Structural nonlinear dynamic response incremental modal overlay analysis method and system

Abstract

The invention discloses a structure nonlinear dynamic response incremental modal overlay analysis method and system, and belongs to the field of aerospace structure dynamics calculation. The method comprises the steps of constructing a finite element model and obtaining an initial matrix; dispersing the time-varying temperature field into a plurality of time increment intervals, updating material parameters in each interval, and calculating an instantaneous matrix; carrying out eigenvalue analysis and converting the kinetic equation into a modal coordinate system; solving a modal response increment by adopting a numerical integration method and converting the modal response increment to a physical coordinate system for superposition; and circularly executing until a full-time-history response is output. According to the method, the problem of rigidity nonlinearity caused by the temperature is solved through incremental linearization and modal order reduction, high calculation precision and high efficiency are achieved, and the method is suitable for dynamic design and analysis of aerospace structures in the high-temperature variable-temperature environment.

Description

Technical Field

[0001] This invention belongs to the field of aerospace structural dynamics calculation technology, specifically relating to a method and system for incremental modal superposition analysis of structural nonlinear dynamic response. Background Technology

[0002] During flight, hypersonic vehicles must withstand a complex force-thermal coupling environment created by the combined effects of severe thermal, acoustic, and vibration loads on their thermal protection structures. The temperature field in the service environment exhibits significant time-varying characteristics, and the elastic modulus of materials changes significantly with temperature, resulting in temperature-dependent nonlinearities in structural stiffness and thus pronounced nonlinearities in the dynamic response. These nonlinear responses not only increase the complexity of dynamic modeling and calculation but also place higher demands on structural safety assessment and design optimization.

[0003] Currently, for calculating the dynamic response of nonlinear structural systems, engineering practice typically employs direct time-domain integration methods (such as the Runge-Kutta method), which solve the structural motion differential equations through successive integrations. This method is suitable for complex time-varying loads, ensuring high computational accuracy while fully considering system nonlinearity. However, for structures whose stiffness changes significantly due to high-temperature environments, the direct integration method requires updating the system matrix and solving the entire system at each time step, resulting in a heavy computational burden and significant convergence difficulties under highly nonlinear conditions.

[0004] As the service conditions of hypersonic vehicles become increasingly demanding, the nonlinear effects of structures under high-temperature and variable-temperature environments become more pronounced. Traditional direct integration methods are insufficient to meet the needs of rapid analysis in engineering practice. Therefore, there is an urgent need to propose a rapid analysis method for nonlinear dynamic responses that can balance computational accuracy and efficiency, in order to meet the requirements of rapid evaluation and design optimization of structural dynamic performance under high-temperature and variable-temperature conditions. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a method and system for incremental modal superposition analysis of structural nonlinear dynamic response, which addresses the shortcomings of the prior art. This method is used to solve the technical problem that the thermal protection structure of hypersonic vehicles and other equipment faces the challenge of balancing accuracy and efficiency in dynamic response calculations due to the degradation of material properties and the temperature-dependent nonlinearity of structural stiffness caused by temperature time-varying operating environments.

[0006] The present invention adopts the following technical solution: An incremental modal superposition analysis method for structural nonlinear dynamic response includes the following steps: A three-dimensional finite element model of the thermal protection structure is constructed by inputting the mechanical property parameters of the material as a function of temperature, the geometric parameters of the structure, and the boundary conditions. The initial mass matrix and initial stiffness matrix of the structure are extracted based on the initial temperature field, and the cutoff mode number and damping ratio are set. The time-varying temperature field is discretized into multiple continuous time increment intervals, and the material parameters are updated according to the current temperature in each time increment interval, thereby calculating the instantaneous mass matrix and instantaneous stiffness matrix of the structure. Within each time increment interval, eigenvalue analysis is performed based on the instantaneous mass matrix and instantaneous stiffness matrix to obtain the corresponding instantaneous modal frequencies and mode shapes, thereby transforming the structure's dynamic equations into a modal coordinate system; In the modal coordinate system, the modal response increment within the current time increment interval is calculated using the numerical integration method. The modal response increment is then transformed to the physical coordinate system to obtain the response increment in the physical coordinate system. This response increment is then superimposed with the physical responses accumulated from all previous time steps to obtain the total response of the current time step. Repeat the above steps, traversing all time increment intervals, and finally output the displacement, velocity, and acceleration response of the structure throughout the entire time history.

