Analysis method and analysis system

Abstract

To provide an analysis method based on a finite element method by which proper verification along an actual condition can be performed.SOLUTION: There is provided an analysis method using a model of an architectural structure formed of a finite element, and the method based on a finite element method in which a computer analyzes the architectural structure, and the method comprises: a joint setting step for setting a joint being a peak of the element, by dividing the model of the architectural structure into a plurality of elements; a vibration application data generating step for generating vibration application data by stepping following a movement operation of a person which is simulation; a joint selecting step (S604-S608) for selecting a joint to which the vibration application data is applied, according to a position relationship between the stepping position simulated in the vibration application data generated by the vibration application data generating step, and a joint in the element in which a floor of the architectural structure is modeled; a vibration application data applying step (S609) for applying the vibration application data, to the joint selected by the joint selecting step; and a response calculating step (S610) for calculating a response in each joint with respect to the vibration application data applied in the vibration application data applying step.SELECTED DRAWING: Figure 21

Description

[Technical field]

[0001] The present invention relates to a method for analyzing a building in a computer simulation based on the finite element method, and an analysis system using the method. [Background technology]

[0002] In buildings and other structures, by understanding at the design stage how vibrations generated by people walking or jogging will affect other areas (for example, other rooms on the same floor as the people moving), it is possible to avoid the trouble of taking measures against vibrations after construction is completed.

[0003] For this purpose, vibration analysis based on the external force applied to the floor when a person walks has been attempted. For example, Patent Document 1 (JP 2020-123385 A) discloses a floor vibration analysis method using a computer to analyze the vibration of a building floor, which includes an input step in which physical data necessary for vibration analysis of the floor and an external force model created using random variables of vibration external forces are input, an analysis step in which the physical data and the external force model are used to calculate parameters indicating a reliability evaluation of the floor by the second moment method, and an output step in which the parameters calculated in the analysis step are output, and in the output step, the values ​​of the parameters at each point on the floor are displayed in an identifiable manner. [Patent Document 1] JP 2020-123385 A Summary of the Invention [Problem to be solved by the invention]

[0004] The inventors have been conducting vibration evaluations of finite element analysis models using the finite element method as analytical models of buildings. Conventionally, in analyses using the finite element method when an excitation force such as human walking acts on a building, evaluations of the movement of the excitation action position on the floor due to walking movement over time were not performed because the data creation and processing was complicated, and instead, a method was adopted in which a load considered to be equivalent to walking movement was excited at limited nodes (for example, only one point considered to be the weakest) for convenience.

[0005] However, with these conventional methods, as the interior space of buildings becomes larger and the span length becomes longer, it becomes difficult to select appropriate nodes to apply the assumed load, or the assumed load equivalent to walking movement does not match the actual moving speed or walking pitch of people, making it difficult to perform accurate analysis and verification in line with actual conditions.

[0006] As a result, there was an issue that the vibrations caused by walking on large-span floors, which are made up of long-span beams, were not properly predicted at the design stage, and if a safe approach was taken to account for the possibility of unexpected vibrations occurring, the structural components would end up being oversized, resulting in increased construction costs. [Means for solving the problem]

[0007] The present invention is adapted to solve the problems and issues described above, and an analysis method based on the finite element method according to the present invention is an analysis method based on the finite element method in which a computer analyzes a building using a model of the building made up of finite elements, and is characterized by having a node setting process of dividing the model of the building into a plurality of elements and setting nodes which are the vertices of the elements, a vibration data generation process of generating vibration data caused by stepping on the building in a simulated human movement, a node selection process of selecting nodes to which the vibration data is applied in accordance with the positional relationship between the stepping position simulated in the vibration data generated in the vibration data generation process and the nodes in the elements modeling the floor of the building, a vibration data application process of applying vibration data to the nodes selected in the node selection process, and a response calculation process of calculating the response at each node to the vibration data applied in the vibration data application process.

[0008] Furthermore, the analysis method based on the finite element method according to the present invention is characterized in that the determination of the stepping position simulated in the vibration data generation process is based on a random number generation process of generating random numbers, a stride length variation calculation process of calculating a stride length variation width from the random numbers generated in the random number generation process and the standard deviation of the stride length, and a stepping position determination process of determining the stepping position from the stride length variation width calculated in the stride length variation width calculation process and an average stride length.

[0009] In addition, the analysis method based on the finite element method according to the present invention is characterized in that the determination of the vibration start timing simulated in the vibration data generation process is based on a random number generation process of generating random numbers, a vibration start timing variation width calculation process of calculating a variation width of the vibration start timing from the random numbers generated in the random number generation process and the standard deviation of the vibration start timing, and a vibration start timing determination process of determining the vibration start timing from the variation width of the vibration start timing calculated in the vibration start timing variation width calculation process and an average value of the vibration start timing.

