Key component thermodynamic acoustic vibration coupling domain free unit simulation method and related equipment

Abstract

The embodiment of the invention discloses a key component thermodynamic sound-vibration coupling domain-division free unit simulation method and related equipment, and the method comprises the steps: building a computational domain, including an acoustic domain and a structural domain, forming the computational domain by a set of the acoustic domain and the structural domain, and enabling an intersection of the acoustic domain and the structural domain to be null; a coupling interface of the acoustic domain and the structural domain meets continuous conditions of force and displacement; the method comprises the following steps: respectively dividing an acoustic domain and a structural domain into a plurality of sub-domains, constructing a finite element unit in each sub-domain, generating a collocation unit, and describing a field variable interpolation relationship of any point in the collocation unit by using an isoparametric unit shape function; the nodes are classified according to the positions of the nodes in the computational domain, and different discrete control equations are established for different types of nodes; the discrete control equations of all the nodes are simultaneous to obtain a system equation set, the system equation set is solved, displacement and sound pressure are calculated, and computational domain multi-physics field coupling analysis is completed. According to the method, the thermodynamic acoustic-vibration coupling response of the key component in the complex load environment can be accurately calculated.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer simulation, and in particular to a key component thermal force-acoustic-vibration coupling sub-domain free element simulation method and related equipment. BACKGROUND

[0002] Hypersonic vehicles (>5Ma) are subjected to extreme acoustic loads (sound pressure level exceeding 175dB, frequency covering 10-10000Hz) composed of inlet noise, engine jet noise and surface aerodynamic noise, and extreme thermal loads (local temperature up to 1650°C) caused by aerodynamic heating under the working conditions of launch, transonic flight and hypersonic cruise. Under the coupling effect of such high sound pressure, wideband noise and high temperature environment, the thin-walled structure of the vehicle is prone to acoustic fatigue. Therefore, it has become a key challenge and urgent need in the design of vehicle structures to carry out thermal-force-acoustic-vibration multi-field coupling analysis and accurately predict the dynamic response of key structures under real environment.

[0003] Currently, for the study of structural dynamic response, especially the acoustic-vibration coupling problem, numerical methods are mostly focused on finite element method (FEM), boundary element method (BEM) and their hybrid forms. Although these methods are widely used, they still face limitations in computational efficiency, model adaptability and solution stability when dealing with the strong coupling and multi-physical field problems mentioned above. SUMMARY

[0004] Therefore, it is necessary to propose a key component thermal force-acoustic-vibration coupling sub-domain free element simulation method and related equipment to overcome the shortcomings of traditional methods in computational efficiency and stability.

[0005] A key component thermal force-acoustic-vibration coupling sub-domain free element simulation method, the method comprising: Step S1: establishing a calculation domain, the calculation domain comprising an acoustic domain and a structural domain, the union of the acoustic domain and the structural domain constituting the calculation domain, and the intersection of the acoustic domain and the structural domain being empty; the coupling interface of the acoustic domain and the structural domain satisfying the continuity conditions of force and displacement; the acoustic domain is described by a wave equation to describe the variation of sound pressure with time and space, and the structural domain adopts a thermoelastic control equation introducing an equivalent thermal drag term corresponding to a steady temperature field to reflect the influence of temperature on structural stiffness and deformation, and boundary conditions are applied to the acoustic domain and the structural domain respectively; Step S2: dividing the acoustic domain into several regular or irregular acoustic sub-domains, dividing the structure domain into several regular or irregular structure sub-domains, constructing acoustic finite element units in each acoustic sub-domain, constructing structure finite element units in each structure sub-domain, further dispersing the acoustic finite element units and the structure finite element units into scattered points, generating a collocation unit according to the surrounding scattered points for each scattered point, and describing the field variable interpolation relationship of any point in the collocation unit by isoparametric element shape functions; Step S3: dividing the nodes into acoustic domain nodes, structure domain nodes, acoustic-structure coupling interface nodes and acoustic-structure coupling interface external boundary nodes according to the positions of the nodes in the calculation domain, dividing the acoustic domain nodes into acoustic internal nodes, acoustic sub-domain interface nodes and acoustic external boundary nodes, dividing the structure domain nodes into structure internal nodes, structure sub-domain interface nodes and structure external boundary nodes, and respectively establishing discrete control equations of the acoustic-structure coupling interface nodes, the acoustic-structure coupling interface external boundary nodes, the acoustic internal nodes, the acoustic sub-domain interface nodes, the acoustic external boundary nodes, the structure internal nodes, the structure sub-domain interface nodes and the structure external boundary nodes; Step S4: combining the discrete control equations of the nodes to obtain a system equation group, solving the system equation group, calculating displacement and acoustic pressure, and completing the multi-physical field coupling analysis of the calculation domain.

