Analysis device, program, and analysis method

Abstract

To provide an analysis device, a program, and an analysis method capable of analyzing a three-dimensional movement of an analysis object with numerical stability.SOLUTION: An analysis device, which analyzes a three-dimensional movement of an analysis object, executes an input accepting process for accepting input of analysis condition information containing data regarding analysis conditions of the analysis object, an analysis process for performing finite element analysis on the basis of the analysis condition information accepted by the input accepting process, and an output process for outputting analysis information obtained by the analysis of the analysis process. The analysis process implements finite element analysis by time integrating a motion equation being discretized so as to satisfy an energy principle, a momentum principle, and an angular momentum principle.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to an analysis device, a program, and an analysis method, and more particularly to an analysis device, a program, and an analysis method for analyzing the three-dimensional movement of an object to be analyzed. [Background technology]

[0002] For example, depending on various purposes, such as analyzing the strength of parts or analyzing the movement or behavior of objects, the forces acting on the parts, objects, etc., and the movement or behavior of the objects are simulated and analyzed.

[0003] Patent Document 1 discloses a technology for simulating extremely low cycle fatigue failure of a mechanical component, which may occur during the strength design of the mechanical component, by using a finite element analysis model of the mechanical component as the object of analysis. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2016-4543 A Summary of the Invention [Problem to be solved by the invention]

[0005] Incidentally, the movement of extremely flexible objects such as thin films or cables, or the movement of rigid structures that include such objects as part of their structure, such as when they are unfolded from a folded state, includes large movements of the entire object as well as tiny local vibrations of the object as elements.

[0006] When numerically analyzing such motion (motion with high geometric nonlinearity), the equations of motion become so-called "rigid equations" that are numerically unstable, meaning that the solutions will diverge unless the finite time interval is made extremely small, making the calculations extremely difficult.

[0007] Therefore, when numerically analyzing the movement of this type of object or structure, the calculations may diverge during the calculation process, which raises concerns that it may not be possible to correctly analyze events that are difficult to predict and that may occur in this type of object.

[0008] The present invention has been made in consideration of the above circumstances, and its objective is to provide an analysis device, program, and analysis method that can analyze the three-dimensional movement of an object to be analyzed with numerical stability. [Means for solving the problem]

[0009] In order to achieve the above-mentioned object, the analysis device of the present invention is an analysis device that analyzes the three-dimensional movement of an object to be analyzed, and executes an input reception process that receives input of analysis condition information including data related to the analysis conditions of the object to be analyzed, an analysis process that performs finite element analysis on the object to be analyzed based on the analysis condition information received in the input reception process, and an output process that outputs the analysis information analyzed in the analysis process, and the analysis process performs finite element analysis by time integrating the equations of motion that have been discretized to satisfy the energy principle, momentum principle, and angular momentum principle.

[0010] According to this, when the equations of motion that have been discretized to satisfy the energy principle, momentum principle, and angular momentum principle for the object being analyzed are integrated over time, energy is conserved during the calculation, so the calculation does not diverge and numerical stability is achieved in the analysis results.

[0011] Therefore, even if the object to be analyzed has flexibility that makes calculations difficult, the three-dimensional motion of such an object to be analyzed can be analyzed appropriately with numerical stability.

[0012] The analysis processing of this analysis device includes outputting a moving image relating to the movement of the object to be analyzed as analysis information, and the object to be analyzed may be a gossamer structure or a gossamer multi-body structure comprising a gossamer structure.

[0013] In order to achieve the above-mentioned object, the program of the present invention is a program for analyzing the three-dimensional motion of an object to be analyzed, and causes an analysis device implemented by a computer to execute an input reception process for receiving input of analysis condition information including data related to the analysis conditions of the object to be analyzed, an analysis process for performing finite element analysis on the object to be analyzed based on the analysis condition information received in the input reception process, and an output process for outputting the analysis information analyzed in the analysis process, wherein the analysis process performs finite element analysis by time integrating the equations of motion that have been discretized to satisfy the energy principle, momentum principle, and angular momentum principle.