[0010] In addition, the analysis method based on the finite element method according to the present invention is characterized in that the determination of the time characteristics of the excitation force simulated in the excitation data generation process is based on a random number generation process of generating random numbers, a time characteristic variation width calculation process of the excitation force of calculating the variation width of the time characteristics of the excitation force from the random numbers generated in the random number generation process and the standard deviation of the time characteristics of the excitation force, and a time characteristic determination process of determining the time characteristics of the excitation force from the variation width of the time characteristics of the excitation force calculated in the time characteristic variation width calculation process and an average value of the time characteristics of the excitation force.

[0011] In addition, the analysis method based on the finite element method according to the present invention includes the steps of: In the node selection step, the floor is divided into a first region and another region, and when the stepping position is in the first region, only one node is selected, and when the stepping position is in the other region, multiple nodes are selected. . The analysis system based on the finite element method according to the present invention is an analysis system based on the finite element method in which a computer analyzes a building using a building model based on finite elements, and includes a node setting unit that divides the building model into a plurality of elements and sets nodes that are vertices of the elements, a vibration data generation unit that generates vibration data due to a stepping motion associated with a simulated human movement, a node selection unit that selects a node to which vibration data is applied in accordance with a positional relationship between a stepping position simulated in the vibration data generated by the vibration data generation unit and a node in an element that models the floor of the building, a vibration data application unit that applies vibration data to the node selected by the node selection unit, and a vibration data application unit that applies vibration data to the vibration data applied by the vibration data application unit. , the element modeling the floor and a response calculation unit that calculates the response at each node. Effect of the Invention

[0012] The analysis method and analysis system based on the finite element method according to the present invention generate vibration data caused by stepping on a floor accompanied by a simulated human movement, apply this vibration data to selected nodes of elements that model a floor, and calculate the response at each node to the vibration data. According to the analysis method and analysis system based on the finite element method according to the present invention, vibration (load) that matches the actual human movement speed and walking pitch is applied to appropriate nodes, making it possible to perform accurate verification according to actual conditions, and since vibration can be predicted at the design stage, there is no need to use excessively large structural members for construction, making it possible to reduce construction costs. [Brief description of the drawings]

[0013] [Figure 1] FIG. 13 is a diagram showing an example of a flowchart of a process for setting structural data and nodes of a building. [Diagram 2] 13 is a diagram illustrating attribute data held by component data. FIG. [Diagram 3] FIG. 1 is a diagram showing division of component data into a hexahedral element (hexahedral mesh) model. [Figure 4] FIG. 13 is a diagram showing an example of a user interface screen displaying structure data of a set building. [Diagram 5] FIG. 13 is a diagram showing an example of setting a trajectory of a moving person in a simulation. [Figure 6] FIG. 13 is a diagram showing the analysis results of an actual person's walking motion. [Figure 7] FIG. 2 is a flowchart showing a vibration data generation process in the analysis method and analysis system according to the embodiment of the present invention. [Figure 8] FIG. 13 is a flowchart showing a subroutine of a stepping position (coordinate) calculation process. [Figure 9] 11A and 11B are diagrams illustrating variations in stepping positions during walking. [Figure 10] FIG. 13 is a flowchart showing a subroutine of a vibration start timing calculation process. [Figure 11]11A and 11B are diagrams illustrating variations in vibration start timing during walking. [Figure 12] FIG. 13 is a flowchart of a subroutine of a process for calculating the time characteristics of an excitation force. [Figure 13] 11A and 11B are diagrams illustrating variations in time characteristics of excitation force during walking. [Figure 14] FIG. 2 is an image diagram of a data structure of vibration data. [Figure 15] FIG. 1 shows nodes in an element that models a floor of a building. [Figure 16] FIG. 13 is a diagram showing an example of division of a floor into areas. [Figure 17] FIG. 13 is a diagram for explaining a pattern of an area (I) in which one node is selected as a node to which vibration data is applied. [Figure 18] FIG. 13 is a diagram for explaining a pattern of an area (II) in which two nodes are selected as nodes to which vibration data is applied. [Figure 19] FIG. 13 is a diagram for explaining a pattern of an area (III) in which two nodes are selected as nodes to which vibration data is applied. [Figure 20] FIG. 13 is a diagram for explaining a pattern of an area (IV) in which four nodes are selected as nodes to which vibration data is applied. [Figure 21] FIG. 1 is a flowchart showing a response calculation process in an analysis method and an analysis system according to an embodiment of the present invention. [Figure 22] FIG. 1 is a diagram illustrating an example of a system configuration of a computer that executes an analysis system 1 according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0014] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. The finite element method is a method for numerically obtaining an approximate solution to a partial differential equation that is difficult to solve analytically. In an analysis method and analysis system based on the finite element method, a computer simulation model of a building or other structure is divided into a plurality of elements (also called "mesh"), and "nodes" that are located on the boundaries of the elements and connect them are set. In the finite element method, an approximate solution to the original equation is obtained by discretizing and approximating a function that is a solution to the partial differential equation for each divided element using an "interpolation function". Numerical values ​​as the result of a computer calculation are usually associated with "elements" or "nodes" that are the vertices of elements. As a result of a calculation on an element, the deformation of the element can be obtained, and as a result of a calculation on a node, the displacement of the node can be obtained. In this specification, the displacement of the node is sometimes referred to as a response at the node.