[0007] Preferably, the initial temperature field is obtained by transient heat transfer finite element calculation, and the initial temperature field is input as a boundary condition into the dynamic calculation process.

[0008] Preferably, the temperature field is treated as a steady field within each time increment interval, and transient heat transfer analysis is performed based on the finite element model to update the material parameters, which include Young's modulus, shear modulus, and coefficient of thermal expansion.

[0009] Preferably, by updating the modal basis as the structural state changes, the dynamic capture of material property degradation and structural stiffness nonlinear effects caused by temperature changes is achieved, wherein the structural state is characterized by the instantaneous mass matrix and the instantaneous stiffness matrix.

[0010] Preferably, the numerical integration method is Newmark-β. Newmark-β obtains the system response at the next time step by constructing the effective stiffness matrix and equivalent load, and then obtains the modal response increment by utilizing the modal displacement of the previous time step. ,speed acceleration The initial values ​​for the next time step are predicted as follows:

[0011]

[0012] in, For time step interval, and For integration parameters, , and Let be the modal displacement, velocity, and acceleration for the next time step, respectively.

[0013] Preferably, the integral parameters β=0.25 and γ=0.5.

[0014] Preferably, before transforming the modal response increment to the physical coordinate system, the method further includes achieving a seamless connection between the old and new modal bases through a modal coordinate projection matrix.

[0015] Preferably, the standard for setting the number of truncated modes is: the effective mass of the modes participating in the response calculation reaches more than 90% of the total mass of the structure.

[0016] Preferably, the boundary conditions include fixed-support boundary conditions and simply supported boundary conditions; the load forms corresponding to the time-varying temperature field include basic excitation load, inertial force and noise pressure load.

[0017] Secondly, embodiments of the present invention provide a structural nonlinear dynamic response incremental modal superposition analysis system, comprising: The module constructs a three-dimensional finite element model of the thermal protection structure. It inputs the mechanical property parameters of the material as a function of temperature, the geometric parameters of the structure, and the boundary conditions. Based on the initial temperature field, it extracts the initial mass matrix and initial stiffness matrix of the structure and sets the truncation mode number and damping ratio. The update module discretizes the time-varying temperature field into multiple continuous time increment intervals, and updates the material parameters according to the current temperature in each time increment interval, thereby calculating the instantaneous mass matrix and instantaneous stiffness matrix of the structure. The conversion module performs eigenvalue analysis based on the instantaneous mass matrix and instantaneous stiffness matrix within each time increment interval to obtain the corresponding instantaneous modal frequencies and mode shapes, thereby converting the structure's dynamic equations to the modal coordinate system. The overlay module calculates the modal response increment within the current time increment interval using a numerical integration method in the modal coordinate system, transforms the modal response increment to the physical coordinate system to obtain the response increment in the physical coordinate system, and overlays this response increment with the physical responses accumulated from all previous time steps to obtain the total response of the current time step. The output module executes in a loop, traversing all time increment intervals, and finally outputs the displacement, velocity, and acceleration response of the structure throughout the entire time history.

[0018] Thirdly, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the above-described method for analyzing the incremental modal superposition of nonlinear dynamic response of a structure.

[0019] Fourthly, embodiments of the present invention provide a computer-readable storage medium including a computer program, which, when executed by a processor, implements the steps of the above-described method for analyzing the incremental mode superposition of nonlinear dynamic response of a structure.

[0020] Fifthly, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the above-described method for analyzing the incremental mode superposition of nonlinear dynamic response of a structure.