[0014] In order to achieve the above-mentioned object, the analysis method of the present invention is an analysis method for analyzing the three-dimensional movement of an object to be analyzed, in which an analysis device implemented by a computer executes an input reception process for receiving input of analysis condition information including data related to the analysis conditions of the object to be analyzed, an analysis process for performing finite element analysis on the object to be analyzed based on the analysis condition information received in the input reception process, and an output process for outputting the analysis information analyzed in the analysis process, and the analysis process performs finite element analysis by time integrating the equations of motion that have been discretized to satisfy the energy principle, momentum principle, and angular momentum principle. [Effects of the Invention]

[0015] According to the present invention, the three-dimensional motion of an object to be analyzed can be analyzed appropriately with numerical stability. [Brief explanation of the drawings]

[0016] [Figure 1] 1 is a block diagram illustrating an overview of an analysis device according to an embodiment of the present invention. [Figure 2] FIG. 10 is a diagram for explaining the outline of the configuration of an object to be analyzed by the analysis device according to the present embodiment. [Figure 3] FIG. 2 is a block diagram illustrating an outline of the configuration of an analysis device according to the present embodiment. [Figure 4] FIG. 2 is a block diagram for explaining an outline of the functions of the analysis device according to the present embodiment. [Figure 5] FIG. 10 is a diagram for explaining an outline of the processing of the analysis device according to the present embodiment. [Figure 6] FIG. 10 is a diagram for explaining an outline of the processing of the analysis device according to the present embodiment. [Figure 7] 10 is a flowchart outlining the processing of the analysis device according to the present embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0017] Next, an analysis device according to an embodiment of the present invention will be described with reference to FIGS.

[0018] 1 is a block diagram illustrating an outline of an analysis device according to the present embodiment. As shown in the figure, analysis device 10 is a device that analyzes the three-dimensional movement of an existing analysis object 100 by simulation based on the operation of user 1.

[0019] In this embodiment, the object to be analyzed 100 is a gossamer structure such as a membrane or cable having extremely flexible properties, or a gossamer multi-body structure that includes this gossamer structure, and analysis is performed by the analysis device 10 using a simulation model in which this gossamer structure or gossamer multi-body structure is simulated.

[0020] 2 is a diagram illustrating the outline of the configuration of a gossamer structure and a gossamer multi-body structure. As shown in the figure, the gossamer structure 110 in this embodiment is a flexible and lightweight membrane-like tensile material 111, but is not limited to this and may be other tensile materials such as a cable or a tube.

[0021] Such a gossamer structure 110 is lightweight, easy to deploy, and easy to store, and has been used conventionally as a structural format for space structures, for example, in a gossamer multibody structure 120 as shown in Figure 2 that deploys and contracts in space.

[0022] In this embodiment, the gossamer multi-body structure 120 includes, for example, three hubs 121, a boom 122 mounted on the hubs 121, and a membrane-like gossamer structure 110 provided on the hubs 121, and is formed in a truss shape when viewed from above.

[0023] In this gossamer multibody structure 120, when a boom 122 is wound around a hub 121, the gossamer structure 110 contracts, and when the boom 122 wound around the hub 121 is extended, the gossamer structure 110 unfolds.

[0024] Although such gossamer structures 110 or gossamer multibody structures 120 have attracted attention as structural styles or space structures, due to their characteristics of being lightweight, deployable, and easy to store, they are strongly affected by gravity and air, making demonstration experiments on the ground difficult.

[0025] On the other hand, when implementing it in space, it is essential to predict its behavior in actual space, and simulation analysis is one method for predicting its behavior in space.

[0026] The gossamer multibody structure is not limited to the above structure, but may be any of various gossamer multibody structures used in outer space.

[0027] In this embodiment, the analysis device 10 shown in FIG. 1 is implemented by a computer, for example, a desktop or notebook computer.

[0028] 3 is a block diagram illustrating an outline of the configuration of the analysis device 10. As shown in the figure, the analysis device 10 mainly comprises a processor 11, a memory 12, a storage 13, a transmission / reception unit 14, and an input / output unit 15, which are electrically connected to each other via a bus 16.