[0006] A key component thermal force-acoustic vibration coupling sub-domain free unit simulation system, the system comprises: A calculation domain establishment module, the calculation domain comprises an acoustic domain and a structure domain, the union of the acoustic domain and the structure domain constitutes the calculation domain, and the intersection of the acoustic domain and the structure domain is empty; the coupling interface of the acoustic domain and the structure domain satisfies the continuity condition of force and displacement; the acoustic domain is described by a wave equation, and the structure domain adopts a thermoelastic control equation with an equivalent thermal drag term corresponding to a steady temperature field; boundary conditions are respectively applied to the acoustic domain and the structure domain; A sub-domain module, the sub-domain module is used for dividing the acoustic domain into several acoustic sub-domains, dividing the structure domain into several structure sub-domains, constructing acoustic finite element units in each acoustic sub-domain, constructing structure finite element units in each structure sub-domain, further dispersing the acoustic finite element units and the structure finite element units into scattered points, generating a collocation unit according to the surrounding scattered points for each scattered point, and describing the field variable interpolation relationship of any point in the collocation unit by isoparametric element shape functions; a discrete model establishing module, which is configured to divide the nodes into acoustic domain nodes, structural domain nodes, acoustic-structural coupling interface nodes and acoustic-structural coupling interface external boundary nodes according to the positions of the nodes in the calculation domain, divide the acoustic domain nodes into acoustic internal nodes, acoustic sub-domain interface nodes and acoustic external boundary nodes, divide the structural domain nodes into structural internal nodes, structural sub-domain interface nodes and structural external boundary nodes, and establish discrete control equations of the acoustic-structural coupling interface nodes, the acoustic-structural coupling interface external boundary nodes, the acoustic internal nodes, the acoustic sub-domain interface nodes, the acoustic external boundary nodes, the structural internal nodes, the structural sub-domain interface nodes and the structural external boundary nodes respectively; a system equation set establishing, solving and analyzing module, which is configured to combine the discrete control equations of the nodes to obtain a system equation set, solve the system equation set, calculate displacements and acoustic pressures, and complete the multi-physical field coupling analysis of the calculation domain.

[0007] A computer readable storage medium storing a computer program, the computer program being executed by a processor to make the processor execute the steps of the key component thermal-acoustic-vibration coupling sub-domain free element simulation method.

[0008] A computer device comprising a memory and a processor, the memory storing a computer program, the computer program being executed by the processor to make the processor execute the steps of the key component thermal-acoustic-vibration coupling sub-domain free element simulation method.

[0009] Implementing the embodiments of the present application will have the following beneficial effects: 1) The present application simulates the dynamic response of the structure to the acoustic field by establishing a calculation domain comprising an acoustic domain and a structural domain (the union of the acoustic domain and the structural domain constitutes the calculation domain, 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 thermal-elastic control equation of the structural domain introduces an equivalent thermal traction term corresponding to the steady-state temperature field, so that the simulation can consider the effect of temperature.

[0011] 3) Discrete based on sub-domain free element method, that is, first sub-domain is divided, then matching point element is generated in the sub-domain, and the field variable interpolation relationship of any point in the matching point element is described by isoparametric element shape function, the nodes are classified, different classification nodes adopt different discrete control equations, the discrete control equations of all nodes are combined to establish a system equation group, the system equation group is solved, the numerical solution of the coupled system in the time domain is realized, the solving method can accurately capture the multi-field coupling response characteristics such as thermal deformation, structure vibration and sound field radiation without relying on traditional element division, and provides an accurate numerical basis for comprehensive performance evaluation of the structure in a complex thermal-mechanical-acoustic-vibration service environment.

