WO2001052193A9 - Method for displaying load transfer displacement of object - Google Patents

Abstract

A first material agent of hexahedron or two-dimensional shape is virtually generated in a position of a load area given to an object. A second material agent of the same shape is generated in an adjacent area other than the load area of the first material agent. A boundary agent is generated on the boundary area of the object. A predetermined load corresponding to the material characteristics is transferred to a material agent adjacent in the direction of the load. A predetermined load corresponding to the strain characteristics of the object and a load subjected to a predetermined displacement constraint at the top face in the direction of the load are transferred to material agent adjacent to a face perpendicular to the direction of the load. A load the value of which is equal to that of the load from the adjacent material agent is transferred in the direction of the load to the boundary of the boundary agent not subjected to displacement constraint, and a load the value of which is equal to that of the load from the adjacent material agent is transferred in the opposite direction of the load to the boundary subjected to displacement constraint. Therefore the process that material agents transfer loads to surfaces other than the load areas under predetermined conditions is simply displayed, thus providing a method for displaying the load transfer displacement of an object.

Description

 Specification

How to display the load transfer displacement of an object

Technical field

 The present invention relates to a method of displaying the load transfer displacement of an object, which displays the displacement of the entire object by displaying the movement of each agent that partitions the inside of the object into a virtual predetermined shape. Background art

 In recent years, CG (Computer Graphics) animation has come to be used frequently in so-called entertainment such as movies and commercials.

 However, in order to reproduce the deformation and movement of an object by CG, it is necessary to create it by trial and error so that it looks exactly like it, or it will be a large facility. Yes, and it has not yet achieved the reduction of artificial load.

 In order to be able to know the displacement due to external force on a structure (object), it has been used for structural analysis of the object (including not only the structure but also non-structural analysis of heat, fluid, etc.). In addition, a finite element method (FEM: Finite Element Method) for numerically solving differential equations has been put into practical use with the advent of high-speed large-scale computers. For example, general-purpose programs such as NASTRAN have been developed.

The finite element method is, in a nutshell, in order to obtain a solution: (1) modeling the target object so that it can be solved by FEM. (2) Decompose into elements (triangles, etc. for two-dimensional, hexahedrons for three-dimensional). 3) Creation of element rigidity matrix 6'④ Creation of overall rigidity matrix. ⑤Create stiffness equation. ⑥Stiffness Equation solving method. Is necessary. For example, in a two-dimensional problem, When a shape element is used, nodes are set at the position of an appointment of the target object of a predetermined shape, and the target object is divided into elements by defining these nodes as vertices of a triangle (element: finite number). A simultaneous linear equation is created using the displacement as an unknown value, and the state of the target object is obtained as a solution from the boundary conditions.

 Therefore, in order to know the displacement of a structure (object) due to external force, the integration of FEM (finite element method), which is a method of accurately analyzing the behavior of the object, and a CG animation system is considered. However, considering the calculation time, it is not practical, and there is a new issue that requires CG Cleaver to acquire some FEM expertise.

 In the three-dimensional image display by computer graphic animation described above, one image is represented by hundreds of thousands to millions of polygons.For example, to display the target object, the target object is formed For this reason, it is necessary to calculate a plurality of polygons by calculation, and to calculate a huge determinant (hundreds of thousands to millions per image) each time, and to calculate the color for the image After humans have assumed the environment settings such as lighting and light sources, they must be calculated by a computer, etc., and then calculated for multiple images.As the size of the program increases, the processing load on the computer increases. Was.

 In addition, in order to express the shape change of an object in a form that is physically satisfying by computer graphic animation, the change can be obtained using the finite element method, but it was originally a huge CG animation program. When a large FEM program is integrated into a program, it is necessary to take into account the fact that the program becomes even larger and the computing time of the computer executing the program is reduced, and the finite element method that requires specialized knowledge is used. There was a problem that a pewter graphic designer had to learn and use it.

Furthermore, in the current CG animation, the movement of the object is smooth, Because the deformation of the object itself is not taken into account, for example, the movement of the person itself moves smoothly, but when the muscle shape remains or the car moves, the car itself moves up and down or left and right However, because the force applied to the tires when turning a curve was not taken into account, there was an unnatural expression in the overall image.