[0021] In a sixth aspect, embodiments of the present invention provide an electronic device, including a computer program, which, when executed by the electronic device, implements the steps of the above-described method for analyzing the incremental mode superposition of nonlinear dynamic response of structures.

[0022] Compared with the prior art, the present invention has at least the following beneficial effects: An incremental modal superposition analysis method for structural nonlinear dynamic response is proposed. This method discretizes the time-varying temperature field into multiple continuous time increment intervals and updates material parameters and system matrices based on instantaneous temperature within each interval, thereby achieving efficient handling of temperature-induced structural stiffness nonlinearity. The global nonlinear problem is decomposed into a series of local linear problems, and the degrees of freedom are significantly reduced through modal coordinate transformation. Combined with Newmark-β integral and response superposition, the method greatly improves computational efficiency while ensuring accuracy, and is particularly suitable for large-scale, highly nonlinear thermo-mechanical coupled dynamic response analysis.

[0023] Furthermore, by using the temperature field obtained from transient heat transfer finite element analysis as the input for dynamic calculation, the physical reality and spatiotemporal consistency of the temperature boundary conditions are ensured, the accuracy of structural response prediction under high temperature conditions is improved, and a true thermo-mechanical sequential coupling simulation is realized.

[0024] Furthermore, by treating the temperature field as a steady field and performing transient heat transfer analysis within each time increment interval to update material parameters, a balance is effectively struck between computational efficiency and model accuracy. This setup avoids the enormous computational overhead of performing thermal analysis in every kinetic substep, while accurately reflecting the degradation behavior of material properties with temperature through updates to key parameters such as Young's modulus, shear modulus, and coefficient of thermal expansion.

[0025] Furthermore, by dynamically updating the modal basis according to the structural state, accurate capture of material property degradation and stiffness nonlinear effects caused by temperature changes is achieved. This avoids the problem of insufficient accuracy of fixed modal basis under strong nonlinear conditions and significantly improves the calculation accuracy of transient response, especially high-frequency response components.

[0026] Furthermore, the Newmark-β method is employed for numerical integration. By constructing the effective stiffness matrix and equivalent loads, the differential equations are transformed into algebraic equations for solution, ensuring the numerical stability of the computational process. This integration scheme is unconditionally stable, applicable to structural dynamics problems, and its recursive form is efficient and easy to implement, providing a reliable tool for solving incremental equations in modal coordinates.

[0027] Furthermore, the preferred integration parameters are β=0.25 and γ=0.5. This combination corresponds to the average acceleration method and possesses the characteristics of unconditional stability, second-order accuracy, and no numerical damping. This choice ensures the computational accuracy of the algorithm while avoiding response distortion caused by numerical damping, making it particularly suitable for long-term transient response analysis.

[0028] Furthermore, before transforming the modal response increments to the physical coordinate system, a modal coordinate projection matrix is ​​introduced to achieve the conversion and connection between the old and new modal bases. This effectively solves the problem of numerical discontinuity that may be caused by the switching of modal bases with temperature changes, ensuring the smoothness and physical authenticity of the full-time response results.

[0029] Furthermore, the standard for setting the number of truncated modes is clarified as follows: the effective mass of the modes participating in the calculation reaches more than 90% of the total mass. This ensures the rationality of modal truncation, minimizing computational load while guaranteeing the accuracy of dynamic response calculation, thus making the method both efficient and reliable.

[0030] Furthermore, please supplement the explanation of the purpose or benefits of the setting according to claim 9, and provide a principle analysis.

[0031] It is understood that the beneficial effects of the second to sixth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0032] In summary, this invention significantly improves computational efficiency while maintaining computational accuracy, effectively solving the problems of heavy computational burden and excessively long cycles associated with traditional direct integration methods. This method achieves efficient solutions for nonlinear responses by dynamically updating the system matrix within a time step and combining modal projection with Newmark-β integration. It boasts advantages such as fast computation, reliable results, and strong engineering applicability, and can be widely applied to the design and analysis of aircraft thermal protection structures and other structures serving in high-temperature and complex environments, demonstrating significant engineering value and promising application prospects.