[0029] The processor 11 is a computing device that controls the operation of the analysis device 10, controls the transmission and reception of data between the elements, and performs processing required to execute application programs.

[0030] In this embodiment, the processor 11 is, for example, a CPU (Central Processing Unit), and executes application programs deployed in a memory 12 (to be described later) to perform various processes.

[0031] The memory 12 is implemented by a main storage device that is configured as a volatile storage device such as a DRAM (Dynamic Random Access Memory).

[0032] The memory 12 is used as a working area for the processor 11, and also stores a BIOS (Basic Input / Output System) that is executed when the information processing device 30 is started up, various setting information, and the like.

[0033] The storage 13 stores data and the like used for various processes by application programs and the like.

[0034] The transmitting / receiving unit 14 connects the analysis device 10 to a network. The transmitting / receiving unit 14 may be compatible with a wireless communication standard such as Wi-Fi, or may be equipped with a short-range communication interface such as Bluetooth (registered trademark) or BLE (Bluetooth Low Energy).

[0035] If necessary, information input devices such as a keyboard and a mouse and output devices such as a display are connected to the input / output unit 15. In this embodiment, a keyboard, a mouse, and a display are connected.

[0036] The bus 16 transmits, for example, address signals, data signals, and various control signals between the processor 11, memory 12, storage 13, transmission / reception unit 14, and input / output unit 15 that are connected to it.

[0037] 4 is a block diagram illustrating an outline of the functions of analysis device 10. As shown in the figure, analysis device 10 includes an input receiving unit 10a, a simulation information storage unit 10b, an analysis condition information storage unit 10c, an analysis unit 10d, and an output unit 10e.

[0038] The simulation information storage unit 10b and the analysis condition information storage unit 10c are realized by partitioning the memory area of ​​the storage 13, and the input receiving unit 10a, the analysis unit 10d, and the output unit 10e are realized by executing the programs stored in the memory 12 by the processor 11.

[0039] In this embodiment, the input receiving unit 10a executes a process of receiving input of simulation information related to a simulation model of the gossamer structure 110 and the gossamer multibody structure 120 as the analysis object 100 (input receiving process).

[0040] Furthermore, in this embodiment, the input receiving unit 10a executes a process of receiving input of analysis condition information relating to the analysis conditions of the gossamer structure 110 and the gossamer multibody structure 120 (input receiving process).

[0041] In this embodiment, the simulation information storage unit 10b stores the simulation information received by the input receiving unit 10a. This simulation information is, for example, a simulation model of the gossamer structure 110 and the gossamer multibody structure 120.

[0042] The analysis condition information storage unit 10c stores the analysis condition information received by the input receiving unit 10a. In this embodiment, this analysis condition information includes, for example, element data, node data, constraint condition data, and material data.

[0043] The element data is data obtained by dividing the object to be analyzed 100 into a finite number of elements, and the node data is data related to the positions on the boundaries between each element, and includes, for example, countable vectors related to positions and relative rotation angles, modified Rodrigues vectors related to spatial rotation and local rotation, etc.

[0044] The constraint condition data is data relating to the conditions for constraining (fixing) the object to be analyzed 100 in three-dimensional space, and the material data is data relating to the material of the object to be analyzed 100, and includes, for example, material constants and step increment values.

[0045] In this embodiment, the analysis unit 10d performs finite element analysis on the analysis object 100 based on the simulation information and analysis condition information received by the input reception unit 10a.

[0046] The mathematical expressions used to explain this finite element analysis are shown in Table 1. [Table 1]

[0047] Generally, when finite element analysis is performed to analyze the three-dimensional motion of an object (object to be analyzed) by simulation, the following equation of motion (1) is solved.

number

[0048] In this case, the equation of motion (1) is said to satisfy the energy principle, momentum principle, and angular momentum principle.

