Beam structure vibration process analysis method, device, computer equipment and storage medium

Abstract

The present application relates to a method, device, computer equipment and storage medium for analyzing the vibration process of a beam structure. The method comprises: obtaining the strain tensor and rotation tensor of the beam structure based on the S‑R and decomposition theorems; obtaining the incremental variation equation of the beam structure based on the strain tensor and rotation tensor; obtaining the system discrete equation during the vibration process of the beam structure based on the incremental variation equation; obtaining the node displacement increment at each moment during the vibration process of the beam structure based on the system discrete equation, the basic parameters of the beam structure and the vibration parameters at each moment during the vibration process of the beam structure. The above-mentioned method, device, computer equipment and storage medium for analyzing the vibration process of a beam structure adopt the S‑R and decomposition theorems to analyze the nonlinear large deformation vibration process of the beam structure, and the calculation results are more accurate and the analysis results are more in line with the actual situation.

Description

Technical Field

[0001] The present application relates to the technical field of nonlinear mechanics, and in particular to a method, device, computer equipment and storage medium for analyzing the vibration process of a beam structure. Background Art

[0002] In structural engineering, with the emergence of various new composite materials, structures are constantly developing in the direction of large-scale or flexibility, and the vibration problem of structures has become increasingly prominent, especially the nonlinear dynamic response plays an extremely important role in the control of structures. As one of the most basic structural units in engineering structures, beam structures are widely used in structural engineering. Therefore, studying the nonlinear dynamic characteristics of beam structures is of great significance to the design and control of engineering structures. Due to its good simplicity and effectiveness, numerical calculation plays an important role in the calculation of engineering structures. Among many methods, the finite element method (FEM) is one of the most mature and widely used numerical methods. However, the finite element has a strong dependence on the unit. For large deformation problems, the distortion of the unit will seriously affect the solution accuracy of the finite element. In addition, most of the current numerical calculation methods for beam structures are based on classical beam theory, such as Euler-Bernoulli beam theory and Timoshenko beam theory. These theories are simplified based on the small deformation linear elastic theory with appropriate assumptions, resulting in inaccurate calculation results when calculating nonlinear large deformation problems. Summary of the invention

[0003] Based on this, it is necessary to provide a beam structure vibration process analysis method, device, computer equipment and storage medium to address the technical problem that the current finite element method calculation method has inaccurate calculation results when calculating nonlinear large deformation problems.

[0004] A beam structure vibration process analysis method, the method comprising:

[0005] Based on SR and decomposition theorem, the strain tensor and rotation tensor of the beam structure are obtained;

[0006] Based on the strain tensor and the rotation tensor, the incremental variation equation of the beam structure is obtained by using the updated dragging coordinate method and the generalized Euler kinematics formula;

[0007] Based on the incremental variational equation, the moving least square method is adopted and boundary conditions are applied to obtain the system discrete equation in the vibration process of the beam structure, wherein the system discrete equation is related to the basic parameters, vibration parameters and node displacement increments of the beam structure in the vibration process;

[0008] The node displacement increments at each moment in the vibration process of the beam structure are obtained based on the system discrete equations, the basic parameters of the beam structure and the vibration parameters of the beam structure at each moment in the vibration process.

[0009] In one embodiment, the step of obtaining the strain tensor and the rotation tensor of the beam structure based on the SR and decomposition theorem includes:

[0010] The vibration process of the beam structure is described in the towing coordinate system.

[0011] In one embodiment, the basic parameters of the beam structure include a linear stiffness matrix, a nonlinear stiffness matrix, a penalty function stiffness matrix and a mass matrix, and the vibration parameters include a node acceleration, an external force vector, a stress integral vector and a penalty function force vector.