[0033] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0034] Figure 1 A logical diagram illustrating a fast calculation method for the nonlinear dynamic response of a structure under high-temperature and variable-temperature service conditions; Figure 2 The examples show the finite element model and response measurement points of a typical structure. Figure 3 The example shows the time-domain curves of the temperature load acting on a typical structure. Figure 4 The figure shows the time-domain curve of the excitation acceleration load in the embodiment; Figure 5 is a comparison diagram of the embodiments, in which (a) is a comparison of the acceleration response of the measuring point, (b) is a comparison of the velocity response of the measuring point, and (c) is a comparison of the displacement response of the measuring point in the embodiments. Figure 6 A schematic diagram of a computer device provided in an embodiment of the present invention; Figure 7 This is a block diagram of a chip provided according to an embodiment of the present invention.

[0035] Among them, 60. Computer equipment; 61. Processor; 62. Memory; 63. Computer program; 600. Electronic device; 610. Processing unit; 620. Storage unit; 6201. Random access memory unit; 6202. Cache memory unit; 6203. Read-only memory unit; 6204. Program / utility; 6205. Program module; 630. Bus; 640. Display unit; 650. Input / output interface; 660. Network adapter; 700. External device. Detailed Implementation

[0036] 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, not all, of the embodiments of the present invention. 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.

[0037] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0038] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0039] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0040] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0041] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0042] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0043] This invention provides an incremental modal superposition analysis method for the nonlinear dynamic response of a structure. Based on the principle of incremental modal superposition, the time-varying temperature field of a structure under high temperature and variable temperature conditions is discretized into multiple time increment intervals. Within each time increment, the nonlinear system is approximated as a linear system. Incremental dynamic equations are established based on the instantaneous mass matrix and stiffness matrix. The response increment is solved by transforming to the modal coordinate system and then superimposed with the result of the previous step in the physical coordinate system, thereby achieving efficient solution of stiffness nonlinear dynamic response under high temperature and variable temperature conditions.

[0044] This invention discloses a method for incremental modal superposition analysis of structural nonlinear dynamic response, comprising the following steps: S1. Establish a three-dimensional finite element model of the thermal protection structure using finite element software, inputting the material temperature-mechanical property relationship, structural geometric parameters, and boundary conditions. Based on the initial service temperature field, extract the initial mass matrix and stiffness matrix of the structure, and set the cutoff mode number and damping ratio; S101. Construct a finite element model of the thermal protection structure based on finite element analysis software, and set the material elastic modulus to change with temperature; S102. Import the initial temperature field and obtain the mass matrix under the initial state. Overall stiffness matrix ; S103. Considering thermal stress, perform prestressed modal analysis of the structure to obtain the modal frequencies and mode shapes in the initial state; S104. Set a reasonable number of truncated modes to ensure that the effective mass of the modes participating in the response calculation reaches more than 90% of the total mass.

[0045] S2. Discretize the time-varying temperature field into multiple time increment intervals, update the material parameters in each interval, and obtain the instantaneous mass matrix and stiffness matrix of the structure. S201. Input external load conditions to divide the entire analysis time history into several smaller time increment intervals. and the corresponding incremental steps ; S202, in each increment interval The internal temperature field is treated as a steady field. Transient heat transfer analysis of the thermal protection structure is carried out based on the finite element model, the material parameters are updated, and the data for each incremental step is obtained. mass matrix of the lower structure and stiffness matrix .

[0046] S3. Perform eigenvalue analysis within each time interval to obtain instantaneous modal frequencies and mode shapes, and transform the dynamic equations to the modal coordinate system; S301, in each increment step Modal analysis is performed to calculate instantaneous modal frequencies and mode shapes, thereby obtaining the instantaneous modal basis. ; S302, Establish The incremental form of the dynamic equations of the thermal protection structure within the interval is obtained through instantaneous modal basis. The incremental dynamic equations are transformed into the modal coordinate system to obtain the incremental equations in the modal coordinate system.

