Key component thermal-acoustic coupling sub-domain free element simulation method and related equipment

Abstract

The embodiment of the application discloses a kind of key components thermosonic coupling sub-domain free element simulation method and related equipment, method includes: establishing calculation domain, including acoustic domain and structure domain, the intersection of acoustic domain and structure domain constitutes calculation domain, and the intersection of acoustic domain and structure domain is empty;Coupling interface of acoustic domain and structure domain meets the continuous condition of force and displacement;Acoustic domain and structure domain are divided into several subdomains respectively, finite element unit is constructed in each subdomain, and generating matching point unit, the field variable interpolation relationship of any point in matching point unit is described with isoparametric element shape function;According to the position of node in calculation domain, different discrete control equations are established for different class nodes respectively;The discrete control equations of each node are combined to obtain system equation group, system equation group is solved, displacement and sound pressure are calculated, and the multi-physical field coupling analysis of calculation domain is completed.The application can accurately calculate the thermal-mechanical-acoustic coupling response of key components under complex load environment.

Description

Technical Field

[0001] This invention relates to the field of computer simulation technology, and in particular to a simulation method and related equipment for a thermo-mechanical-acoustic-vibration coupled domain free element of a key component. Background Technology

[0002] Hypersonic vehicles (> Mach 5) face extreme acoustic loads (sound pressure levels exceeding 175 dB, frequency range 10-10000 Hz) during launch, transonic flight, and hypersonic cruise, as well as extreme thermal loads (local temperatures reaching 1650°C) caused by aerodynamic heating. These loads are comprised of intake noise from the air intake, engine exhaust noise, and surface aerodynamic noise. Under the coupled effects of this high sound pressure, wideband noise, and high-temperature environment, thin-walled structures of the vehicle are prone to acoustic fatigue. Therefore, conducting multi-field coupled thermo-mechanical-acoustic-vibration analysis to accurately predict the dynamic response of critical structures under real-world conditions has become a key challenge and urgent requirement in vehicle structural design.

[0003] Currently, numerical methods for studying structural dynamic response, especially acoustic-vibration coupling problems, are mostly concentrated on the finite element method (FEM), boundary element method (BEM), and their hybrid forms. Although these methods are widely used, they still face limitations in terms of computational efficiency, model adaptability, and solution stability when dealing with the aforementioned strongly coupled, multiphysics problems. Summary of the Invention

[0004] Based on this, it is necessary to address the above problems by proposing a domain-specific free element simulation method and related equipment for the thermo-mechanical-acoustic-vibration coupling of key components. This method achieves high-precision simulation of the strong thermo-mechanical-acoustic-vibration coupling effect and overcomes the shortcomings of traditional methods in terms of computational efficiency and stability.

[0005] A simulation method for thermo-mechanical-acoustic-vibration coupled domain free element of a key component, the method comprising: Step S1: Establish a computational domain, which includes an acoustic domain and a structural domain. The set of the acoustic domain and the structural domain constitutes the computational domain, and the intersection of the acoustic domain and the structural domain is empty. The coupling interface of the acoustic domain and the structural domain satisfies the continuity conditions of force and displacement. The acoustic domain describes the variation of sound pressure with time and space through a wave equation. The structural domain adopts a thermoelastic control equation that introduces an equivalent thermal traction term corresponding to the steady-state temperature field to reflect the influence of temperature on structural stiffness and deformation. Boundary conditions are applied to the acoustic domain and the structural domain respectively. Step S2: Divide the acoustic domain into several regular or irregular acoustic subdomains, divide the structural domain into several regular or irregular structural subdomains, construct acoustic finite element elements in each acoustic subdomain, construct structural finite element elements in each structural subdomain, further discretize the acoustic finite element elements and the structural finite element elements into scattered points, generate collocation elements for each scattered point based on the scattered points around it, and use isoparametric element shape functions to describe the field variable interpolation relationship of any point in the collocation element; Step S3: Based on the position of the node within the computational domain, divide the node into acoustic domain nodes, structural domain nodes, acoustic-structural coupling interface nodes, and acoustic-structural coupling interface external boundary nodes; further divide the acoustic domain nodes into acoustic interior nodes, acoustic subdomain interface nodes, and acoustic external boundary nodes; and divide the structural domain nodes into structural interior nodes, structural subdomain interface nodes, and structural external boundary nodes; establish discrete control equations for the acoustic-structural coupling interface nodes, acoustic-structural coupling interface external boundary nodes, acoustic interior nodes, acoustic subdomain interface nodes, acoustic external boundary nodes, structural interior nodes, structural subdomain interface nodes, and structural external boundary nodes, respectively. Step S4: Combine the discrete control equations of each node to obtain a system equation set, solve the system equation set, calculate the displacement and sound pressure, and complete the multiphysics coupling analysis of the computational domain.