[0012] In one embodiment, the incremental variation equation of the beam structure obtained based on the strain tensor and the rotation tensor by using the updated dragging coordinate method and the generalized Euler kinematics formula includes:

[0013] Obtaining the internal force power, inertia force power and external force virtual power of the beam structure;

[0014] Based on the internal force power, inertia force power and external force virtual power of the beam structure, a variational relationship during the vibration of the beam structure is obtained;

[0015] In one embodiment, after obtaining the node displacement increments at each moment during the vibration of the beam structure, the method further includes:

[0016] Post-processing calculations of physical quantities such as strain and stress are performed based on the node displacement increments.

[0017] In one embodiment, applying the boundary conditions comprises:

[0018] Apply constant load or variable load.

[0019] In one embodiment, applying the boundary condition further comprises:

[0020] The penalty function method is used to impose displacement boundary conditions.

[0021] A beam structure vibration process analysis device, the device comprising:

[0022] Tensor acquisition module, used to obtain the strain tensor and rotation tensor of the beam structure based on SR and decomposition theorem;

[0023] An incremental variation equation acquisition module is used to obtain the incremental variation equation of the beam structure based on the strain tensor and the rotation tensor by using an updated dragging coordinate method and a generalized Euler kinematics formula;

[0024] A system discrete equation acquisition module is used to obtain the system discrete equation in the vibration process of the beam structure based on the incremental variation equation, using the moving least square method and applying boundary conditions, wherein the system discrete equation is related to the basic parameters of the beam structure, the vibration parameters and the node displacement increments in the vibration process;

[0025] The node displacement increment acquisition module is used to obtain the node displacement increment at each moment in the vibration process of the beam structure based on the system discrete equation, the basic parameters of the beam structure and the vibration parameters of the beam structure at each moment in the vibration process.

[0026] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented:

[0027] Based on SR and decomposition theorem, the strain tensor and rotation tensor of the beam structure are obtained;

[0028] Based on the strain tensor and the rotation tensor, the incremental variation equation of the beam structure is obtained by using the updated dragging coordinate method and the generalized Euler kinematics formula;

[0029] Based on the incremental variational equation, the moving least square method is adopted and boundary conditions are applied to obtain the system discrete equation in the vibration process of the beam structure, wherein the system discrete equation is related to the basic parameters, vibration parameters and node displacement increments of the beam structure in the vibration process;

[0030] The node displacement increments at each moment in the vibration process of the beam structure are obtained based on the system discrete equations, the basic parameters of the beam structure and the vibration parameters of the beam structure at each moment in the vibration process.

[0031] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the following steps:

[0032] Based on SR and decomposition theorem, the strain tensor and rotation tensor of the beam structure are obtained;

[0033] Based on the strain tensor and the rotation tensor, the incremental variation equation of the beam structure is obtained by using the updated dragging coordinate method and the generalized Euler kinematics formula;

[0034] Based on the incremental variational equation, the moving least square method is adopted and boundary conditions are applied to obtain the system discrete equation in the vibration process of the beam structure, wherein the system discrete equation is related to the basic parameters, vibration parameters and node displacement increments of the beam structure in the vibration process;

[0035] The node displacement increments at each moment in the vibration process of the beam structure are obtained based on the system discrete equations, the basic parameters of the beam structure and the vibration parameters of the beam structure at each moment in the vibration process.

[0036] The above-mentioned beam structure vibration process analysis method, device, computer equipment and storage medium obtain the strain tensor and rotation tensor of the beam structure by adopting SR and decomposition theorem, and based on the strain tensor and rotation tensor, adopt the updated dragging coordinate method and the generalized Euler kinematics formula to obtain the incremental variation equation of the beam structure. Based on the incremental variation equation, the moving least squares method is adopted and boundary conditions are applied to obtain the system discrete equation in the beam structure vibration process, and the method of obtaining the node displacement increment based on the system discrete equation is used to analyze the nonlinear large deformation vibration process of the beam structure, so that the calculation result is more accurate and the analysis result is more in line with the actual situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A schematic diagram of a flow chart of a beam structure vibration process analysis method according to an embodiment of the present invention;

[0038] Figure 2 A schematic diagram of a towing coordinate system of a beam structure vibration process analysis method according to an embodiment of the present invention;