[0047] The incremental equation is as follows:

[0048] in, , , , It is a modal force.

[0049] S4. Calculate the modal response increment within the time step using numerical integration, and then transfer the results back to the physical coordinate system for superposition. S401. Solve the incremental dynamic equations using the Newmark-β numerical integration method, utilizing the modal displacements from the previous time step. ,speed acceleration Predict the initial value for the next time step: (2) (3) In this invention, the preferred embodiment is... , This ensures the stability of the algorithm; S402. Calculate the effective stiffness matrix: (4) Construct equivalent load: (5) in, , ; S403, Solve the linear equation: (6) Calculate the system response at the next time step: (7) (8) (9) S404. Pass the modal incremental response through: (10) Convert the actual response increment to the physical coordinate system and add it to the cumulative result of the previous time increment: (11) (12) S5. Repeat the above steps to output the dynamic response results such as displacement, velocity, and acceleration throughout the process, so as to realize the rapid analysis of the dynamic response of stiffness nonlinear system under high temperature and variable temperature conditions.

[0050] S501. Project the physical response calculated in the current time step onto a new modal space as the initial condition for the next time step calculation to ensure the continuity of the response: (13) S502. Repeat steps S2 to S5 until the full load time history is completed, and obtain the full nonlinear dynamic response of the thermal protection structure under high temperature and variable temperature conditions.

[0051] In another embodiment of the present invention, a structural nonlinear dynamic response incremental modal superposition analysis system is provided. This system can be used to implement the above-mentioned structural nonlinear dynamic response incremental modal superposition analysis method. Specifically, the structural nonlinear dynamic response incremental modal superposition analysis system includes a construction module, an update module, a conversion module, a superposition module, and an output module.

[0052] The construction module builds a three-dimensional finite element model of the thermal protection structure, inputs the mechanical property parameters of the material as a function of temperature, the geometric parameters of the structure and the boundary conditions, extracts the initial mass matrix and initial stiffness matrix of the structure based on the initial temperature field, and sets the cutoff mode number and damping ratio. The update module discretizes the time-varying temperature field into multiple continuous time increment intervals, and updates the material parameters according to the current temperature in each time increment interval, thereby calculating the instantaneous mass matrix and instantaneous stiffness matrix of the structure. The conversion module performs eigenvalue analysis based on the instantaneous mass matrix and instantaneous stiffness matrix within each time increment interval to obtain the corresponding instantaneous modal frequencies and mode shapes, thereby converting the structure's dynamic equations to the modal coordinate system. The overlay module calculates the modal response increment within the current time increment interval using a numerical integration method in the modal coordinate system, transforms the modal response increment to the physical coordinate system to obtain the response increment in the physical coordinate system, and overlays this response increment with the physical responses accumulated from all previous time steps to obtain the total response of the current time step. The output module executes in a loop, traversing all time increment intervals, and finally outputs the displacement, velocity, and acceleration response of the structure throughout the entire time history.

[0053] This invention provides a terminal device comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or corresponding function. The processor described in this embodiment can be used for the operation of a structural nonlinear dynamic response incremental mode superposition analysis method, including: A three-dimensional finite element model of the thermal protection structure is constructed. The mechanical properties of the material as a function of temperature, the structural geometric parameters, and boundary conditions are input. The initial mass matrix and initial stiffness matrix of the structure are extracted based on the initial temperature field, and the truncated mode number and damping ratio are set. The time-varying temperature field is discretized into multiple continuous time increment intervals. Within each time increment interval, the material parameters are updated according to the current temperature, thereby calculating the instantaneous mass matrix and instantaneous stiffness matrix of the structure. Within each time increment interval, eigenvalue analysis is performed based on the instantaneous mass matrix and instantaneous stiffness matrix to obtain the corresponding instantaneous modal frequencies and mode shapes, thus transforming the structure's dynamic equations to a modal coordinate system. In the modal coordinate system, the modal response increment within the current time increment interval is calculated using numerical integration. This modal response increment is then transformed to the physical coordinate system to obtain the response increment in the physical coordinate system. This response increment is then superimposed with the accumulated physical responses of all previous time steps to obtain the total response of the current time step. The above steps are repeated iteratively, traversing all time increment intervals, and finally, the displacement, velocity, and acceleration responses of the structure throughout the entire time history are output.