[0006] A simulation system for a key component with thermo-mechanical-acoustic-vibration coupling in a domain of free elements, the system comprising: A computational domain establishment module is provided, comprising an acoustic domain and a structural domain. The set of the acoustic domain and the structural domain constitutes the computational domain, and the intersection of the acoustic domain and the structural domain is empty. The coupling interface between the acoustic domain and the structural domain satisfies the continuity conditions of force and displacement. The acoustic domain describes the variation of sound pressure with time and space using a wave equation, and the structural domain adopts a thermoelastic control equation that introduces an equivalent thermal traction term corresponding to the steady-state temperature field, applying boundary conditions to the acoustic domain and the structural domain respectively. The domain division module is used to divide the acoustic domain into several acoustic subdomains and the structural domain into several structural subdomains. An acoustic finite element unit is constructed within each acoustic subdomain, and a structural finite element unit is constructed within each structural subdomain. The acoustic and structural finite element units are further discretized into scattered points. Each scattered point generates a collocation element based on its surrounding scattered points. An isoparametric element shape function is used to describe the field variable interpolation relationship at any point within the collocation element. A discrete model building module is used to classify the nodes into acoustic domain nodes, structural domain nodes, acoustic-structural coupling interface nodes, and acoustic-structural coupling interface external boundary nodes according to their positions in the computational domain; to classify the acoustic domain nodes into acoustic interior nodes, acoustic subdomain interface nodes, and acoustic external boundary nodes; and to classify the structural domain nodes into structural interior nodes, structural subdomain interface nodes, and structural external boundary nodes; and to establish discrete control equations for the acoustic-structural coupling interface nodes, acoustic-structural coupling interface external boundary nodes, acoustic interior nodes, acoustic subdomain interface nodes, acoustic external boundary nodes, structural interior nodes, structural subdomain interface nodes, and structural external boundary nodes, respectively. The system equations establishment, solution and analysis module is used to establish and solve the discrete control equations of each node to obtain the system equations, solve the system equations, calculate displacement and sound pressure, and complete the multiphysics coupling analysis of the computational domain.

[0007] A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the thermal-acoustic-vibration coupling domain free element simulation method for key components as described above.

[0008] A computer device includes a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the thermal-acoustic-vibration coupled domain free element simulation method for key components as described above.

[0009] Implementing the embodiments of the present invention will have the following beneficial effects: 1) This invention simulates the dynamic response of a sound field to a structure by establishing a computational domain that includes an acoustic domain and a structural domain (the set of the acoustic domain and the structural domain constitutes the computational domain, and the intersection of the acoustic domain and the structural domain is empty, and the coupling interface of the acoustic domain and the structural domain satisfies the continuity condition of force and displacement).

[0010] 2) The thermoelastic control equation of the structural domain introduces the equivalent thermal traction term corresponding to the steady-state temperature field, so that the simulation can take into account the effect of temperature.

[0011] 3) Discretization is based on the domain-specific free element method. First, subdomains are divided, and then collocational elements are generated within the subdomains. The field variable interpolation relationship at any point within the collocational elements is described by isoparametric element shape functions. By classifying the nodes, different discrete control equations are used for nodes of different categories. The discrete control equations of all nodes are combined to establish a system equation set. Solving the system equation set enables the numerical solution of the coupled system in the time domain. This solution method can accurately capture the multi-field coupled response characteristics such as thermal deformation, structural vibration, and acoustic radiation without relying on traditional element division. It provides an accurate numerical basis for the comprehensive performance evaluation of structures in complex thermal-mechanical-acoustic-vibration service environments.

[0012] 4) This invention can accurately calculate the thermo-mechanical-acoustic-vibration coupling response of key components under complex load conditions. Attached Figure Description

[0013] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] in: Figure 1 This is a flowchart illustrating the steps of a simulation method for a key component's thermo-acoustic-vibration coupled domain free element in one embodiment of the present invention. Figure 2 This is a flowchart of a simulation method for a key component's thermo-acoustic-vibration coupled domain free element in one embodiment of the present invention; Figure 3 This is a schematic diagram of the overall computational domain in one embodiment of the present invention; Figure 4 This is a schematic diagram of the computational domain division in one embodiment of the present invention; Figure 5 for Figure 4 Enlarged view of the bolded subdomains 2A and 3A; Figure 6 This is a structural block diagram of a simulation system for a key component, a thermo-acoustic-vibration coupled domain free element, in one embodiment of the present invention. Figure 7 This is a structural block diagram of a computer device according to one embodiment of the present invention. Detailed Implementation

[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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 skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] refer to Figure 1 and Figure 2 This invention provides a simulation method for thermo-acoustic-vibration coupled domain free element, comprising the following steps: Step S1: Reference Figure 3 A computational domain is established, comprising an acoustic domain and a structural domain. The set of the acoustic and structural domains constitutes the computational domain, and the intersection of the acoustic and structural domains is empty. The coupling interface between the acoustic and structural domains satisfies the continuity conditions of force and displacement. The acoustic domain describes the variation of sound pressure with time and space using a wave equation, while the structural domain adopts a thermoelastic control equation that introduces an equivalent thermal traction term corresponding to the steady-state temperature field to reflect the influence of temperature on structural stiffness and deformation. Boundary conditions are applied to the acoustic and structural domains respectively.

[0017] In this step, the acoustic domain is used to describe the propagation characteristics of sound waves in the sound transmission medium, while the structural domain is used to characterize the structural dynamic response under thermal loads. The two domains achieve strong coupling at the coupling interface through displacement continuity and surface force equilibrium conditions, thereby accurately reflecting the mutual influence between the sound field and structural vibration under thermal conditions, and thus completing the thermo-mechanical-acoustic-vibration coupled response analysis of the structure under complex loads.