[0039] Figure 3 is a schematic diagram of a beam structure according to an embodiment of the present invention;

[0040] Figure 4 A schematic diagram of a constant force load in a beam structure vibration process analysis method according to an embodiment of the present invention;

[0041] Figure 5 A schematic diagram of the variation of node displacement increments of a beam structure with time according to an embodiment of the present invention;

[0042] Figure 6 A schematic diagram of a pulse load of a beam structure vibration process analysis method according to another embodiment of the present invention;

[0043] Figure 7 A schematic diagram of the variation of node displacement increments over time obtained by analyzing the beam structure vibration process analysis method according to another embodiment of the present invention;

[0044] Figure 8 This is a schematic diagram of the change of node displacement increment over time obtained by traditional analytical method;

[0045] Fig. 9 It is a structural block diagram of a beam structure vibration process analysis device according to an embodiment of the present invention;

[0046] Fig.10 FIG. 4 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0048] See also Figure 1 , Figure 1 The figure is a flow chart of a beam structure vibration process analysis method according to an embodiment of the present invention.

[0049] In this embodiment, the beam structure vibration process analysis method includes:

[0050] Step 100, based on SR and decomposition theorem, obtain the strain tensor and rotation tensor of the beam structure.

[0051] SR and decomposition theorem proof: Given a possible displacement function, this function is single-valued and continuous in the domain of the deformed point set, and has a first-order derivative everywhere, then this motion transformation can always be uniquely decomposed into the direct sum of orthogonal and symmetric transformations. Orthogonal transformations represent the rotation of point sets, while symmetric transformations represent the deformation of point sets.

[0052] Step 110: Based on the strain tensor and the rotation tensor, an incremental variation equation of the beam structure is obtained by using an updated dragging coordinate method and a generalized Euler kinematics formula.

[0053] The calculus of variations is a branch of mathematics that developed in the late 17th century. It is a field of mathematics that deals with functions, as opposed to ordinary calculus, which deals with functions of numbers. It ultimately seeks extremal functions: functions that make functionals reach their maximum or minimum values. The calculus of variations originated from some specific physics problems, which were eventually studied and solved by mathematicians. Some classic problems on curves are expressed in this form: an example is the brachistocentre, the path along which a particle can travel from point A to a point B not directly below it in the shortest time under the influence of gravity. The expression representing the descent time must be minimized in all curves from A to B.

[0054] In this embodiment, the variation of the incremental variation equation is velocity.

[0055] Step 120, based on the incremental variation equation, using the moving least squares method and applying boundary conditions, obtain the system discrete equation during the vibration process of the beam structure, wherein the system discrete equation is related to the basic parameters, vibration parameters and node displacement increments of the beam structure during the vibration process.

[0056] It can be understood that the boundary conditions are external working conditions in actual situations, specifically, displacement or load conditions, such as how much load is applied to a certain position of the structure.

[0057] Step 130, obtaining the node displacement increments at each moment in the vibration process of the beam structure based on the system discrete equations, the basic parameters of the beam structure, and the vibration parameters at each moment in the vibration process of the beam structure.

[0058] Specifically, the basic parameters of the beam structure and the vibration parameters of the beam structure at each moment during the vibration process are substituted into the system discrete equation, and the node displacement increment at each moment during the vibration process of the beam structure can be solved.

[0059] The above-mentioned analytical method for the vibration process of the beam structure adopts SR and decomposition theorem to obtain the strain tensor and rotation tensor of the beam structure, and based on the strain tensor and rotation tensor, adopts the updated dragging coordinate method and the generalized Euler kinematics formula to obtain the incremental variation equation of the beam structure, and based on the incremental variation equation, adopts the moving least squares method and applies boundary conditions to obtain the system discrete equation in the vibration process of the beam structure, and obtains the method of node displacement increment based on the system discrete equation, so as to analyze the nonlinear large deformation vibration process of the beam structure, and the calculation result is more accurate and the analytical result is more in line with the actual situation.