[0015] In the analysis method and the analysis system based on the finite element method according to the present invention, a model of a building set based on the finite element method is set on a computer, and data on vibration caused by walking or jogging accompanying the movement of people is given to the nodes as described above, and the response of each node to the vibration is simulated. For this purpose, a model of the building to be analyzed is first set, and then the model is divided into elements, and the nodes are set. Next, a process of setting the structural data of the building and setting the nodes on a computer simulation is described. An example of such a process is described below. Note that in FIG. 1, an example of setting the structural data of the building using hexahedral elements is described, but the shape when dividing the structural data of the building into elements into meshes is not limited to hexahedral, and the present invention can be applied to other shapes as well. For example, the present invention can be applied even when each member data is set using planar elements or line elements.

[0016] FIG. 1 is a diagram showing an example of a flowchart for setting structural data and nodes of a building. Processing based on such a flowchart can be executed by a computer, which will be described later. In this processing, it is assumed that the user selects from multiple component data and constructs and sets the structural data of the building to be analyzed using the finite element method, but the method for constructing and setting the structural data of the building in this manner does not need to be limited to this method, and other methods may be used for setting the structural data and nodes of the building.

[0017] In the following explanation, the "components" that make up the structural data of a building are not real, but are merely computer-simulated. When it is particularly important to emphasize that the "components" are computer-simulated, the "components" may be referred to as "component data." Note that in this specification, the names of actual components (e.g., "column components") may also be used for data used to simulate the actual components.

[0018] 1, in step S100, the process of setting structural data and nodes of a building is started, and then the process proceeds to step S101, where an initial screen (not shown) of the analysis system according to the present invention is displayed. In step S01, the user requests the system to create a "new project."

[0019] In step S102, the user is requested to set the basic framework structure of the building that the user is going to construct, such as the number of floors, grid center, span, etc.

[0020] In step S02, it is assumed that the user performs input using a keyboard or a pointing device (input unit 18). The user is required to input the number of floors and floor height of the building, the number of grid centers in the X and Y directions, their numbers, span widths, etc., using the keyboard or pointing device (input unit 18).

[0021] In step S103, the user is requested to arrange and set components (data) in accordance with the floor settings and grid center settings. Here, it is preferable that the types of component data include "joint components," "column components," "beam components," "floor slab components," "wall components," and the like. Such component data is configured so that data registered as a library in an external storage device (18) or the like can be used. It is also preferable that such a library also stores data on the materials that each of the component data is made of, allowing the user to select as appropriate. Correspondingly, in step S03, the user selects, arranges, and sets the component data using a keyboard or pointing device (input unit 18).

[0022] In the next step S104, the user is requested to input information about each component (dimensions, material, number of divisions). In response to this, in step S04, the user inputs the dimensions, material, and number of divisions of the component using a keyboard or pointing device (input unit 18). Here, specific examples of information about components will be described with reference to Figs. 2 and 3.

[0023] 2 is a diagram for explaining attribute data held by component data. There are various types of attribute data, but in order to realize the analysis method based on the finite element method and the analysis system based on the finite element method according to the present invention, the component data holds, as attributes, at least data related to the vertices of the component (data), data related to the dimensions of the component (data), and data related to the material of the component (data).

[0024] For example, each of the components, "joint components," "column components," "beam components," "floor slab components," and "wall components," has a shape composed of a hexahedral region. As shown in FIG. 2, each component data holds data related to the vertices, which are the corners of the rectangular parallelepiped shape of the hexahedron. Furthermore, each component data has dimensional data, such as W (width), H (height), and D (depth). The user inputs this dimensional data in step S04.

[0025] The structural data defining a building can be said to be a collection of a plurality of component data as described above, arranged at predetermined coordinates.

[0026] In this example, for the sake of simplicity, the explanation will be given using an example in which each component data has a hexahedral rectangular prism shape, but this is not a mandatory requirement, and it is also possible to handle anisotropic components such as deck slab components.

[0027] In addition, in the component data library, it is preferable that, for example, under "column component," data on the material of the column component is classified, such as "steel column," "RC column," etc. In step S04, the user inputs such material data.

[0028] FIG. 3 is a diagram showing division of component data into a hexahedral element (hexahedral mesh) model. A hexahedral element (hexahedral mesh) model is the smallest unit used in analysis using the finite element method. The corners of this hexahedral element (hexahedral mesh) model are specifically called "nodes." In step S04, the user inputs the division (number) of such component data.

[0029] After going through the above steps, in step S105, each component data in the building's structural data is divided into elements as shown in Figure 3, in step S106, the vertices of each element are set as "nodes," and the process ends in step S108.

[0030] An example of the structural data and nodes of a building that have been set using the above process is shown below. Figure 4 shows an example of a user interface screen that displays the structural data of a building that has been set, and shows the structural data of a floor portion of a certain floor of the building. In Figure 4, X1, X2, X3, ..., Y1, X2, X3, ... indicate grid centers. Also, the short diagonal lines indicate "column components." The intersections of the various lines become "nodes."