[0018] In the coupled system, the acoustic domain primarily describes the variation of sound pressure with time and space through the wave equation; the structural domain introduces an equivalent thermal traction term corresponding to the steady-state temperature field into the thermoelastic control equation to reflect the influence of temperature on structural stiffness and deformation. This coupled modeling and interface-based collaborative solution strategy allows for the simultaneous solving of the dynamic response relationships among the four fields of heat, force, vibration, and sound within a unified computational framework, providing theoretical support for the transient response calculation of complex thermo-mechanical-acoustic-vibration coupled systems.

[0019] In a specific embodiment of the present invention, the wave equation is:

[0020] in, For sound pressure, For the speed of sound, For internal source terms, For the density of the medium, For Hamiltonian operators, It is a spatial coordinate vector. It is a time variable. For the acoustic domain.

[0021] The boundary conditions for the wave equation in the acoustic domain include three types: (a) Sound pressure boundary conditions, where the sound pressure on such boundaries is a given value:

[0022] For the boundary, in particular, when given the sound pressure boundary When the amplitude is 0, this type of boundary is also called an acoustic soft boundary, such as the free boundary of an open space or the boundary of a flexible membrane. When sound waves reach this boundary, they will be reflected with the same amplitude but opposite phase. When the value is non-zero, it can simulate a scenario where "the boundary itself is a sound source" (such as when the sound pressure on the surface of the loudspeaker diaphragm is known), and directly radiate sound waves into the domain.

[0023] (b) Structural acceleration boundary conditions, where the normal acceleration of the medium on such boundaries is a given value:

[0024] in, The direction of the outward normal to the boundary. Given a normal acceleration... When the amplitude is 0, this type of boundary is also called an acoustic hard boundary, such as a rigid wall or a metal surface. When sound waves reach this boundary, they will be reflected with the same amplitude and phase. When the value is non-zero, it can simulate the scenario of "structural vibration driving sound field" (such as the sound waves generated by the vibration of machine shell), and indirectly calculate the sound pressure gradient at the boundary through structural acceleration, and then radiate sound waves into the domain.

[0025] (c) Impedance boundary conditions, where the acoustic impedance on such boundaries is a given value:

[0026] When the acoustic impedance given on an impedance boundary is equal to the acoustic impedance of the acoustic medium in the acoustic domain, this type of boundary is also called an absorbing boundary. When the incident sound wave reaches this boundary, it will be completely absorbed and will not affect the computational domain. It is used to simulate an infinite sound field. When the right-hand side of equation (4) approaches 0, the impedance boundary approaches the acoustic hard boundary. Therefore, when the acoustic impedance on the boundary is much greater than the acoustic impedance of the sound transmission medium, the boundary can achieve an effect similar to the acoustic hard boundary.

[0027] The thermoelastic governing equation of the structural domain can be expressed as:

[0028] in, For stress tensor; For structural density; The damping coefficient; For physical strength; For the problem dimension; repeating indicators To express summation, For structural domain, For displacement.

[0029] Stress tensor The strain tensor can be used through the following constitutive relation. and temperature T This means that a thermal stress term is introduced to reflect the effect of temperature on structural stiffness and deformation in an equivalent thermal traction manner, thereby considering the thermal load effect caused by the temperature field in the governing equations:

[0030] If the material is isotropic and linear thermoelasticity is used, the strain tensor in equation (6) Thermally corrected elastic constitutive tensor subscript Indices for spatial coordinates, used to describe the linear relationship between stress and strain in elastic materials in different directions, thermal term coefficients. The following correspondence exists:

[0031]

[0032]

[0033]

[0034] in, Shear modulus; Poisson's ratio; The coefficient of linear expansion; It has symmetry, that is .

[0035] Substituting equation (7) into equation (6), and then substituting the result into equation (5), we obtain the second-order partial differential equation of the thermoelastic control equation of the structural domain, which can be expressed as:

[0036] in, For the elastic constitutive tensor, the subscript is... Indices for spatial coordinates are used to describe the linear relationship between stress and strain in elastic materials in different directions. For temperature, For displacement, It is a spatial coordinate vector. It is a time variable. The coefficient of thermal term, For structural density; The damping coefficient; For physical strength; For the problem dimension; repeating indicators To express summation, This is a structural domain.

[0037] Boundary conditions for a structural domain include two types: (a) Displacement boundary conditions, where the displacement on such boundaries is a given value:

[0038] (b) Surface force boundary conditions, where the surface forces on such boundaries are given values:

[0039] Substituting equations (6) and (7) into equation (11), we get:

[0040] The acoustic domain and structural domain can establish an acoustic-structural coupling relationship through displacement continuity conditions and surface force equilibrium conditions.

[0041] (a) Displacement continuity condition: The vibration displacement of the acoustic medium and the structure at the interface is the same. Since it is more convenient to establish equations based on acceleration in the acoustic field, and the displacement continuity condition is equivalent to the acceleration continuity condition, considering equation (3), the coupling equation can be written as:

[0042] (b) Surface force equilibrium condition: the surface force on the structural domain at the coupling interface is equal to the sound pressure in the acoustic domain. Considering equation (11), the coupling equation can be written as:

[0043] Equations (13) and (14) are the coupling conditions at the thermo-mechanical-acoustic-vibration coupling interface. These conditions can reflect the interaction between sound waves and structures, thus forming a strongly coupled acoustic-vibration system.

