: the lower end support clamp is completely fixed, the upper end indenter moves downward at a constant speed, and load and displacement data are collected by force sensor and displacement sensor.

6. The simulation method for quasi-zero stiffness composite material structures based on TPU material according to claim 1, characterized in that, In step 5, the governing equations for the explicit dynamic analysis step are obtained using the central difference method: ， The quality scaling factor is set to no more than 10, and the time step satisfies the Courant condition. Alternatively, the Riks method in Abaqus / Standard can be used to track the negative stiffness response of the structure after buckling. in, For the quality matrix, For external force vectors, For internal force vectors, For displacement, For speed, For acceleration, The time step is set to 10; to ensure quasi-static conditions, the mass scaling factor is set to no more than 10, and the time step satisfies the Courant-Friedrichs-Lewy stability condition. For the smallest unit size, The material wave velocity; or the Riks method in Abaqus / Standard can be used to track the negative stiffness response of the structure after buckling.

7. The simulation method for quasi-zero stiffness composite material structures based on TPU material according to claim 1, characterized in that, In step 5, the criterion for determining the quasi-zero stiffness platform segment is: near the static equilibrium position, the structural stiffness... satisfy At this time, the natural frequency of the structure Approaching zero.

8. The simulation method for quasi-zero stiffness composite material structures based on TPU material according to claim 1, characterized in that, In step 6, the assessment criterion for structural safety is: extract the maximum Mises stress of the TPU core layer and PLA support, and determine whether it is less than the yield strength of the corresponding material. The formula for calculating Mises equivalent stress is: ， in , , Principal stress, The Mises equivalent stress was used; at the same time, repeated loading-unloading simulation was used to verify whether the structure could still recover its original state after multiple bucklings.

9. The simulation method for quasi-zero stiffness composite material structures based on TPU material according to claim 1, characterized in that, The method further includes step 7: performing batch simulations of quasi-zero stiffness structures under different unit cell array arrangements, analyzing the influence of the number of horizontal arrays on the effective load value, and the influence of the number of vertical array layers on the length of the quasi-zero stiffness platform segment.

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