[0049] The energy principle that is said to be satisfied by this equation of motion (1) is that "the rate of change of mechanical energy over time is equal to the power due to a non-conservative external force," and is expressed by the following equation (2).

number

[0050] The momentum principle, which is said to be satisfied by the equation of motion (1), is that "the time rate of change of momentum is equal to the sum of the external forces," and is expressed by the following equation (3).

number

[0051] The angular momentum principle that is satisfied by the equation of motion (1) is that "the time rate of change of angular momentum is equal to the sum of the moments of external forces," and is expressed by the following equation (4).

number

[0052] Incidentally, although the above equation of motion (1) can be defined so as to satisfy the energy principle, momentum principle, and angular momentum principle in terms of the instantaneous rate of change over time, when an object to be analyzed moves in a highly geometrically nonlinear manner, if one tries to analyze this movement, the equation becomes a "rigid equation" as described above.

[0053] In the first place, solving the equation of motion (1) leads to numerical instability. However, when trying to solve the "stiff equations," as shown in Figure 5, there is a concern that even in a conservative system, the energy increases during the calculation, causing the calculation to diverge even further, making the calculation extremely difficult, resulting in even greater numerical instability.

[0054] Therefore, it is possible to derive a discretized equation of motion that satisfies the energy principle, momentum principle, and angular momentum principle in an incremental relationship so that energy does not fluctuate during the calculation (energy momentum method), and then solve the derived discretized equation of motion to ensure stability in the calculation.

[0055] In this embodiment, when performing finite element analysis to analyze the three-dimensional movement of the object to be analyzed 100 by simulation, the analysis unit 10d performs the analysis by solving the equations of motion formulated by the energy momentum method (analysis processing).

[0056] Discretized equations of motion are formulated that satisfy the incremental energy principle, momentum principle, and angular momentum principle.

[0057] First, the incremental energy principle states that "the increment of mechanical energy is equal to the power due to a non-conservative external force," and is expressed by the following equation (5).

number

[0058] The momentum principle of incremental relationships states that "the increment of momentum is equal to the sum of the impulses due to external forces," and is expressed by the following equation (6).

number

[0059] The principle of incremental angular momentum states that "the increment of angular momentum is equal to the sum of the angular impulses of the external forces," and is expressed by the following equation (7).

number

[0060] Here, since it is not possible to integrate the equation of motion (1) so as to satisfy the incremental energy principle, momentum principle, and angular momentum principle, in order to solve the equation of motion (1), a discretized equation of motion is derived by solving the following discretized virtual work principle (8).

number

[0061] First, the mechanical energy increment ΔΠ, momentum increment ΔP, and angular momentum ΔL are formulated. Generally, in nonlinear finite element analysis, the mechanical energy ΔΠ is expressed by the following equation (9).

number

[0062] Therefore, the increment is

number

[0063] In this case, the term with a tilde above the partial differential can be expressed as a discrete differential that satisfies the following equation (11).

number

[0064] therefore,

number

[0065] At this time, the potential energy U in As a property of , the following relationship holds.

number

number

[0066] Next, the momentum and angular momentum are

number

number

[0067] In this case, the increment of mechanical energy is calculated using the discretized internal force as follows:

number

number

number

number

number

[0068] Applying these to each increment equation,

number

number

number

[0069] In this case, if we consider equations (13) and (14), it is obvious that equation (23) holds true. Therefore, in order for the increments of mechanical energy and angular momentum to hold, we need only satisfy the following equations (25) and (26).

number

number

[0070] So, for any p,

number

number

[0071] This equation (28) is satisfied by defining each variable as shown in the following equations (29) to (32).

number

number

number

number

[0072] In this case, Δθ is a parameter that satisfies equations (29) to (32). p If we adopt the modified Rodrigues parameter #1, Δθ p The existence of can be confirmed.

[0073] Furthermore, the properties of orthonormal basis matrices are as follows:

number

number

[0074] From the above, the increments of mechanical energy, momentum and angular momentum are

number

number

number

[0075] From the above, we have completed the formulation of internal forces that satisfy the incremental form of mechanical energy, momentum, and angular momentum.