[0060] It can be understood that before step 100, the vibration process of the beam structure is also placed in the towing coordinate system for description. Figure 2 , Figure 2 It is a schematic diagram of a dragging coordinate system of a beam structure vibration process analysis method according to an embodiment of the present invention.

[0061] In another embodiment, obtaining the strain tensor and rotation tensor of the beam structure based on the SR and decomposition theorem specifically includes:

[0062] It is directly given by SR and the decomposition theorem:

[0063] Strain tensor:

[0064] Rotate a tensor:

[0065] Among them, u i | j is the displacement component; is the Kronecker symbol; is the axis unit vector

[0066]

[0067] Where θ is the average rotation angle

[0068]

[0069] In another embodiment, based on the strain tensor and the rotation tensor, the incremental variation equation of the beam structure is obtained by using the updated dragging coordinate method and the generalized Euler kinematics formula, including obtaining the internal force power, inertia force power and external force imaginary power of the beam structure; obtaining the variational relationship of the beam structure during vibration based on the internal force power, inertia force power and external force imaginary power of the beam structure; and obtaining the incremental variation equation of the beam structure based on the strain tensor, the rotation tensor and the variational relationship. Specifically including:

[0070] Based on the potential energy rate principle, the variation at time t+Δt is

[0071]

[0072] In formula (5), δ is the variation symbol; J is the functional; is the stress tensor; t+Δt V j || i Indicates the speed at time t+Δt t+Δt V i On the Covariant Basis Vector of the Drag System at Time t+Δt t+Δt g i The covariant derivative of ; t+Δt W ine and t+Δt W ext are inertia force power and external force virtual power respectively

[0073] t+Δt W ine =∫ Ω(t+Δt) ρ t+Δt A i δ t+Δt V i dΩ (6)

[0074]

[0075] Where ρ is the density; A i is the acceleration; P and f are the surface force and body force respectively.

[0076] Based on the updated dragging coordinate method and the generalized Euler kinematics formula, combined with the stress-strain constitutive relation, the geometric equations (1) and (2) are substituted into equation (5), and appropriate assumptions and simplifications are used to obtain the incremental variation equation of the global weak form meshless method:

[0077]

[0078] The superscript “-” indicates that the corresponding physical quantity is in the initial towing coordinate system at time t. The physical quantity below; is the elastic matrix; and represent the strain rate and rotation rate, respectively.

[0079] Exemplarily, based on the incremental variation equation, the moving least squares method is adopted, and boundary conditions are applied to obtain the system discrete equation in the vibration process of the beam structure, which specifically includes:

[0080] The moving least squares method is used to discretize the field quantity, and the penalty function method is used to impose the displacement boundary condition to obtain the system discrete equation

[0081] [ t K L - t K N +K α ]{ t Δu}+ t M t+Δt A= t+Δt R- t F+F α (9)

[0082] in, t K L , t K N , K α , t M are the linear stiffness matrix, nonlinear stiffness matrix, penalty function stiffness matrix, and mass matrix respectively; t Δu represents the node displacement increment, which is generally an unknown quantity; t+Δt A is the node acceleration, which is the dynamic term in the system equation and is calculated using the Newmark method; t+Δt R. t F.K α are the external force vector, stress integral vector, and penalty function force vector respectively. The system equation (9) is the standard calculation format of the analytical method for the vibration process of beam structures and can be directly used in the design of numerical programs.

[0083] Specifically, applying boundary conditions includes applying a constant force load or a variable force load.

[0084] It can be understood that by substituting the linear stiffness matrix, nonlinear stiffness matrix, penalty function stiffness matrix, mass matrix, node acceleration, external force vector, stress integral vector and penalty function force vector into equation (9), the node displacement increment can be obtained: t Δu.