[0031] As explained above, the analysis method and analysis system of the present invention provide data on vibrations caused by people walking, jogging, etc., associated with the movement of people to set nodes in structural data of a building set on a computer, and simulate the response of each node to this data.

[0032] For this purpose, a "Movement trajectory setting" button, a "Movement condition setting" button, an "Execute" button, etc. can be provided on the user interface screen shown in Fig. 4. By pressing these buttons with a pointing device (input unit 18) or the like, the user can input execution commands.

[0033] "Movement trajectory setting" is a button that allows the user to set the trajectory of a moving person that they wish to simulate. FIG. 5 is a diagram showing an example of setting the trajectory of a moving person in a simulation. In the figure, the white circles indicate the nodes of the elements that model the floor. Also, the footprint indicates the position of the step that accompanies the moving motion of the moving person. The load caused by such a step is originally spread two-dimensionally, but in this embodiment, it is assumed that the point where the vibration (load) caused by the step is applied is concentrated at one point, and this point is shown in the figure by a black circle in the footprint.

[0034] The user can use the "Movement trajectory setting" button to set, for example, a movement trajectory as shown in (A) or (B) in FIG. 5. In addition, the "Movement condition setting" button is used to set the speed, stride length, physique and weight (the magnitude of the excitation force) of the person moving in the simulation. After making these settings, the "Execute" button is pressed to execute calculations based on the analysis system according to the present invention. In the trajectories shown in (A) and (B), it is assumed that the points where the excitation (load) due to the stepping motion is applied are on a straight line, but the points where the excitation (load) is applied do not necessarily need to be based on such an assumption.

[0035] In the analysis method and analysis system according to the present invention, first, data on excitation applied to a building floor by a moving person is generated. In this case, in the present invention, the time characteristics of the excitation force due to the actual walking motion of a person are used. FIG. 6 is a diagram showing the analysis results of the actual walking motion of a person. In FIG. 6, the state of stepping for one step in the walking motion of a person shown in (A) can be decomposed as shown in (B). If the excitation (load) due to such a stepping motion of one step is applied to one point indicated by a black circle in the figure, the time-excitation force profile (time characteristics of the excitation force) will be as shown in (C). What is characteristic of the time characteristics of the excitation force is that a sharp peak at the time of stepping is followed by two gentle peaks.

[0036] In the analysis method and analysis system according to the present invention, basically, excitation force data is generated based on the time characteristics of the excitation force due to such a stepping motion, but since the stepping motion during actual walking varies, the excitation force data is generated while taking the variation into consideration. Figure 7 is a diagram showing a flowchart of the excitation data generation process in the analysis method and analysis system according to the embodiment of the present invention.

[0037] 7, when the vibration data generation process is started in step S200, the information set in the previous "movement trajectory setting" and "moving person condition setting" is acquired in step S201. Then, in step S202, the variable N is set to 1. Here, the variable N represents the Nth step in the simulated walking.

[0038] Next, in step S203, a subroutine for calculating the stepping position (coordinates) is executed. Fig. 8 is a diagram showing a flowchart of the subroutine for calculating the stepping position (coordinates). Fig. 9 is a diagram for explaining the variation in the stepping position in the walking motion.

[0039] In the analysis method and analysis system according to the present invention, the step position (coordinates) in the simulation in the vibration data is determined taking into consideration the variation in the step length. Specifically, the step length of the step is calculated by (the variation width of the step length) + (the average step length), and the coordinates of the step position are calculated based on the step length thus calculated.

[0040] In the algorithm of this embodiment, if the standard deviation of the stride length is σ1 as shown in Fig. 9, a value within the range of 2σ1 is determined based on a random number to calculate (the variation width of the stride length). Details will be described based on the flowchart in Fig. 8.

[0041] In Fig. 8, when the step position (coordinate) calculation process subroutine is started in step S300, an integer random number R is generated in step S301. Here, the random number R satisfies -M1 ≦ R1 ≦ +M1. Also, M1 is a positive integer. For example, if M1 is 3, one of the following values ​​is generated as the random number R1: -3, -2, -1, 0, 1, 2, or 3.

[0042] In step S302, the (variation range of stride length) is calculated from the generated random number R1 and standard deviation σ1 by (variation range of stride length)=(R1 / 2M1)×σ1.

[0043] Next, in step S303, the (step length of the step forward) is calculated by (step length of the step forward)=(variation in step length)+(average step length).

[0044] In the next step S304, the coordinates of the stepping position on the extension line of the set trajectory are determined based on the calculated (step length of the stepping), and in step S305, the process returns to the original routine.

[0045] As described above, in the analysis method and analysis system according to the present invention, since the stride length varies when an actual person walks, a simulation is performed using vibration data including the stride length variation, so that more accurate predictions can be made.

[0046] Returning to the flowchart of Fig. 7, in step S204, a subroutine for calculating the vibration start timing is executed. Fig. 10 is a flowchart of the subroutine for calculating the vibration start timing. Fig. 11 is a diagram for explaining the variation in the vibration start timing in walking.