[0012] 4) The application can accurately calculate the thermal-mechanical-acoustic-vibration coupling response of the key component under a complex load environment. BRIEF DESCRIPTION OF DRAWINGS

[0013] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0014] Among them: Figure 1 The flow chart of the key component thermal-mechanical-acoustic-vibration coupling sub-domain free element simulation method in an embodiment of the present application is shown in the figure. Figure 2 The flow chart of the key component thermal-mechanical-acoustic-vibration coupling sub-domain free element simulation method in an embodiment of the present application is shown in the figure. Figure 3 The schematic diagram of the overall calculation domain in an embodiment of the present application is shown in the figure. Figure 4 The schematic diagram of the calculation domain sub-domain in an embodiment of the present application is shown in the figure. Figure 5 The Figure 4 The local enlarged view of the sub-domain 2A and 3A in the bold area in the figure. Figure 6 The structure block diagram of the key component thermal-mechanical-acoustic-vibration coupling sub-domain free element simulation system in an embodiment of the present application is shown in the figure. Figure 7 The structure block diagram of the computer equipment in an embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0015] The technical solutions in the embodiments of the present application will be clearly and completely described with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort fall within the protection scope of the present application.

[0016] With reference to Figure 1 and Figure 2 , the present application provides a thermal-acoustic-vibration coupling sub-domain free unit simulation method, comprising the following steps: Step S1: With reference to Figure 3 , a calculation domain is established, the calculation domain comprises an acoustic domain and a structure domain, the acoustic domain and the structure domain constitute the calculation domain, and the intersection of the acoustic domain and the structure domain is empty; the coupling interface of the acoustic domain and the structure domain satisfies the continuity condition of force and displacement; the acoustic domain is described by a wave equation to describe the variation law of sound pressure with time and space, the structure domain adopts a thermoelastic control equation introducing an equivalent thermal drag term corresponding to a steady temperature field to reflect the influence of temperature on the stiffness and deformation of the structure, and boundary conditions are respectively applied to the acoustic domain and the structure domain.

[0017] In this step, the acoustic domain is used to describe the propagation characteristics of sound waves in a sound transmission medium, and the structure domain is used to represent the dynamic response of the structure under the action of thermal load. The two are strongly coupled through the displacement continuity condition and the surface force balance condition at the coupling interface, so as to accurately reflect the mutual influence of the sound field and the structure vibration under the action of the thermal environment, and then complete the thermal-force-acoustic-vibration coupling response analysis of the structure under the action of complex load.

[0018] In the coupling system, the acoustic domain mainly describes the variation law of sound pressure with time and space through a wave equation; the structure domain introduces an equivalent thermal drag term corresponding to a steady temperature field in a thermoelastic control equation to reflect the influence of temperature on the stiffness and deformation of the structure. Through this coupling modeling and interface collaborative solving strategy, the dynamic response relationship between the four fields of heat, force, vibration and sound can be solved synchronously in a unified calculation framework, which provides theoretical support for the transient response calculation of complex thermal-force-acoustic-vibration coupling systems.

[0019] In an embodiment of the present application, the wave equation is:

[0020] wherein, is the sound pressure, is the sound velocity, is the internal source term, is the medium density, is the Hamiltonian operator, is a spatial coordinate vector, is a time variable, For acoustic domain.

[0021] There are three types of boundary conditions for acoustic domain wave equation: (a) Acoustic pressure boundary condition, the acoustic pressure on this type of boundary is given:

[0022] For boundary, especially when the given acoustic pressure boundary is 0, this type of boundary is also called acoustic soft boundary, such as the free boundary of open space, flexible membrane boundary, when the acoustic wave reaches this boundary, it will be reflected with the same amplitude and opposite phase. When is nonzero, it can simulate the scenario that "the boundary itself is a sound source" (such as the sound pressure on the surface of the loudspeaker diaphragm is known), directly radiating sound waves into the domain.

[0023] (b) Structural acceleration boundary condition, the normal acceleration of the medium on this type of boundary is given:

[0024] where, is the outward normal direction of the boundary. When the given normal acceleration is 0, this type of boundary is also called acoustic hard boundary, such as rigid walls, metal surfaces, etc., when the acoustic wave reaches this boundary, it will be reflected with the same amplitude and the same phase. When is nonzero, it can simulate the scenario that "structure vibration drives sound field" (such as the sound waves generated by the vibration of the machine shell), indirectly calculate the acoustic pressure gradient at the boundary through the structural acceleration, and then radiate sound waves into the domain.