[0085] In another embodiment, after obtaining the node displacement increments at each moment during the vibration process of the beam structure, a post-processing calculation of physical quantities such as strain and stress based on the node displacement increments is also included. Specifically, a graph of the node displacement increments and time during the vibration process of the beam structure can be drawn based on the node displacement increments, that is, the node displacement increments at each moment are matched with time to observe the changes of the node displacement increments over time. It can be understood that in other embodiments, other post-processing calculation methods can be used.

[0086] See also Figures 3 to 5 , Figure 3 is a schematic diagram of a beam structure according to an embodiment of the present invention, Figure 4 Schematic diagram of a constant force load in a beam structure vibration process analysis method according to an embodiment of the present invention, Figure 5 Schematic diagram of the variation of node displacement increment of a beam structure with time according to an embodiment of the present invention. Specifically, the beam structure is a cantilever beam, where L and D represent the length and width of the cantilever beam, respectively, and E, μ, and ρ represent Young's modulus, Poisson's ratio, and density, respectively. The basic parameters of the beam structure are: L = 10m, D = 1m, E = 3×10 7 Pa, μ=0.34, ρ=1000kg / m 3 A constant vertical load (1×10 4 Pa), action time 10s, such as Figure 4 shown. Figure 5 The comparison curves of the displacement increment of the midpoint of the right end of the cantilever beam calculated by the method of the present invention and the abaqus method over time are given in the figure.

[0087] See also Figures 6 to 8 , Figure 6 Schematic diagram of pulse load of a beam structure vibration process analysis method according to another embodiment of the present invention, Figure 7 This is a schematic diagram of the variation of node displacement increments over time obtained by analyzing the beam structure vibration process analysis method according to another embodiment of the present invention. Figure 8 Schematic diagram of the variation of node displacement increments over time obtained by traditional analytical methods. It can be understood that the beam structure of this embodiment is also Figure 3 The basic parameters of the cantilever beam are: L = 48m, D = 12m, E = 3×10 7 Pa,μ=0.3,ρ=1000kg / m 3 The right end of the cantilever beam is subjected to Figure 6 Triangular pulse load shown. Figure 7 , Figure 8 The curve diagrams of the displacement enhancement of the midpoint of the right end of the beam versus time obtained by the beam structure vibration process analysis method of the present invention and the traditional analysis method are compared and it can be obtained that the two have a good degree of agreement.

[0088] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0089] In one embodiment, Fig. 9 As shown, a beam structure vibration process analysis device is provided, comprising: a tensor acquisition module 200, an incremental variational equation acquisition module 210, a system discrete equation acquisition module 220 and a node displacement increment acquisition module 230, wherein:

[0090] The tensor acquisition module 200 is used to obtain the strain tensor and rotation tensor of the beam structure based on SR and decomposition theorem.

[0091] The incremental variation equation acquisition module 210 is used to obtain the incremental variation equation of the beam structure based on the strain tensor and the rotation tensor by using the updated dragging coordinate method and the generalized Euler kinematics formula.

[0092] The incremental variation equation acquisition module 210 is further used for:

[0093] Obtaining the internal force power, inertia force power and external force virtual power of the beam structure;

[0094] Based on the internal force power, inertia force power and external force virtual power of the beam structure, a variational relationship during the vibration of the beam structure is obtained;

[0095] Based on the strain tensor, rotation tensor and variational relationship, an incremental variational equation of the beam structure is obtained.

[0096] The system discrete equation acquisition module 220 is used to obtain the system discrete equation during the vibration process of the beam structure based on the incremental variation equation, using the moving least squares method and applying boundary conditions. The system discrete equation is related to the basic parameters, vibration parameters and node displacement increments of the beam structure during the vibration process.

[0097] The node displacement increment acquisition module 230 is used to obtain the node displacement increment at each moment in the vibration process of the beam structure based on the system discrete equation, the basic parameters of the beam structure and the vibration parameters of the beam structure at each moment in the vibration process.