[0047] In the analysis method and analysis system according to the present invention, the vibration start timing in the simulation of the vibration data is determined taking into consideration the variation in the step timing (timing of starting vibration) during walking. Specifically, the vibration start timing is calculated by (variation width of vibration start timing) + (average value of vibration start timing).

[0048] In the algorithm of this embodiment, if the standard deviation of the stride length is σ2 as shown in Fig. 11, a value within the range of 2σ2 is determined based on a random number to calculate (the variation width of the vibration start timing). Details will be described based on the flowchart in Fig. 10.

[0049] In Fig. 10, when the vibration start timing calculation process subroutine is started in step S400, an integer random number R is generated in step S401. Here, the random number R satisfies -M2 ≦ R2 ≦ +M2. Also, M2 is a positive integer. This M2 may be the same value as M1.

[0050] In step S402, the variation width of the vibration start timing is calculated from the generated random number R and standard deviation σ2 by (variation width of the vibration start timing)=(R2 / 2M2)×σ2.

[0051] Next, in step S403, the (vibration start timing) is calculated by (vibration start timing)=(variation range of vibration start timing)+(average value of vibration start timing), and in step S404, the process returns to the original routine.

[0052] As described above, in the analysis method and analysis system according to the present invention, in consideration of the fact that there is variation in step timing (vibration start timing) when an actual person walks, a simulation is performed using vibration data including the variation in vibration start timing, so that more accurate predictions can be made.

[0053] Returning to the flowchart of Fig. 7, in step S205, a subroutine for calculating the time characteristics of the excitation force is executed. Fig. 12 is a diagram showing a flowchart of the subroutine for calculating the time characteristics of the excitation force. Fig. 13 is a diagram for explaining the variation in the time characteristics of the excitation force in walking motion.

[0054] In the analysis method and analysis system according to the present invention, the time characteristic of the excitation force in the simulation of the vibration data is determined in consideration of the variation in the time characteristic of the excitation force. Specifically, the time characteristic of the excitation force is calculated by (the variation width of the time characteristic of the excitation force) + (the average value of the time characteristic of the excitation force).

[0055] In the algorithm of this embodiment, if the standard deviation of the stride length is σ3 as shown in Fig. 13, any value within the range of 2σ3 is determined based on random numbers to calculate (the variation width of the time characteristic of the excitation force). Details will be described based on the flowchart in Fig. 12.

[0056] In Fig. 10, when a subroutine for calculating the time characteristic of the excitation force is started in step S500, an integer random number R3 is generated in step S501. Here, the random number R3 satisfies -M3 ≦ R3 ≦ +M3. Also, M3 is a positive integer. This M3 may be the same value as M2 and M1.

[0057] In step S502, the (variation width of the time characteristic of the excitation force) is calculated from the generated random number R and standard deviation σ3 by (variation width of the time characteristic of the excitation force)=(R3 / 2M3)×σ3.

[0058] Next, in step S503, the time characteristic of the excitation force is calculated by (time characteristic of the excitation force)=(variation range of the time characteristic of the excitation force)+(average value of the time characteristic of the excitation force), and in step S504, the process returns to the original routine.

[0059] As described above, in the analysis method and analysis system according to the present invention, since the time characteristics of the excitation force vary when an actual person walks, a simulation is performed using excitation data including the variation in the time characteristics of the excitation force, making it possible to make more accurate predictions.

[0060] Returning to the flowchart of FIG. 7, in step S206, the stepping position (coordinates), vibration start timing, and time characteristics of the vibration force in the Nth step calculated in steps S203 to S205 are stored as vibration data.

[0061] In step S207, it is determined whether or not the generation of vibration data for all the moving trajectories of the set moving person is completed. If the determination in step S207 is NO, the process proceeds to step S208, N is incremented by 1, and the process returns to step S203. On the other hand, if the determination in step S207 is YES, the process proceeds to step S209, and the vibration data generation process is terminated.

[0062] The vibration data generated by the above vibration data generation process has three pieces of data for each step taken by the simulated moving person: the step position (coordinates), the vibration start timing, and the time characteristic of the vibration force. Figure 14 is an image diagram of the data structure of the vibration data.

[0063] For example, the vibration data for the first step has (x1, y1) as the stepping position coordinates, T1 as the time of vibration start timing, and the time characteristic of the vibration force has a time-vibration force profile as shown in the figure.

[0064] When applying the vibration data to a node, two pieces of data, namely, the vibration start timing and the time characteristics of the vibration force, are used out of the three pieces of data, namely, the step position (coordinates), the vibration start timing, and the time characteristics of the vibration force. In this specification, applying the vibration data to a node means applying the data of the "time characteristics of the vibration force" to the node of interest from the time of the "vibration start timing".

[0065] In the analysis method and analysis system according to the present invention, the vibration data generated as described above is applied to the nodes in the finite element analysis model of the building, and the response of each node to the vibration data is calculated. Here, in the present invention, the nodes to which the vibration data is applied are appropriately selected according to the stepping position coordinates in the vibration data. A specific method for selecting the nodes to which the vibration data is applied according to the stepping position coordinates will be described below.