[0054] Please see Figure 6The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When executed by the processor 61, the computer program 63 implements the method for estimating the concentration of radioactive iodine species in the containment vessel after an accident, as described in this embodiment. To avoid repetition, these details are not elaborated here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the incremental modal superposition analysis system for the nonlinear dynamic response of the structure in this embodiment. To avoid repetition, these details are not elaborated here.

[0055] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 6 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0056] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0057] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or RAM of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc., provided on the computer device 60.

[0058] Furthermore, the memory 62 may include both internal storage units of the computer device 60 and external storage devices. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0059] Please see Figure 7 The terminal device is an electronic device 600, which is manifested in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including storage unit 620 and processing unit 610), a display unit 640, etc.

[0060] The storage unit stores program code, which can be executed by the processing unit 610 to perform the steps described in the method section of this specification according to various exemplary embodiments of the present invention. For example, the processing unit 610 can perform actions such as... Figure 1 The steps are shown in the figure.

[0061] Storage unit 620 may include a readable medium in the form of a volatile storage unit, such as random access memory (RAM) 6201 and / or cache memory 6202, and may further include a read-only memory (ROM) 6203.

[0062] Storage unit 620 may also include a program / utility 6204 having a set (at least one) program module 6205, such program module 6205 including but not limited to: operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.

[0063] Bus 630 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the multiple bus structures.

[0064] Electronic device 600 can also communicate with one or more external devices 700 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 600, and / or with any device that enables electronic device 600 to communicate with one or more other computing devices (e.g., router, modem). This communication can be performed via input / output interface 650. Furthermore, electronic device 600 can also communicate with one or more networks (e.g., local area network, wide area network, and / or public network, such as the Internet) via network adapter 660. Network adapter 660 can communicate with other modules of electronic device 600 via bus 630. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms.

[0065] Example 4 This invention also provides a storage medium, specifically a computer-readable storage medium, which is a memory device in a terminal device for storing programs and data. It is understood that the computer-readable storage medium here can include both built-in storage media in the terminal device and extended storage media supported by the terminal device; it can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor, which can be one or more computer programs (including program code). More specific examples of the computer-readable storage medium include: an electrical connection with one or more wires, a portable disk, a hard disk, random access memory, read-only memory, erasable programmable read-only memory, optical fiber, portable compact disk read-only memory, optical storage device, magnetic storage device, or any suitable combination thereof.

[0066] Computer-readable storage media also include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium can also be any readable medium other than a readable storage medium that can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium can be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, radio frequency, etc., or any suitable combination thereof.

[0067] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0068] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the incremental modal superposition analysis method for structural nonlinear dynamic response in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor in the following steps: A three-dimensional finite element model of the thermal protection structure is constructed. The mechanical properties of the material as a function of temperature, the structural geometric parameters, and boundary conditions are input. The initial mass matrix and initial stiffness matrix of the structure are extracted based on the initial temperature field, and the truncated mode number and damping ratio are set. The time-varying temperature field is discretized into multiple continuous time increment intervals. Within each time increment interval, the material parameters are updated according to the current temperature, thereby calculating the instantaneous mass matrix and instantaneous stiffness matrix of the structure. Within each time increment interval, eigenvalue analysis is performed based on the instantaneous mass matrix and instantaneous stiffness matrix to obtain the corresponding instantaneous modal frequencies and mode shapes, thus transforming the structure's dynamic equations to a modal coordinate system. In the modal coordinate system, the modal response increment within the current time increment interval is calculated using numerical integration. This modal response increment is then transformed to the physical coordinate system to obtain the response increment in the physical coordinate system. This response increment is then superimposed with the accumulated physical responses of all previous time steps to obtain the total response of the current time step. The above steps are repeated iteratively, traversing all time increment intervals, and finally, the displacement, velocity, and acceleration responses of the structure throughout the entire time history are output.