[0098] For the specific definition of the beam structure vibration process analysis device, please refer to the definition of the beam structure vibration process analysis method mentioned above, which will not be repeated here. Each module in the above-mentioned beam structure vibration process analysis device can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0099] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as follows: Fig.10 As shown. The computer device includes a processor, a memory, a network interface, a display screen and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a method for analyzing the vibration process of a beam structure is implemented. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covering the display screen, or a button, trackball or touchpad set on the computer device housing, or an external keyboard, touchpad or mouse, etc.

[0100] Those skilled in the art will understand that Fig.10 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0101] In one embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, the following steps are implemented:

[0102] Based on SR and decomposition theorem, the strain tensor and rotation tensor of the beam structure are obtained;

[0103] Based on the strain tensor and the rotation tensor, the incremental variation equation of the beam structure is obtained by using the updated dragging coordinate method and the generalized Euler kinematics formula;

[0104] Based on the incremental variational equation, the moving least square method is adopted and boundary conditions are applied to obtain the system discrete equation in the vibration process of the beam structure, wherein the system discrete equation is related to the basic parameters, vibration parameters and node displacement increments of the beam structure in the vibration process;

[0105] The node displacement increments at each moment in the vibration process of the beam structure are obtained based on the system discrete equations, the basic parameters of the beam structure and the vibration parameters of the beam structure at each moment in the vibration process.

[0106] In one embodiment, when the processor executes the computer program, the following steps are also implemented:

[0107] The vibration process of the beam structure is described in the towing coordinate system.

[0108] In one embodiment, when the processor executes the computer program, the following steps are also implemented:

[0109] Obtaining the internal force power, inertia force power and external force virtual power of the beam structure;

[0110] Based on the internal force power, inertia force power and external force virtual power of the beam structure, a variational relationship during the vibration of the beam structure is obtained;

[0111] Based on the strain tensor, rotation tensor and variational relationship, an incremental variational equation of the beam structure is obtained.

[0112] In one embodiment, when the processor executes the computer program, the following steps are also implemented:

[0113] Post-processing calculations of physical quantities such as strain and stress are performed based on the node displacement increments.

[0114] In one embodiment, when the processor executes the computer program, the following steps are also implemented:

[0115] Apply constant load or variable load.

[0116] In one embodiment, when the processor executes the computer program, the following steps are also implemented:

[0117] The penalty function method is used to impose displacement boundary conditions.

[0118] In one embodiment, a computer readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, the following steps are implemented:

[0119] Based on SR and decomposition theorem, the strain tensor and rotation tensor of the beam structure are obtained;

[0120] Based on the strain tensor and the rotation tensor, the incremental variation equation of the beam structure is obtained by using the updated dragging coordinate method and the generalized Euler kinematics formula;

[0121] Based on the incremental variational equation, the moving least square method is adopted and boundary conditions are applied to obtain the system discrete equation in the vibration process of the beam structure, wherein the system discrete equation is related to the basic parameters, vibration parameters and node displacement increments of the beam structure in the vibration process;

[0122] The node displacement increments at each moment in the vibration process of the beam structure are obtained based on the system discrete equations, the basic parameters of the beam structure and the vibration parameters of the beam structure at each moment in the vibration process.

[0123] In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

[0124] The vibration process of the beam structure is described in the towing coordinate system.

[0125] In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

[0126] Obtaining the internal force power, inertia force power and external force virtual power of the beam structure;

[0127] Based on the internal force power, inertia force power and external force virtual power of the beam structure, a variational relationship during the vibration of the beam structure is obtained;

[0128] Based on the strain tensor, rotation tensor and variational relationship, an incremental variational equation of the beam structure is obtained.

[0129] In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

[0130] Post-processing calculations of physical quantities such as strain and stress are performed based on the node displacement increments.

[0131] In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

[0132] Apply constant load or variable load.

[0133] In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

[0134] The penalty function method is used to impose displacement boundary conditions.