[0044] The initial conditions throughout the computational domain, including sound pressure and its first time derivative in the acoustic domain, and displacement and velocity in the structural domain, can be expressed as:

[0045] in, , .

[0046] Step S2: Divide the acoustic domain into several regular or irregular acoustic subdomains, and divide the structural domain into several regular or irregular structural subdomains. Construct acoustic finite element elements in each acoustic subdomain and structural finite element elements in each structural subdomain. Further discretize the acoustic and structural finite element elements into scattered points. Generate collocation elements for each scattered point based on the surrounding scattered points. Use isoparametric element shape functions to describe the field variable interpolation relationship at any point within the collocation element.

[0047] In this step, the present invention employs the domain-specific free element method, which divides the acoustic domain and the structural subdomain into several subdomains, making it applicable to complex geometric models.

[0048] In the process of domain partitioning, selecting higher-order elements from the finite element method can effectively avoid the calculation failure caused by the distortion of collocation elements in the traditional free element method, while maintaining high efficiency and numerical stability, making it applicable to complex geometric models and having high computational accuracy.

[0049] Specifically, in one particular embodiment, reference is made to... Figure 4 It includes the acoustic domain and the structural domain 5. Based on the geometric characteristics and material distribution of the structure, the complex overall acoustics is divided into several regular or irregular acoustic subdomains 1 / 2A / 3A / 4 / 6. Figure 4 Enlarged views of the bolded subdomains 2A and 3A are shown below. Figure 5 As shown, acoustic subdomain interface 7 is the interface between acoustic subdomains 2B and 3B. Each acoustic subdomain is divided into quadrilateral finite element elements 8. The element nodes are scattered point sets formed within the subdomain. Each node generates collocation elements 9 based on the surrounding nodes. Its enlarged view is shown below. Figure 5 As shown, the collocation unit includes 9 collocation points.

[0050] To facilitate more stable subsequent calculations, especially for subdomains with complex shapes, it is preferable to use mapping techniques to transfer the collocation points from the global coordinate system. Transform to a coordinate system defined in the local coordinate system The rule calculation domain is as follows.

[0051] Mapping can be performed using the following shape functions:

[0052] in, This represents the number of mapping nodes used in the point allocation unit.

[0053] For two-dimensional problems, 8-node or 12-node elements are typically used. For three-dimensional problems, 20-node or 34-node elements are typically used. For two-dimensional 8-node elements:

[0054] For a 20-node 3D element:

[0055] In equations (17) and (18), For the first The shape function of each node, also called the interpolation function, is a function of the natural coordinates of any point within the element. Among them, the node numbers in equations (17) and (18) are consistent with the node numbers of the elements used in the ordinary finite element method.

[0056] In this step, to balance the ability to describe complex geometries with the simplicity of numerical implementation, the isoparametric element technique, commonly used in the finite element method, is employed to discretize the structural and acoustic domains when constructing collocational elements. Taking a two-dimensional problem as an example, the isoparametric element technique uses geometric mapping to transform the regular local coordinates... Mapping to physical coordinate system Isoparametric transformations between them.

[0057] To achieve interpolation of local variables, this invention employs Lagrange isoparametric elements. For a one-dimensional Lagrange element, its shape function can be expressed by the interpolation formula:

[0058] in, For local coordinates, The number of nodes in that direction. This represents the node's index in the local coordinate direction. Based on the one-dimensional shape function rules, a three-dimensional Lagrange isoparametric element is further constructed to describe the interpolation relationship of field variables at any point within the three-dimensional collocation element:

[0059] in, These represent the number of nodes along the three local coordinate directions, with subscripts indicating the number of nodes. Based on node sequence number The permutation and combination are determined. For the commonly used 27-node three-dimensional hexahedral element, the number of nodes in the three directions is usually taken as... .

[0060] Shape functions allow interpolation of element variables using nodal values ​​within the element. For the global computational domain, spatial coordinates... Displacement Harmony and sound pressure It can be represented as:

[0061] As shown in equation (21), the shape function is used to interpolate field variables within the element through nodal values. To further obtain the gradient and higher-order derivatives of the variables with respect to spatial coordinates, we can first calculate the partial derivatives of the shape function with respect to spatial coordinates. Let... For nodes The shape function in the configuration unit is a local coordinate. The explicit function. According to the chain rule, the shape function with respect to spatial coordinates can be obtained. The first and second partial derivatives, i.e. and Accordingly, arbitrary node variables The derivative with respect to spatial coordinates can be expressed as:

[0062]

[0063] in, In this invention, sound pressure is represented. Variables and displacements Quantity.

[0064] In the above equations, the first two derivatives of the shape functions can be obtained directly from the following equations:

[0065]

[0066] in, It is a Jacobian matrix.

[0067] After obtaining the spatial partial derivatives of the unit shape function with respect to the global coordinates, the control equations, boundary conditions and coupling conditions in the entire computational domain can be uniformly expressed as shape functions and their spatial partial derivatives according to equations (21), (22) and (23), and a system equation set can be established with the sound pressure and displacement of each node as the main unknowns.