[0025] (c) Impedance boundary condition, the acoustic impedance on this type of boundary is given:

[0026] When the given acoustic impedance on the impedance boundary is equal to the acoustic impedance of the acoustic medium in the acoustic domain, this type of boundary is also called absorbing boundary, when the incident acoustic wave reaches this boundary, it will be completely absorbed, and will not affect the calculation domain, which is used to simulate the infinite sound field domain. When the acoustic impedance , the right term of equation (4) tends to 0, the impedance boundary tends to the acoustic hard boundary, therefore, when the acoustic impedance on the boundary is much larger than the acoustic impedance of the medium, the boundary can achieve similar effect to the acoustic hard boundary.

[0027] The thermal-elastic governing equation of the structural domain can be expressed as:

[0028] where, is the stress tensor; is the structural density; is the damping coefficient; is the body force; is the problem dimension; repeated indices denotes summation, is the domain, is the displacement.

[0029] Stress tensor The strain tensor and temperature T can be expressed by the following constitutive relation, in which the thermal stress term is introduced to reflect the effect of temperature on structural stiffness and deformation in the manner of equivalent thermal traction, so as to consider the thermal load effect caused by the temperature field in the governing equation:

[0030] If the material is isotropic and linear thermoelastic, the strain tensor in equation (6), the elastic constitutive tensor after thermal correction, the subscript is the index of the spatial coordinate direction, which is used to describe the linear relationship between stress and strain of the elastic material in different directions, and the thermal term coefficient has the following corresponding relationship:

[0031]

[0032]

[0033]

[0034] wherein, is the shear modulus; is the Poisson's ratio; is the linear expansion coefficient; has symmetry, i.e. .

[0035] Equation (7) is brought into equation (6), and the obtained result is brought into equation (5) again, so as to obtain the second-order partial differential equation of the domain thermoelastic governing equation, which can be expressed as:

[0036] wherein, is the elastic constitutive tensor, the subscript is the index of the spatial coordinate direction, which is used to describe the linear relationship between stress and strain of the elastic material in different directions, is the temperature, is the displacement, is the spatial coordinate vector, is the time variable, is the thermal coefficient, is the structural density; is the damping coefficient; is the body force; is the problem dimension; repeated indices denotes summation, is the domain.

[0037] The boundary conditions of the domain include two types: (a) Displacement boundary condition, the displacement on this type of boundary is given:

[0038] (b) Surface force boundary condition, the surface force on this type of boundary is given:

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

[0040] The acoustic domain and the structural domain can achieve the establishment of the acoustic-structural coupling relationship through the displacement continuity condition and the surface force balance condition.

[0041] (a) Displacement continuity condition, the vibration displacement of the acoustic medium and the structure on the interface is the same. Since it is more convenient to establish equations in terms of 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 balance condition, the surface force on the structural domain on the coupling interface is equal to the acoustic pressure in the acoustic domain, considering equation (11), the coupling equation can be written as:

[0043] Equations (13) and (14) are the coupling conditions on the thermo-mechanical-acoustic-structural coupling interface. These conditions can reflect the interaction between the acoustic wave and the structure, thus forming a strong acoustic-structural coupling system.

[0044] The initial conditions in the entire calculation domain include the acoustic pressure and the first-order time derivative of the acoustic pressure in the acoustic domain, as well as the displacement and velocity in the structural domain, which can be expressed as:

[0045] where, , .

[0046] Step S2: dividing the acoustic domain into several regular or irregular acoustic sub-domains, dividing the structure domain into several regular or irregular structure sub-domains, constructing acoustic finite element units in each acoustic sub-domain, constructing structure finite element units in each structure sub-domain, further discretizing the acoustic finite element units and the structure finite element units into scattered points, generating a collocation unit according to surrounding scattered points for each scattered point, and describing the field variable interpolation relationship of any point in the collocation unit by isoparametric unit shape functions.