[0135] The above-mentioned beam structure vibration process analysis method, device, computer equipment and storage medium obtain the strain tensor and rotation tensor of the beam structure by adopting SR and decomposition theorem, and based on the strain tensor and rotation tensor, adopt the updated dragging coordinate method and the generalized Euler kinematics formula to obtain the incremental variation equation of the beam structure. Based on the incremental variation equation, the moving least squares method is adopted and boundary conditions are applied to obtain the system discrete equation in the beam structure vibration process, and the method of obtaining the node displacement increment based on the system discrete equation is used to analyze the nonlinear large deformation vibration process of the beam structure, so that the calculation result is more accurate and the analysis result is more in line with the actual situation.

[0136] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database 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. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0137] The technical features of the above embodiments may be arbitrarily combined. To make the description concise, 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.

[0138] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A beam structure vibration process analysis method, characterized in that: The method comprises: Based on SR and decomposition theorem, the strain tensor and rotation tensor of the beam structure are obtained; Based on the strain tensor and the rotation tensor, the incremental variation equation of the beam structure is obtained by using the updated dragging coordinate method and the generalized Euler kinematics formula; Based on the incremental variational equation, the moving least square method is adopted and boundary conditions are applied to obtain the system discrete equation in the vibration process of the beam structure, wherein the system discrete equation is related to the basic parameters, vibration parameters and node displacement increments of the beam structure in the vibration process; The node displacement increments at each moment in the vibration process of the beam structure are obtained based on the system discrete equations, the basic parameters of the beam structure and the vibration parameters of the beam structure at each moment in the vibration process.

2. The beam structure vibration process analysis method according to claim 1, characterized in that: The method for obtaining the strain tensor and rotation tensor of the beam structure based on SR and decomposition theorem includes: The vibration process of the beam structure is described in the towing coordinate system.

3. The beam structure vibration process analysis method according to claim 1, characterized in that: The basic parameters of the beam structure include a linear stiffness matrix, a nonlinear stiffness matrix, a penalty function stiffness matrix and a mass matrix, and the vibration parameters include a node acceleration, an external force vector, a stress integral vector and a penalty function force vector.

4. The beam structure vibration process analysis method according to claim 1, characterized in that: The incremental variation equation of the beam structure obtained based on the strain tensor and the rotation tensor by using the updated dragging coordinate method and the generalized Euler kinematics formula includes: Obtaining the internal force power, inertia force power and external force virtual power of the beam structure; Based on the internal force power, inertia force power and external force virtual power of the beam structure, a variational relationship during the vibration of the beam structure is obtained; Based on the strain tensor, rotation tensor and variational relationship, an incremental variational equation of the beam structure is obtained.

5. The beam structure vibration process analysis method according to claim 1, characterized in that: After obtaining the node displacement increments at each moment during the vibration process of the beam structure, the method further includes: Post-processing calculations of strain and stress physical quantities are performed based on the node displacement increments.

6. The beam structure vibration process analysis method according to claim 1, characterized in that: The applied boundary conditions include: Apply constant load or variable load.

7. The beam structure vibration process analysis method according to any one of claims 1 to 6, characterized in that: The applied boundary conditions include: The penalty function method is used to impose displacement boundary conditions.

8. A beam structure vibration process analysis device, characterized in that: The device comprises: Tensor acquisition module, used to obtain the strain tensor and rotation tensor of the beam structure based on SR and decomposition theorem; An incremental variation equation acquisition module is used to obtain the incremental variation equation of the beam structure based on the strain tensor and the rotation tensor by using an updated dragging coordinate method and a generalized Euler kinematics formula; A system discrete equation acquisition module is used to obtain the system discrete equation in the vibration process of the beam structure based on the incremental variation equation, using the moving least square method and applying boundary conditions, wherein the system discrete equation is related to the basic parameters of the beam structure, the vibration parameters and the node displacement increments in the vibration process; The node displacement increment acquisition module is used to obtain the node displacement increment at each moment in the vibration process of the beam structure based on the system discrete equation, the basic parameters of the beam structure and the vibration parameters of the beam structure at each moment in the vibration process.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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