[0068] Step S3: Based on the node's position within the computational domain, divide the nodes into acoustic domain nodes, structural domain nodes, acoustic-structural coupling interface nodes, and acoustic-structural coupling interface external boundary nodes. Divide the acoustic domain nodes into acoustic interior nodes, acoustic subdomain interface nodes, and acoustic external boundary nodes. Divide the structural domain nodes into structural interior nodes, structural subdomain interface nodes, and structural external boundary nodes. Establish discrete control equations for acoustic-structural coupling interface nodes, acoustic-structural coupling interface external boundary nodes, acoustic interior nodes, acoustic subdomain interface nodes, acoustic external boundary nodes, structural interior nodes, structural subdomain interface nodes, and structural external boundary nodes, respectively.

[0069] In this step, by classifying nodes according to their positions within the computational domain and using different unit control equations for different nodes, the physical differences between the acoustic domain and the structural domain can be accurately described.

[0070] For nodes in the acoustic domain, considering a homogeneous medium, and substituting equations (22) and (23) into equation (1), we can obtain the discrete equations for the nodes inside the acoustic domain:

[0071] For an acoustic subdomain interface node, which is shared by two or more subdomains, the acceleration balance condition is satisfied, i.e.:

[0072] in, This represents the number of faces in the subdomain (i.e., element) containing this node. Indicates the node at the 1st Normal acceleration on each subdomain surface, superscript This indicates that the node is located on the subdomain interface. For different subdomains, this represents the node's local coordinates. There are also differences; for example, a UI node shared by two subdomains can be represented as... Finally, the discrete equations for the acoustic subdomain interface nodes can be obtained:

[0073] in, Indicates the first The outward normal direction of each face.

[0074] For external boundary nodes in the acoustic domain, compared to subdomain interface nodes, the sum of vibration accelerations in all directions at the node equals the surface vibration acceleration. The discrete equation can be expressed as:

[0075] Among them, superscript This indicates that the node is located on the external boundary, and the acceleration term in equation (29) has different forms for different boundary conditions. For the sound pressure boundary, the sound pressure value at the node is known and does not need to be solved by the above equation; for the structural acceleration boundary... For impedance boundaries, there are .

[0076] For the internal nodes in the structural domain, substituting equations (22) and (23) into equation (9) yields the discrete equations for the internal nodes:

[0077] For the boundary nodes of the subdomains within the structural domain, the surface force equilibrium condition is satisfied, namely:

[0078] Substituting equations (12), (22), and (23) into equation (31), we obtain the discrete equations for the interface nodes of the structural subdomains:

[0079] For the external boundary nodes in the structural domain, the right side of equation (31) is the boundary surface force, compared to the subdomain interface node equation. Therefore, the discrete equation of the external boundary nodes of the structure can be expressed as:

[0080] For the coupling interface node between the acoustic and structural domains, applying the above coupling conditions, i.e., equations (13) and (14), the discrete equations of the acoustic-structural coupling interface node can be derived:

[0081]

[0082] Similarly, for the external boundary nodes of the coupling boundary between the acoustic and structural domains, applying the above coupling conditions, and adding normal acceleration and surface force to the right side of equations (34a) and (34b), the discrete equations for the external boundary nodes of the acoustic-structural coupling interface are derived:

[0083]

[0084] in, The expression is the same as in equation (29).

[0085] Step S4: Combine the discrete control equations of each node to obtain the system equation set, solve the system equation set, calculate the displacement and sound pressure, and complete the multiphysics coupling analysis of the computational domain.

[0086] The final system of equations can be expressed as:

[0087] in, Let be the coefficient matrix of the unknown sound pressure in each equation. This is the coefficient matrix of the unknown displacement in the acceleration continuity condition (discrete equation (34a)). Let be the coefficient matrix of the unknown sound pressure in the surface force equilibrium condition (discrete equation (34b)). This is the coefficient matrix of the unknown displacements in each equation. This represents the boundary condition vector in the acoustic domain. is the boundary condition vector in the structural domain.

[0088] When solving the time-domain thermo-acoustic-vibration coupling problem, At each moment, it is necessary to formulate the system equations and solve for the unknown physical quantities at each node at that moment. In a dimensional problem, if the discretized computational domain contains Nodes in an acoustic domain Nodes in a solid domain and If there are nodes on the coupling boundary, then the coefficient matrix has both rows and columns. Furthermore, the coefficient matrix is ​​a sparse matrix.

[0089] Preferably, in solving the system equations, the Newmark difference scheme is used to approximate the time derivatives of the unknowns, that is, it is assumed that the second time derivatives of the unknowns occur within a time interval. The internal linear variation is investigated, and the following difference schemes for the unknowns and their first time derivatives are proposed:

[0090]

[0091] in, For time step, and To determine the parameters based on accuracy and stability requirements, this invention employs the unconditionally stable Newmark difference scheme, i.e. , .

[0092] By parameters , Substituting into equations (37) and (38) above, we can obtain:

[0093]

[0094] in, This represents sound pressure or displacement. By substituting equations (39) and (40) into the above discrete equations containing time derivatives, the time derivatives of unknown sound pressure and displacement can be expressed using known sound pressure, displacement, and their practical derivatives.