[0069] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchain. The processors involved in the embodiments provided in this application may be, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc.

[0070] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0071] Application examples: This example validates the effectiveness of the proposed incremental modal superposition analysis method for the nonlinear dynamic response of structures under high-temperature and variable-temperature service conditions. Please refer to [link / reference]. Figure 2 For the finite element simulation analysis model of a typical thermal protection plate structure, the incremental modal superposition method and the direct integration method are used to solve the dynamic response of the structure under time-varying temperature.

[0072] Table 1

[0073] Table 2

[0074] Boundary conditions: One end is fixed and the other end is free. The time-domain curve of the temperature load acting on the structure is as follows: Figure 3 As shown; Loading conditions: A random load spectrum is applied to the entire structure, as shown... Figure 4 As shown in Figures 5A, 5B, and 5C, the dynamic response of the structure under time-varying temperatures was solved using the incremental modal superposition method and the direct integration method based on the model. The damping ratio was set to 0.015, the solution step size was 0.0005 s, the total solution time was 5 s, and the number of cutoff modes was set to 20. The total calculation time for the incremental modal superposition method was 40.3 s, and the calculation time for the direct integration method was 127.7 s. The acceleration, velocity, and displacement response curves are shown in Figures 5A, 5B, and 5C, respectively. The root mean square values ​​of the acceleration, velocity, and displacement response curves were calculated and are shown in Table 3. The calculation results show that for this structure, the incremental modal superposition method can accurately calculate the nonlinear dynamic response of the structure under high-temperature variable temperature conditions, and the computational scale is relatively small.

[0075] Table 3

[0076] In summary, this invention provides an incremental modal superposition analysis method and system for structural nonlinear dynamic response. Compared with the traditional direct integration method, it significantly reduces the computational scale and the number of matrix operations while ensuring computational accuracy, thus greatly improving solution efficiency. This method can accurately capture the nonlinear effects of material stiffness caused by temperature changes and effectively ensure the numerical continuity and stability of the response calculation process. With its high efficiency, accuracy, and adaptability to complex service environments, this method has broad application prospects and promotional value in the analysis of thermal protection structures for hypersonic vehicles, the prediction of thermo-mechanical coupling responses of spacecraft, and the dynamic design and evaluation of other temperature-sensitive structures.

[0077] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0078] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0079] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0080] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0081] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0082] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0083] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random-access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0084] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus, and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0085] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0086] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0087] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for incremental modal superposition analysis of structural nonlinear dynamic response, characterized in that, Includes the following steps: A three-dimensional finite element model of the thermal protection structure is constructed by inputting the mechanical property parameters of the material as a function of temperature, the geometric parameters of the structure, and the boundary conditions. The initial mass matrix and initial stiffness matrix of the structure are extracted based on the initial temperature field, and the cutoff mode number and damping ratio are set. The time-varying temperature field is discretized into multiple continuous time increment intervals, and the material parameters are updated according to the current temperature in each time increment interval, thereby calculating the instantaneous mass matrix and instantaneous stiffness matrix of the structure. Within each time increment interval, eigenvalue analysis is performed based on the instantaneous mass matrix and instantaneous stiffness matrix to obtain the corresponding instantaneous modal frequencies and mode shapes, thereby transforming the structure's dynamic equations into a modal coordinate system; In the modal coordinate system, the modal response increment within the current time increment interval is calculated using the numerical integration method. The modal response increment is then transformed to the physical coordinate system to obtain the response increment in the physical coordinate system. This response increment is then superimposed with the physical responses accumulated from all previous time steps to obtain the total response of the current time step. Repeat the above steps, traversing all time increment intervals, and finally output the displacement, velocity, and acceleration response of the structure throughout the entire time history.