[0066] Fig. 15 is a diagram showing nodes in an element that models a floor of a building, and Fig. 16 is a diagram showing an example of division of regions on the floor shown in Fig. 15. As shown in the diagram, the x direction of each node is divided into a region within ±δ and a region outside of this range. Similarly, the y direction of each node is divided into a region within ±δ and a region outside of this range. Note that such division of regions is merely an example, and any other division of regions may be used.

[0067] In the analysis method and analysis system according to the present invention, the node to which the vibration data is applied is selected according to the positional relationship between the stepping position coordinate in the vibration data and the node. The node to which the vibration data is applied is selected according to which of the divided regions the stepping position coordinate of the vibration data exists in. When multiple nodes are selected, the vibration force in the vibration data is appropriately apportioned. The following describes the area defined based on the node. Fig. 17 is a diagram explaining the pattern of area (I) where one node is selected as the node to which vibration data is applied. The pattern of area (I) is an area within ±δ in the x direction of the node of interest and within ±δ in the y direction, and corresponds to the area indicated by diagonal lines in the figure.

[0068] If the stepping position coordinates in the excitation data are within region (I), the excitation force in the excitation data is applied only to the nodes that belong to that region. In the figure, the black circle (stepping position coordinates) of the foot shape is within the diagonal line region in the upper right, so the excitation force F in the excitation data (hereinafter, the excitation force is referred to as F. This F is a function of time as shown in Figure 6(C)) is applied to all nodes (n+1,m+1).

[0069] That is, F n+1,m+1 =F Hereinafter, the excitation force applied to the node (n, m) is F n,m This is expressed as follows.

[0070] Fig. 18 is a diagram explaining the pattern of region (II) where two nodes are selected as nodes to which vibration data is applied. When focusing on two nodes adjacent in the x direction, the pattern of region (II) is a region within ±δ in the y direction, a region that deviates from +δ in the positive x direction for the left node, and a region that deviates from -δ in the negative x direction for the right node, which corresponds to the region indicated by diagonal lines in the figure.

[0071] If the stepping position coordinates in the excitation data are within region (II), the excitation force in the excitation data is applied to the nodes on the left and right of the region in proportion to the inverse ratio of the distance from the node.In the figure, the black circle (stepping position coordinates) of the foot shape is within the lower shaded region, so the excitation force F in the excitation data is applied to the two nodes (n,m) and (n+1,m) in proportion to the inverse ratio of the distance.

[0072] That is, for node (n,m), F n,m ={(1 / a) / (1 / a+1 / b)}×F is applied, For node (n+1,m), F n+1,m ={(1 / b) / (1 / a+1 / b)}×F is applied.

[0073] Fig. 19 is a diagram for explaining the pattern of region (III) in which two nodes are selected as nodes to which vibration data is applied. With respect to two nodes adjacent in the y direction, the pattern of region (III) is a region within ±δ in the x direction, a region that deviates from +δ in the positive y direction for the lower node, and a region that deviates from -δ in the negative y direction for the upper node, which corresponds to the region indicated by diagonal lines in the figure.

[0074] If the stepping position coordinates in the excitation data are within region (III), the excitation force in the excitation data is applied to the nodes on the left and right of the region in proportion to the inverse ratio of the distance from the node. In the figure, the black circle (stepping position coordinates) of the foot shape is within the left-hand shaded region, so the excitation force F in the excitation data is applied to the two nodes (n,m) and (n,m+1) in proportion to the inverse ratio of the distance.

[0075] That is, for node (n,m), F n,m ={(1 / c) / (1 / c+1 / d)}×F is applied, For node (n,m+1), F n,m+1 ={(1 / d) / (1 / c+1 / d)}×F is applied.

[0076] Fig. 20 is a diagram for explaining the pattern of region (IV) in which four nodes are selected as nodes to which vibration data is applied. With respect to the four nodes forming a rectangle, the pattern of region (IV) is a region that deviates from +δ in the positive x direction for the left node, a region that deviates from -δ in the negative x direction for the right node, a region that deviates from +δ in the positive y direction for the lower node, and a region that deviates from -δ in the negative y direction for the upper node, which corresponds to the region indicated by diagonal lines in the figure.

[0077] If the stepping position coordinates in the excitation data are within region (IV), the excitation force in the excitation data is applied to the nodes on the left and right of the region in proportion to the inverse ratio of the distance from the node.In the figure, the black circle of the foot (stepping position coordinates) is within the left-hand shaded region, so the excitation force F in the excitation data is applied in proportion to the inverse ratio of the distance to the four nodes (n,m), (n+1,m), (n,m+1), and (n+1,m+1).

[0078] That is, for node (n,m), F n,m ={(1 / a) / (1 / a+1 / b)}×{(1 / c) / (1 / c+1 / d)}×F is applied, For node (n+1,m), F n+1,m ={(1 / b) / (1 / a+1 / b}×{(1 / c) / (1 / c+1 / d)}×F is applied, For node (n,m+1), F n,m+1 ={(1 / a) / (1 / a+1 / b)}×{(1 / d) / (1 / c+1 / d)}×F is applied, For node (n+1,m+1), F n+1,m+1={(1 / b) / (1 / a+1 / b)}×{(1 / d) / (1 / c+1 / d)}×F is applied.