[0076] Next, we will consider the formulation of discretized external forces. To formulate external forces, we consider the increment of external work. Generally, external forces are conservative external forces ΔW C and non-conservative external force ΔW nc Since it is composed of two components, the increment of external work can be written as the following equation (38).

number

[0077] In this equation (38), if we consider the work due to conservative external forces, we get

number

number

number

[0078] Furthermore, the non-conservative external force ΔW nc Regarding, if we use the trapezoidal rule to approximate,

number

number

number

number

[0079] From the above, the formulation of the discretized external force is complete.

[0080] By the way, by finding the discretized internal and external forces, it can be seen that the principle of virtual work shown in equation (8) is synonymous with the incremental energy principle shown in equation (5). Whether or not the incremental momentum principle and angular momentum principle shown in equations (6) and (7) are satisfied when solving the principle of virtual work depends on whether or not the following equations (46) and (47) are established.

number

number

[0081] Since this condition is synonymous with the condition for the equation of motion (1) to hold, the discretized equation of motion can be obtained as shown in the following equation (48).

number

[0082] This equation (48) can be written as the following equation (49).

number

[0083] where:

number

number

[0084] In this embodiment, the analysis unit 10d solves the equation of motion (48) by time integration, which is discretized so as to satisfy the incremental energy principle, momentum principle, and angular momentum principle.

[0085] In this way, by time integrating the equation of motion (48) that is discretized so as to satisfy the energy principle, momentum principle, and angular momentum principle in the object of analysis, as shown in Figure 6, in the case of a conservative system, the calculation does not diverge because energy is conserved during the calculation, and numerical stability is achieved.

[0086] In this embodiment, the output unit 10e shown in FIG. 4 executes a process of outputting analysis information analyzed based on the analysis process performed by the analysis unit 10d (output process).

[0087] In this embodiment, the analysis information is various analysis results relating to the three-dimensional movement of the gossamer structure 110 or the gossamer multibody structure 120 as the analysis object 100 .

[0088] This analysis information includes, for example, numerical data such as acting force, position, velocity, rotation, stress and strain for each node, kinetic energy, strain energy, momentum, angular momentum for each element, and numerical data regarding the nodes that make up the element.

[0089] Furthermore, by processing the data related to the nodes in chronological order, it is possible to output, as analytical information, a moving image of the state in which the object to be analyzed 100 moves in three dimensions. For example, a moving image of the gossamer multibody structure 120 shown in Fig. 2 unfolding from a folded state in space is output as analytical information.

[0090] Next, an outline of the processing performed by the analysis device 10 according to this embodiment will be described.

[0091] 7 is a flowchart outlining the processing of the analysis device 10. As shown in the figure, in step S1, simulation information input by operation of the user 1 is accepted (input acceptance processing), and the accepted simulation information is stored in the simulation information storage unit 10b.

[0092] Subsequently, in step S2, analysis condition information input by operation of the user 1 is accepted (input acceptance process), and the accepted analysis condition information is stored in the analysis condition information storage unit 10c.

[0093] Next, in step S3, based on the received simulation information and analysis condition information, element nodal force vectors appearing as internal forces and element tangent matrices obtained by differentiating these element nodal force vectors with coordination variables are solved.

[0094] In this embodiment, element nodal vectors and element tangent matrices for elements of the gossamer structure 110 or gossamer multibody structure 120, such as a cable, a triangular membrane, a quadrilateral membrane, or a self-extending boom, are solved.

[0095] Once the element nodal force vectors and element tangent matrices have been solved, in step S4, the global nodal force vectors appearing as internal forces and the global tangent matrix obtained by differentiating this global nodal force vector with respect to the coordination variables are added together based on the solved element nodal force vectors and element tangent matrices.

[0096] Furthermore, in step S5, holonomic constraints are applied, which are analytically expressed by equations that depend only on generalized coordinates and time. In this embodiment, constraints such as rigid point connections, relative rotation, and uniaxial relative rotation are applied as holonomic constraints.