2. The incremental modal superposition analysis method for structural nonlinear dynamic response according to claim 1, characterized in that, The initial temperature field is obtained by transient heat transfer finite element calculation, and the initial temperature field is input as a boundary condition into the dynamic calculation process.

3. The incremental modal superposition analysis method for structural nonlinear dynamic response according to claim 1, characterized in that, Within each time increment interval, the temperature field is treated as a steady field, and transient heat transfer analysis is performed based on the finite element model to update the material parameters, which include Young's modulus, shear modulus, and coefficient of thermal expansion.

4. The incremental modal superposition analysis method for structural nonlinear dynamic response according to claim 1, characterized in that, By updating the modal basis with the structural state, the dynamic capture of material property degradation and structural stiffness nonlinear effects caused by temperature changes can be achieved. The structural state is characterized by the instantaneous mass matrix and the instantaneous stiffness matrix.

5. The incremental modal superposition analysis method for structural nonlinear dynamic response according to claim 1, characterized in that, The numerical integration method is Newmark-β. Newmark-β constructs the effective stiffness matrix and equivalent loads, solves the linear equations to obtain the system response at the next time step, and then obtains the modal response increment, using the modal displacements from the previous time step. ,speed acceleration The initial values ​​for the next time step are predicted as follows: in, For time step interval, and For integration parameters, , and Let be the modal displacement, velocity, and acceleration for the next time step, respectively.

6. The incremental modal superposition analysis method for structural nonlinear dynamic response according to claim 5, characterized in that, The integral parameters are β=0.25 and γ=0.

5.

7. The incremental modal superposition analysis method for structural nonlinear dynamic response according to claim 1, characterized in that, Before transforming the modal response increment to the physical coordinate system, the method also includes achieving seamless connection between the old and new modal bases through the modal coordinate projection matrix.

8. The incremental modal superposition analysis method for structural nonlinear dynamic response according to claim 1, characterized in that, The standard for setting the number of truncated modes is that the effective mass of the modes participating in the response calculation reaches more than 90% of the total mass of the structure.

9. The incremental modal superposition analysis method for structural nonlinear dynamic response according to claim 1, characterized in that, The boundary conditions include fixed-support boundary conditions and simply supported boundary conditions; the load forms corresponding to the time-varying temperature field include basic excitation load, inertial force and noise pressure load.

10. A system for analyzing the incremental modal superposition of structural nonlinear dynamic response, characterized in that, include: The module constructs a three-dimensional finite element model of the thermal protection structure. It inputs the mechanical property parameters of the material as a function of temperature, the geometric parameters of the structure, and the boundary conditions. Based on the initial temperature field, it extracts the initial mass matrix and initial stiffness matrix of the structure and sets the truncation mode number and damping ratio. The update module discretizes the time-varying temperature field into multiple continuous time increment intervals, and updates the material parameters according to the current temperature in each time increment interval, thereby calculating the instantaneous mass matrix and instantaneous stiffness matrix of the structure. The conversion module performs eigenvalue analysis based on the instantaneous mass matrix and instantaneous stiffness matrix within each time increment interval to obtain the corresponding instantaneous modal frequencies and mode shapes, thereby converting the structure's dynamic equations to the modal coordinate system. The overlay module calculates the modal response increment within the current time increment interval using a numerical integration method in the modal coordinate system, transforms the modal response increment to the physical coordinate system to obtain the response increment in the physical coordinate system, and overlays this response increment with the physical responses accumulated from all previous time steps to obtain the total response of the current time step. The output module executes in a loop, traversing all time increment intervals, and finally outputs the displacement, velocity, and acceleration response of the structure throughout the entire time history.

Images