[0095] In the acoustic domain, substituting equation (39) into equation (26) yields the governing equations for the internal nodes in the Newmark difference scheme, which can be expressed as:

[0096] Substituting equation (40) into the discrete equation (29) of the impedance boundary, we obtain the discrete equation of the outer boundary node of the impedance boundary under the Newmark difference scheme, which can be expressed as:

[0097] In the structural domain, substituting equations (39) and (40) into equation (30), we obtain the governing equations for the internal nodes under the Newmark difference scheme, which can be expressed as:

[0098] In the coupled interface, substituting equation (39) into equation (34a), we obtain the discrete equations of the interface nodes under the Newmark difference scheme, which can be expressed as:

[0099] Similarly, substituting equation (40) into equation (35a), we obtain the discrete equations for the external interface nodes of the impedance boundary under the Newmark differential scheme, which can be expressed as:

[0100]

[0101] Therefore, a time-progression scheme for solving the thermo-mechanical-acoustic-vibration coupling problem using the domain-free element method is constructed. Based on the initial condition (15), the second-order derivatives of sound pressure and displacement with respect to time are calculated by substituting them into the governing equations (1) and (9). Within each time step, the acoustic-structure coupled system equations are reassembled based on the known quantities from the previous time step, and the sound pressure at each node at the current time is obtained by solving these equations. and displacement And by using equations (37) and (38), the first and second time derivatives of the sound pressure and displacement at each node at that moment can be obtained, and the calculation of the next time step can be performed.

[0102] Observing all the final discrete equations, including equations (28), (29), (32), (33), (34b), (35b), and (41-45), it can be seen that the coefficients of the unknowns, sound pressure and displacement, in the system equations are independent of time. Starting from the second time step, it is only necessary to recalculate the right-hand vector of the system equations. coefficient matrix It can be solved directly in the first time step, and remains unchanged throughout the entire calculation process.

[0103] This invention achieves numerical solution of coupled systems in the time domain through spatial discretization and time difference schemes. This solution method can accurately capture the multi-field coupled response characteristics such as thermal deformation, structural vibration and sound field radiation without relying on traditional element division, providing an accurate numerical basis for the comprehensive performance evaluation of structures in complex thermal-mechanical-acoustic-vibration service environments.

[0104] The key component thermo-acoustic-vibration coupled domain free element simulation method of the present invention also includes: Step S5: Divide the structural domain into finite element units (for domain subdivision processing), then discretize the finite element units into scattered points. Each scattered point generates collocation elements based on its surrounding scattered points, and uses the density of the collocation elements as the design variable for topology optimization. With the goal of minimizing the overall mass of the structure, apply constraints, including the calculation results of step S4. Establish a mathematical model for topology optimization, perform topology optimization, and obtain the optimized structure. Calculate the optimized structure using the methods of steps S1 to S4 to analyze its dynamic stability. If the requirements are met, the topology-optimized structure is obtained. If the requirements are not met, change the constraints and perform topology optimization in step S5 again.

[0105] Based on the numerical solutions in steps S1 to S4, this step performs topology optimization design on the structure to further improve the overall performance of the structure under the coupled thermal-mechanical-acoustic-vibration environment.

[0106] Specifically, the structural domain Divided into There are 1 coordinate element, and the design variable vector is defined as follows: ,in Indicates the first The relative density of each element. Both the volume and physical properties of the structure can be expressed as design variables. The function is defined as follows: With the goal of minimizing the overall structural mass, displacement constraints, equilibrium conditions, and natural frequency constraints are applied to establish a corresponding topology optimization mathematical model. The mathematical expression of this model is:

[0107] in, Indicates the first The pseudo density of each element in the draft direction; Indicates the maximum allowable displacement of the structure; Represents the overall stiffness matrix of the structure; Represents the overall displacement vector of the structure; Represents the overall load vector of the structure. ,in Indicates static load. Indicates temperature load. Indicates sound pressure load; This represents the first-order natural frequency of the structure.

[0108] This mathematical model can achieve global optimization of structural layout under thermal-mechanical-acoustic-vibration load conditions, taking into account both structural lightweighting and multi-physical performance requirements.

[0109] In summary, the calculation method of the present invention has the following beneficial effects: 1. This invention can accurately calculate the thermo-mechanical-acoustic-vibration coupling response of key components under complex load environments.

[0110] 2. Furthermore, based on the thermal-mechanical-acoustic-vibration load environment, a topology optimization analysis is performed on the structure. This method is more comprehensive and stable.

[0111] 3. The domain-free element method combines the advantages of isoparametric elements in the finite element method with the advantage of forming independent isoparametric elements based on each configuration point in the meshless method. Due to the interpolation property of the element shape function, its boundary conditions can be directly applied based on the algebraic / differential relationship on the boundary, making it easy to realize multi-field coupled calculation.

[0112] 4. From thermo-mechanical-acoustic-vibration coupling analysis to topology optimization design and result verification, the entire process of structural design is realized, resulting in higher efficiency.