[0047] In this step, the present application adopts the domain-free unit method to divide the acoustic domain and the structure sub-domain into several sub-domains, which can be applied to complex geometric models.

[0048] In the domain division process, high-order units in the finite element method are preferably used for domain division, which can effectively avoid the calculation failure caused by the deformation of the collocation unit in the traditional free unit method, while maintaining high efficiency and numerical stability, so that it can be applied to complex geometric models and has high calculation accuracy.

[0049] Specifically, in a specific embodiment, referring to Figure 4 , the acoustic domain and the structure domain 5 are divided into several regular or irregular acoustic sub-domains 1 / 2A / 3A / 4 / 6 according to the geometric characteristics and material distribution of the structure, Figure 4 The local enlarged view of the sub-domains 2A and 3A in the bold area is shown in Figure 5 , the acoustic sub-domain interface 7 is the interface between the acoustic sub-domains 2B and 3B, each acoustic sub-domain is divided into quadrilateral finite element units 8, the unit nodes are a set of scattered points formed inside the sub-domain, and each node generates a collocation unit 9 according to the surrounding nodes, the enlarged view of which is shown in Figure 5 , the collocation unit includes 9 collocation points.

[0050] In order to facilitate subsequent calculation and stability, especially for sub-domains with complex shapes, preferably, the collocation points are transformed from the global coordinate system to a regular calculation domain defined in the local coordinate system .

[0051] The mapping can be performed by the following shape functions:

[0052] wherein, is the number of mapping nodes used in the collocation unit.

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

[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 comprises: Step S1: establishing a calculation domain, the calculation domain comprising an acoustic domain and a structure domain, the union of the acoustic domain and the structure domain constituting the calculation domain, and the intersection of the acoustic domain and the structure domain being empty; the coupling interface of the acoustic domain and the structure domain satisfying the continuity condition of force and displacement; the acoustic domain describing the variation law of sound pressure with time and space by a wave equation, and the structure domain adopting a thermoelastic governing equation introducing an equivalent thermal drag term corresponding to a steady-state temperature field, and boundary conditions being respectively applied to the acoustic domain and the structure domain; Step S2: dividing the acoustic domain into a plurality of acoustic sub-domains and dividing the structure domain into a plurality of structure sub-domains, constructing an acoustic finite element unit in each acoustic sub-domain and constructing a structure finite element unit in each structure sub-domain, and further discretizing the acoustic finite element unit and the structure finite element unit into scattered points, each scattered point generating a patch element unit according to the surrounding scattered points, and describing the field variable interpolation relationship of any point in the patch element unit by isoparametric element shape functions; Step S3: according to the position of the nodes in the calculation domain, dividing the nodes into acoustic domain nodes, structure domain nodes, acoustic-structure coupling interface nodes and acoustic-structure coupling interface external boundary nodes, dividing the acoustic domain nodes into acoustic internal nodes, acoustic sub-domain interface nodes and acoustic external boundary nodes, dividing the structure domain nodes into structure internal nodes, structure sub-domain interface nodes and structure external boundary nodes, and respectively establishing the discrete governing equations of the acoustic-structure coupling interface nodes, the acoustic-structure coupling interface external boundary nodes, the acoustic internal nodes, the acoustic sub-domain interface nodes, the acoustic external boundary nodes, the structure internal nodes, the structure sub-domain interface nodes and the structure external boundary nodes; Step S4: combining the discrete governing equations of the nodes to obtain a system equation group, solving the system equation group, calculating the displacement and sound pressure, and completing the multi-physical field coupling analysis of the calculation domain.

2. The method of claim 1, wherein, The method further comprises: Step S5: dividing the structure domain into finite element units, discretizing the finite element units into scattered points, each scattered point generating a patch element unit according to the surrounding scattered points, taking the density of the patch element unit as a design variable of topology optimization, taking the minimization of the overall mass of the structure as the target, applying constraint conditions including the calculation results of step S4, establishing a topology optimization mathematical model, performing topology optimization, obtaining an optimized structure, and using the method of steps S1-S4 to calculate and analyze the dynamic stability of the optimized structure, if the requirements are met, obtaining the topology-optimized structure, and if the requirements are not met, changing the constraint conditions and performing the topology optimization of step S5 again.