[0079] Next, a process for calculating a response at each node based on the generated vibration data will be described. Fig. 21 is a flowchart showing a response calculation process in the analysis method and analysis system according to the embodiment of the present invention.

[0080] In FIG. 21, in step S600, the response calculation process is started, and then in step S601, a variable N representing the number of steps in the simulation is set to N=1.

[0081] In step S602, the vibration data of the Nth step is read in. In the next step S603, the stepping position coordinates in the vibration data are compared with the set nodes and areas.

[0082] In step S604, it is determined whether the stepping position coordinate in the vibration data is in the area (I) described above. If the determination result in step S604 is YES, the process proceeds to step S605, where one node belonging to the area (I) in which the stepping position coordinate exists is selected. All of the vibration data (time characteristics of the vibration force) are applied to the one node. On the other hand, if the determination result in step S604 is NO, the process proceeds to step S606.

[0083] In step S606, it is determined whether the stepping position coordinate in the vibration data exists in either of the regions (II) or (III) described above. If the determination result in step S606 is YES, the process proceeds to step S607, where two nodes forming the region (II) or (III) in which the stepping position coordinate exists are selected. The vibration data (time characteristics of the vibration force) are divided in inverse proportion to the distance and applied to the two nodes. On the other hand, if the determination result in step S606 is NO, the process proceeds to step S608.

[0084] In step S608, since the stepping position coordinate in the excitation data is present in the remaining area (IV), four nodes forming the area (IV) in which the stepping position coordinate exists are selected. The excitation data (time characteristics of the excitation force) is proportionally divided in inverse proportion to the distance and applied to the four nodes.

[0085] In step S609, excitation data (time characteristics of excitation force) is applied to the selected nodes from the time of the excitation start timing. In step S610, the response (displacement) at each node is calculated based on the algorithm of the finite element method. Note that the algorithm for calculating the response (displacement) at each node is appropriately selected from known conventional algorithms.

[0086] In step S611, the result calculated in step S609 is stored in the external storage device 20 or the like. In step S612, it is determined whether or not the response calculation process has been completed for all the steps recorded in the vibration data. If the determination result in step S612 is NO, the process proceeds to step S613, where the variable N is incremented by 1, and the process returns to step S602. On the other hand, if the determination result in step S612 is YES, the process proceeds to step S614, where the response calculation process is terminated.

[0087] As described above, the analysis method based on the finite element method and the analysis system based on the finite element method according to the present invention generate vibration data caused by stepping on a floor accompanied by a simulated human movement, apply this vibration data to selected nodes of the elements that model the floor, and calculate the response at each node to the vibration data. According to the analysis method based on the finite element method and the analysis system based on the finite element method according to the present invention, vibration (load) that matches the actual human movement speed and walking pitch is applied to appropriate nodes, making it possible to perform accurate verification according to actual conditions, and since vibration prediction can be performed at the design stage, there is no need to use excessively large structural members for construction, making it possible to reduce construction costs.

[0088] A computer system capable of executing the analysis method based on the finite element method described above will be described below. Fig. 22 is a diagram showing an example of the system configuration of a computer that executes the analysis system according to the embodiment of the present invention.

[0089] In FIG. 22, reference numeral 10 denotes a system bus, 11 denotes a CPU (Central Processing Unit), 12 denotes RAM (Random Access Memory), 13 denotes ROM (Read Only Memory), 14 denotes a communication control unit that manages communication with external information devices, 15 denotes an input control unit such as a keyboard controller, 16 denotes an output control unit, 17 denotes an external storage device control unit, 18 denotes an input unit consisting of input devices such as a keyboard, pointing device, and mouse, 19 denotes an output unit such as a printing device, 20 denotes an external storage device such as an HDD (Hard Disk Drive), 21 denotes a graphics control unit, and 22 denotes a display device.

[0090] In FIG. 22, the CPU 11 performs arithmetic processing such as searching and acquiring data by communicating with external devices according to a program ROM in the ROM 13 or a program stored in a large-capacity external storage device 20, processing output data that includes a mixture of figures, images, characters, tables, etc., and managing a database stored in the external storage device 20.

[0091] CPU 11 also performs overall control of each device connected to system bus 10. An operating system program (hereinafter referred to as OS), which is a basic program for controlling CPU 11, and the like are stored in a program ROM in ROM 13 or in external storage device 20. Various data used for output data processing and the like are also stored in ROM 13 or in external storage device 20. RAM 12, which is the main memory, functions as the main memory, work area, and the like of CPU 11.

[0092] The input control unit 15 controls an input unit 18 such as a keyboard or a pointing device (not shown), while the output control unit 16 controls the output of an output unit 19 such as a printer.