[0113] Reference Figure 6 The present invention also discloses a simulation system for a key component thermo-acoustic-vibration coupled domain free element, comprising: The computational domain establishment module includes an acoustic domain and a structural domain. The set of the acoustic domain and the structural domain constitutes the computational domain, and the intersection of the acoustic domain and the structural domain is empty. The coupling interface between the acoustic domain and the structural domain satisfies the continuity conditions of force and displacement. The acoustic domain describes the variation of sound pressure with time and space through the wave equation, and the structural domain adopts the thermoelastic control equation that introduces the equivalent thermal traction term corresponding to the steady-state temperature field. Boundary conditions are applied to the acoustic domain and the structural domain respectively. The domain division module is used to divide the acoustic domain into several acoustic subdomains and the structural domain into several structural subdomains. Acoustic finite element elements are constructed in each acoustic subdomain and structural finite element elements are constructed in each structural subdomain. The acoustic finite element elements and structural finite element elements are further discretized into scattered points. Each scattered point generates collocation elements based on its surrounding scattered points. The field variable interpolation relationship of any point in the collocation element is described by isoparametric element shape functions. The discrete model building module is used to classify nodes into acoustic domain nodes, structural domain nodes, acoustic-structural coupling interface nodes, and acoustic-structural coupling interface external boundary nodes based on their positions within the computational domain. It further classifies acoustic domain nodes into acoustic interior nodes, acoustic subdomain interface nodes, and acoustic external boundary nodes, and structural domain nodes into structural interior nodes, structural subdomain interface nodes, and structural external boundary nodes. The module then establishes discrete governing equations for each of these categories. The system equations establishment, solution, and analysis module is used to establish and solve the discrete control equations of each node to obtain the system equations, solve the system equations, calculate displacement and sound pressure, and complete the multiphysics coupling analysis of the computational domain.

[0114] The key component thermo-mechanical-acoustic-vibration coupled domain free element simulation system of the present invention further includes: a topology optimization module, which is used to divide the structural domain into finite element elements, then discretize the finite element elements into scattered points, each scattered point generates collocation elements based on its surrounding scattered points, and uses the density of the collocation elements as the design variable for topology optimization. With the goal of minimizing the overall mass of the structure, constraints are applied, including the calculation results of step S4. A topology optimization mathematical model is established, and topology optimization is performed to obtain the optimized structure. The optimized structure is then calculated using the methods of steps S1 to S4 to analyze the dynamic stability. If the requirements are met, the topology-optimized structure is obtained; if the requirements are not met, the constraints are changed and topology optimization is performed again in step S5.

[0115] Figure 7 An internal structural diagram of a computer device in one embodiment is shown. This computer device can specifically be a terminal or a server. Figure 7 As shown, the computer device includes a processor, memory, and network interface connected via a system bus. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and may also store a computer program. When executed by the processor, this computer program enables the processor to perform a simulation of the thermo-mechanical-acoustic-vibration coupling domain free element of a key component. The internal memory may also store a computer program, which, when executed by the processor, enables the processor to perform a simulation of the thermo-mechanical-acoustic-vibration coupling domain free element of the key component. Those skilled in the art will understand that… Figure 7 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0116] In one embodiment, the present invention provides a computer device including a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the aforementioned key component thermo-acoustic-vibration coupled domain free element simulation method.

[0117] In one embodiment, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the steps of the aforementioned key component thermo-acoustic-vibration coupled domain free element simulation method.

[0118] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0119] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0120] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims. Please enter the specific implementation details.

Claims

1. A key component thermo-acoustic-vibration coupling sub-domain free unit simulation method, characterized in that, The method includes: Step S1: Establish a computational domain, which includes an acoustic domain and a structural domain. The set of the acoustic domain and the structural domain constitutes the computational domain, and the intersection of the acoustic domain and the structural domain is empty. The coupling interface of the acoustic domain and the structural domain satisfies the continuity conditions of force and displacement. The acoustic domain describes the variation of sound pressure with time and space through a wave equation. The structural domain adopts a thermoelastic control equation that introduces an equivalent thermal traction term corresponding to the steady-state temperature field. Boundary conditions are applied to the acoustic domain and the structural domain respectively. Step S2: Divide the acoustic domain into several acoustic subdomains and the structural domain into several structural subdomains. Construct acoustic finite element units in each acoustic subdomain and structural finite element units in each structural subdomain. Further discretize the acoustic finite element units and the structural finite element units into scattered points. Generate collocation units for each scattered point based on the scattered points around it. Use isoparametric element shape functions to describe the field variable interpolation relationship of any point in the collocation unit. Step S3: Based on the position of the nodes of the finite element unit within the computational domain, divide the nodes into acoustic domain nodes, structural domain nodes, acoustic-structural coupling interface nodes, and acoustic-structural coupling interface external boundary nodes; further divide the acoustic domain nodes into acoustic internal nodes, acoustic subdomain interface nodes, and acoustic external boundary nodes; and divide the structural domain nodes into structural internal nodes, structural subdomain interface nodes, and structural external boundary nodes; establish discrete control equations for the acoustic-structural coupling interface nodes, acoustic-structural coupling interface external boundary nodes, acoustic internal nodes, acoustic subdomain interface nodes, acoustic external boundary nodes, structural internal nodes, structural subdomain interface nodes, and structural external boundary nodes, respectively. Step S4: Combine the discrete control equations of each node to obtain a system equation set, solve the system equation set, calculate the displacement and sound pressure, and complete the multiphysics coupling analysis of the computational domain.