[0097] Subsequently, in step S6, the equation obtained by applying the holonomic constraint conditions is solved by the Newton method, and the displacement increment of the force acting on the elements of the analysis object 100 is calculated.

[0098] The results of the analysis performed in steps S2 to S6 are output as analysis information in step S7 (output process). The analysis information in this case is information relating to the instantaneous movement of the analysis object 100 at a certain time step.

[0099] In step S8, if the processes of steps S2 to S7 are repeated at preset time steps (for example, time steps within a range of 0 to 60 seconds), the analysis information is processed in chronological order and output as final analysis information.

[0100] In this case, the analysis information is information relating to the continuous, highly geometrically nonlinear motion of the object to be analyzed 100 that is repeated at preset time steps.

[0101] In this way, by time-integrating the equations of motion that have been discretized to satisfy the energy principle, momentum principle, and angular momentum principle for the object to be analyzed 100, energy is conserved during the calculation, so the calculation does not diverge and numerical stability is achieved in the analysis results.

[0102] Therefore, the three-dimensional movement of the object to be analyzed 100, which has been extremely difficult to analyze accurately, can be analyzed appropriately with numerical stability.

[0103] In particular, in this embodiment, the object to be analyzed 100 is a gossamer structure 110 or a gossamer multi-body structure 120 that moves with high geometric nonlinearity, and it is possible to obtain analytical results with high numerical stability without solving "rigid equations" that are difficult to calculate when analyzing the movement of these objects.

[0104] Therefore, it is possible to carry out highly reliable simulation analysis of structural types or space structures that are difficult to demonstrate on the ground.

[0105] The present invention is not limited to the above-described embodiment, and various modifications are possible without departing from the spirit of the invention.

[0106] In the above embodiment, the object to be analyzed 100 is described as a gossamer structure 110 and a gossamer multibody structure 120, but it is not limited to these and may be a tensile material or any structure using this tensile material.

[0107] In the above embodiment, the analysis device 10 is described as being implemented on a computer used by user 1, but for example, the analysis device 10 may be a computer implemented in a cloud environment and accessed via a computer used by user 1. [Explanation of symbols]

[0108] 1 user 10 Analysis device 100 Analysis Objects 110 Gossamer structure (object to be analyzed) 120 Gossamer multi-body structure (object of analysis)

Claims

1. An analysis device for analyzing three-dimensional motion of an analysis object, comprising: an input receiving process for receiving input of analysis condition information including data on analysis conditions for the analysis object; an analysis process for performing a finite element analysis on the analysis object based on the analysis condition information received in the input reception process; an output process for outputting the analysis information analyzed in the analysis process; The analysis process includes: performing the finite element analysis by time integrating the equations of motion that are discretized so as to satisfy the energy principle, momentum principle, and angular momentum principle; Analysis device.

2. The analysis process includes: outputting a moving image relating to the movement of the analysis object as the analysis information. The analysis device according to claim 1 .

3. The object to be analyzed is A gossamer structure and a gossamer multibody structure having the gossamer structure. The analysis device according to claim 1 or 2.

4. A program for analyzing three-dimensional motion of an object to be analyzed, A computer-implemented analysis device, an input receiving process for receiving input of analysis condition information including data on analysis conditions for the analysis object; an analysis process for performing a finite element analysis on the analysis object based on the analysis condition information received in the input reception process; an output process for outputting the analysis information analyzed in the analysis process; The analysis process includes: performing the finite element analysis by time integrating the equations of motion that are discretized so as to satisfy the energy principle, momentum principle, and angular momentum principle; program.

5. An analysis method for analyzing three-dimensional motion of an analysis object, comprising: a computer-implemented analysis device, an input receiving process for receiving input of analysis condition information including data on analysis conditions for the analysis object; an analysis process for performing a finite element analysis on the analysis object based on the analysis condition information received in the input reception process; an output process for outputting the analysis information analyzed in the analysis process; The analysis process includes: performing the finite element analysis by time integrating the equations of motion that are discretized so as to satisfy the energy principle, momentum principle, and angular momentum principle; Analysis method.

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