3. The method of claim 1 or 2, wherein, The wave equation is: wherein is the sound pressure, is the sound velocity, is the internal source term, is the medium density, is the Hamiltonian operator, is the spatial coordinate vector, is the time variable, is the acoustic domain.

4. The method of claim 1 or 2, wherein, The thermoelastic governing equation introducing an equivalent thermal drag term corresponding to a steady-state temperature field is: wherein, is the elastic constitutive tensor, with the index is an index of spatial coordinate direction, used to describe the linear relationship between stress and strain of the elastic material in different directions, is temperature, is displacement, is a spatial coordinate vector, is a time variable, is a thermal term coefficient, is a structure density; is a damping coefficient; is a body force; is a problem dimension; repeated indices denotes summation, is a domain.

5. The method of claim 1 or 2, wherein, The boundary conditions of the acoustic domain include three types: (a) sound pressure boundary condition, the sound pressure on this type of boundary being a given value; (b) structure acceleration boundary condition, the normal acceleration of the medium on this type of boundary being a given value; and (c) structure displacement boundary condition, the displacement of the medium on this type of boundary being a given value. (c) impedance boundary condition, the acoustic impedance on such boundary is given; The boundary conditions of the domains include two types: (a) displacement boundary condition, the displacement on such boundary is given; (b) surface force boundary condition, the surface force on such boundary is given.

6. The method of claim 1 or 2, wherein, The points are transformed from the global coordinate system to the regular computational domain defined in the local coordinate system by a mapping technique.

7. The method of claim 1 or 2, wherein, In the process of establishing the discrete control equations of each domain, the Newmark difference format is used to approximate the time derivative of unknown quantities.

8. A key component thermo-acoustic-vibration coupling sub-domain free unit simulation system, characterized in that, The system comprises: a calculation domain establishing module, the calculation domain comprises an acoustic domain and a structure domain, the union of the acoustic domain and the structure domain constitutes the calculation domain, and the intersection of the acoustic domain and the structure domain is empty; the coupling interface of the acoustic domain and the structure domain satisfies the continuity condition of force and displacement; the acoustic domain is described by a wave equation for the variation of acoustic pressure with time and space, and the structure domain adopts a thermoelastic control equation with an equivalent thermal drag term corresponding to a steady temperature field, and boundary conditions are applied to the acoustic domain and the structure domain respectively; a domain dividing module, which is used to divide the acoustic domain into a plurality of acoustic sub-domains, divide the structure domain into a plurality of structure sub-domains, construct acoustic finite element units in each acoustic sub-domain, construct structure finite element units in each structure sub-domain, further discretize the acoustic finite element units and the structure finite element units into scattered points, and describe the field variable interpolation relationship of any point in a collocation unit according to the surrounding scattered points of each scattered point by isoparametric element shape functions; a discrete model establishing module, which is used to divide the nodes into acoustic domain nodes, structure domain nodes, acoustic-structure coupling interface nodes and acoustic-structure coupling interface external boundary nodes according to the positions of the nodes in the calculation domain, divide the acoustic domain nodes into acoustic internal nodes, acoustic sub-domain interface nodes and acoustic external boundary nodes, divide the structure domain nodes into structure internal nodes, structure sub-domain interface nodes and structure external boundary nodes, and establish discrete control equations of the acoustic-structure coupling interface nodes, the acoustic-structure coupling interface external boundary nodes, the acoustic internal nodes, the acoustic sub-domain interface nodes, the acoustic external boundary nodes, the structure internal nodes, the structure sub-domain interface nodes and the structure external boundary nodes respectively; a system equation set establishing, solving and analyzing module, which is used to combine the discrete control equations of each node to obtain a system equation set, solve the system equation set, calculate displacement and acoustic pressure, and complete the multi-physical field coupling analysis of the calculation domain.

9. A computer readable storage medium storing a computer program, the computer program being executed by a processor to make the processor execute the steps of the key component thermal-acoustic-structure coupling domain-free element simulation method according to any one of claims 1 to 7.

10. A computer device comprising a memory and a processor, the memory storing a computer program, the computer program, when executed by the processor, causing the processor to perform the steps of the key component thermo-acoustic-vibration coupling subdomain free unit simulation method according to any one of claims 1 to 7.

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