2. The simulation method for key component thermo-mechanical-acoustic-vibration coupled domain free element according to claim 1, characterized in that, The method further includes: Step S5: Divide the structural domain into finite element units, discretize the finite element units into scattered points, generate collocation units for each scattered point based on its surrounding scattered points, and use the density of the collocation units as the design variable for topology optimization. With the goal of minimizing the overall mass of the structure, apply constraints, including the calculation results of step S4. Establish a topology optimization mathematical model, perform topology optimization, and obtain the optimized structure. Calculate the optimized structure using the methods of steps S1 to S4 to analyze its dynamic stability. If the requirements are met, obtain the topology-optimized structure; if not, change the constraints and perform topology optimization in step S5 again.

3. The simulation method for key components using thermo-mechanical-acoustic-vibration coupled domain-specific free elements according to claim 1 or 2, characterized in that, The wave equation is: in, For sound pressure, For the speed of sound, For internal source terms, For the density of the medium, For Hamiltonian operators, It is a spatial coordinate vector. It is a time variable. For the acoustic domain.

4. The simulation method for key components using thermo-mechanical-acoustic-vibration coupled domain-specific free elements according to claim 1 or 2, characterized in that, The thermoelastic control equation for the equivalent thermal traction term corresponding to the introduced steady-state temperature field is: in, For the elastic constitutive tensor, the subscript is... Indices for spatial coordinates are used to describe the linear relationship between stress and strain in elastic materials in different directions. For temperature, For displacement, It is a spatial coordinate vector. It is a time variable. The coefficient of thermal term, For structural density; The damping coefficient; For physical strength; For the problem dimension; repeating indicators To express summation, This is a structural domain.

5. The simulation method for key components using thermo-mechanical-acoustic-vibration coupled domain-specific free elements according to claim 1 or 2, characterized in that, The boundary conditions of the acoustic domain include three types: (a) Sound pressure boundary conditions, where the sound pressure on such boundaries is a given value; (b) Structural acceleration boundary conditions, where the normal acceleration of the medium on such boundaries is a given value; (c) Impedance boundary conditions, where the acoustic impedance on such boundaries is a given value; The boundary conditions of the structural domain include two types: (a) Displacement boundary conditions, where the displacement on such boundaries is a given value; (b) Surface force boundary conditions, where the surface forces on such boundaries are given values.

6. The simulation method for key components using thermo-mechanical-acoustic-vibration coupled domain-specific free elements according to claim 1 or 2, characterized in that, The collocation points are moved from the global coordinate system using mapping techniques. Transform to a coordinate system defined in the local coordinate system The rule calculation domain is as follows.

7. The simulation method for key components using thermo-mechanical-acoustic-vibration coupled domain-specific free elements according to claim 1 or 2, characterized in that, In establishing the discrete control equations, the Newmark difference scheme is used to approximate the time derivatives of the unknowns.

8. A simulation system for a key component with thermo-mechanical-acoustic-vibration coupling, a domain-specific free element, characterized in that, The system includes: A computational domain establishment module is provided, comprising an acoustic domain and a structural domain. The set of the acoustic domain and the structural domain constitutes the computational domain, and the intersection of the acoustic domain and the structural domain is empty. The coupling interface between the acoustic domain and the structural domain satisfies the continuity conditions of force and displacement. The acoustic domain describes the variation of sound pressure with time and space using a wave equation, and the structural domain adopts a thermoelastic control equation that introduces an equivalent thermal traction term corresponding to the steady-state temperature field, applying boundary conditions to the acoustic domain and the structural domain respectively. The domain division module is used to divide the acoustic domain into several acoustic subdomains and the structural domain into several structural subdomains. An acoustic finite element unit is constructed within each acoustic subdomain, and a structural finite element unit is constructed within each structural subdomain. The acoustic and structural finite element units are further discretized into scattered points. Each scattered point generates a collocation element based on its surrounding scattered points. An isoparametric element shape function is used to describe the field variable interpolation relationship at any point within the collocation element. A discrete model establishment module is used to classify the nodes of the finite element element into acoustic domain nodes, structural domain nodes, acoustic-structural coupling interface nodes, and acoustic-structural coupling interface external boundary nodes according to their positions in the computational domain; further classify the acoustic domain nodes into acoustic interior nodes, acoustic subdomain interface nodes, and acoustic external boundary nodes; and classify the structural domain nodes into structural interior nodes, structural subdomain interface nodes, and structural external boundary nodes; and establish discrete governing equations for the acoustic-structural coupling interface nodes, acoustic-structural coupling interface external boundary nodes, acoustic interior nodes, acoustic subdomain interface nodes, acoustic external boundary nodes, structural interior nodes, structural subdomain interface nodes, and structural external boundary nodes, respectively. The system equations establishment, solution and analysis module is used to establish and solve the discrete control equations of each node to obtain the system equations, solve the system equations, calculate displacement and sound pressure, and complete the multiphysics coupling analysis of the computational domain.

9. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the simulation method for the thermo-acoustic-vibration coupled domain free element of a key component as described in any one of claims 1 to 7.

10. A computer device comprising a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the thermal-acoustic-vibration coupling domain free element simulation method for key components as described in any one of claims 1 to 7.

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