[0093] The external storage device control unit 17 controls access to an external storage device 20 such as an HDD (Hard Disk Drive) or a solid state drive (SSD) that stores a boot program, various applications, font data, user files, edit files, printer drivers, etc. A system program for realizing the analysis system based on the finite element method of the present invention is stored in the above-mentioned external storage device 20. The graphic control unit 21 is configured to perform drawing processing of information to be displayed on the display device 22.

[0094] In addition, the communication control unit 14 controls communication with external devices via the network, and is configured to enable the system to obtain data required by the system from databases held by external devices on the Internet or an intranet, and to transmit information to external devices.

[0095] In addition to the operating system program (hereinafter referred to as OS), which is the control program of CPU 11, the external storage device 20 also has installed therein and stores therein a system program for operating the analysis system of the present invention on CPU 11, and data used by this system program, etc.

[0096] Data used in the system program realizing the analysis system based on the finite element method of the present invention is basically assumed to be stored in the external storage device 20, but in some cases, it is also possible to configure the system to acquire this data from an external device on the Internet or an intranet via the communication control unit 14. Also, data used in the system program realizing the analysis system based on the finite element method of the present invention can be configured to be acquired from various media such as USB memory, CD, and DVD. The analysis system based on the finite element method of the present invention can be realized by executing a program on a computer configured as described above.

[0097] As described above, the analysis method based on the finite element method and the analysis system 1 based on the finite element method according to the present invention generate vibration data caused by stepping on a floor accompanied by a simulated human movement, apply this vibration data to selected nodes of the elements that model the floor, and calculate the response at each node to the vibration data. According to the analysis method based on the finite element method and the analysis system 1 based on the finite element method according to the present invention, vibration (load) that matches the actual human movement speed and walking pitch is applied to appropriate nodes, making it possible to perform accurate verification according to actual conditions, and since vibration prediction can be performed at the design stage, there is no need to use excessively large structural members for construction, making it possible to reduce construction costs. [Explanation of symbols]

[0098] 1. Analysis system based on the finite element method 10. System bus 11...CPU(Central Processing Unit) 12...RAM(Random Access Memory) 13. ROM (Read Only Memory) 14. Communications control section 15 Input control section 16 Output control section 17 External storage device control unit 18 Input section 19. Output section 20...External storage device 21 Graphics control section 22. Display device

Claims

1. A finite element method for analyzing a building using a computer-based finite element model of the building, comprising the steps of: A node setting process for dividing a building model into a plurality of elements and setting nodes which are vertices of the elements; A vibration data generating step for generating vibration data generated by stepping on the simulated human moving motion; a node selection step of selecting a node to which the vibration data is to be applied according to a positional relationship between a stepping position simulated in the vibration data generated in the vibration data generation step and a node in an element that models a floor of a building; a vibration data applying step of applying vibration data to the nodes selected in the node selecting step; a response calculation step of calculating a response at each node of an element that models the floor to the vibration data applied in the vibration data application step.

2. The determination of the stepping position to be simulated in the vibration data generation step is A random number generating step of generating random numbers; a step width variation calculation step of calculating a step width variation from the random number generated in the random number generation step and a standard deviation of the step width; 2. The analysis method according to claim 1, further comprising a stepping position determining step of determining a stepping position from the stride variation calculated in the stride variation calculation step and an average stride value.

3. The vibration start timing to be simulated in the vibration data generation step is determined by: A random number generating step of generating random numbers; a vibration start timing variation width calculation step of calculating a variation width of the vibration start timing from the random number generated in the random number generation step and a standard deviation of the vibration start timing; 3. The analysis method according to claim 1, further comprising a vibration start timing determination step of determining the vibration start timing from a variation width of the vibration start timing calculated in the vibration start timing variation width calculation step and an average value of the vibration start timing.

4. The determination of the time characteristics of the excitation force to be simulated in the excitation data generation step includes: A random number generating step of generating random numbers; a calculation step of calculating a variation width of the time characteristic of the excitation force from the random number generated in the random number generation step and a standard deviation of the time characteristic of the excitation force; a time characteristic determination step of determining the time characteristic of the excitation force from the variation width of the time characteristic of the excitation force calculated in the time characteristic variation width calculation step and an average value of the time characteristic of the excitation force; The analysis method according to any one of claims 1 to 3, characterized in that the analysis method is based on the following:

5. In the node selection step, The floor is divided into one area and another area, When the step position is within one region, only one node is selected, 5. The analysis method according to claim 1, wherein when the stepping position is within another region, a plurality of nodes are selected.

6. An analysis system based on the finite element method in which a computer analyzes a building using a finite element model of the building, A node setting unit that divides a building model into a plurality of elements and sets nodes that are vertices of the elements; A vibration data generating unit that generates vibration data caused by stepping on the simulated human moving motion; a node selection unit that selects a node to which the vibration data is applied according to a positional relationship between a stepping position simulated in the vibration data generated by the vibration data generation unit and a node in an element that models a floor of a building; a vibration data application unit that applies vibration data to the nodes selected by the node selection unit; and a response calculation unit that calculates a response at each node of an element that models the floor to the vibration data applied by the vibration data application unit.

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