 The present invention has been made in view of the above-described conventional circumstances, and generates virtual agents in a matrix based on the load applied to an object, and the individual agents are deformed. It is another object of the present invention to provide a method of displaying a load transfer displacement of an object which can easily display a state of a target object by transmitting a load under predetermined conditions. Disclosure of the invention

In order to achieve the above object, the invention according to claim 1 of the present application is a method for displaying a load transmission displacement of an object on a rigid body subject to displacement constraint from the periphery in a boundary not subject to displacement constraint from the periphery. A hexahedral or planar first material agent virtually generated in the object at a load position given to an arbitrary position of the object, and a surface other than the surface receiving the load of the first material agent A second material agent of the same shape virtually generated on an adjacent surface of the object, and similarly, sequentially, in the object, a boundary and the Z or the displacement constraint that are not subjected to the displacement constraint with the object. The third, fourth, eleventh material agents virtually generated up to the boundary with the rigid body to receive, and the boundary surface between the object and the boundary not subjected to the displacement constraint and the contact surface of the rigid body subject to the Z or displacement constraint Virtually The material agent comprises: a predetermined load corresponding to a material property of the upper surface and the lower surface of the object in the load direction with respect to the load direction; A predetermined load corresponding to the distortion characteristics of the object is applied to a plane perpendicular to the direction. A boundary agent generated in a boundary that receives a predetermined displacement constraint on the upper surface in the load direction of another material agent adjacent to the material agent and that does not receive the displacement ^] The boundary agent generated in the rigid body subjected to the displacement constraint transmits a load of the same value in the load direction with respect to the load from the material agent, and the load is inverted with respect to the load from the adjacent material edge. A method of transmitting a load having the same value as the load in the direction and displaying the load transmission displacement of the object.

Further, the invention according to claim 2 of the present application relates to the display method according to claim 1, wherein the first to n-th material agents transmit a load when a transmitted load is larger than a predetermined threshold value. It is generated in the direction. Further, the invention according to claim 3 of the present application is a computer readable program storing a program of a method for displaying a load transmission displacement of an object on a rigid body subjected to displacement constraint from the periphery in a boundary not subject to displacement constraint from the periphery on the computer screen. A hexahedral or planar first material agent virtually generated in the object at a load position given to an arbitrary position of the object, and a first material agent of the first material agent. A second material agent of the same shape virtually generated on an adjacent surface other than the surface receiving the load, and, similarly, sequentially, in the same object, a boundary that is not subject to the object and the displacement constraint and / or A third, fourth,... N-th material agent virtually generated up to the boundary with the rigid body subject to the displacement constraint; And / or a boundary agent having a predetermined shape that is virtually generated on a contact surface of a rigid body subjected to displacement constraint. In the material agent, the upper surface and the lower surface of the object are arranged in the load direction with respect to the load direction. In addition, a predetermined load according to the material property, a predetermined load corresponding to the strain characteristic of the object, and a load of another material agent adjacent to the material agent are provided on a surface perpendicular to the load direction. Predetermined displacement on top of direction The boundary agent generated in the boundary where the load is not constrained is transmitted, and the load from the adjacent material agent is transmitted in the load direction with the same value, The boundary agent generated in the rigid body subjected to displacement constraint transmits the load of the same value as the load in the opposite direction to the load from the adjacent material agent and displays the load transfer displacement of the object Method.

 Furthermore, the invention according to claim 4 of the present application relates to a computer-readable recording medium recording the program according to claim 3, wherein the first to n-th material agents have a predetermined load to be transmitted. It is characterized in that it is generated in the direction of load transmission when it is larger than the threshold value. BRIEF DESCRIPTION OF THE FIGURES

 FIG. 1 is a configuration diagram showing agentization of a target object for displaying a load transfer displacement of the object according to an embodiment of the present invention.

 FIG. 2 is an operation conceptual diagram when a predetermined input load is applied to a material agent of an object in order to display a load transfer displacement of the object according to one embodiment of the present invention.

 FIG. 3 is an operation conceptual diagram when a predetermined input load is applied to a two-dimensional material agent in order to display a load transmission displacement of an object according to one embodiment of the present invention.

FIG. 4 is a diagram illustrating a case where a predetermined input load is applied to a two-dimensional material agent in order to display a load transmission displacement of an object according to an embodiment of the present invention, in a direction perpendicular to the direction of the input load. FIG. 4 is a conceptual diagram of an operation based on a load transmitted to a vehicle. 'FIG. 5 shows a case where a predetermined input load is applied to a two-dimensional material agent in order to display the load transfer displacement of an object according to an embodiment of the present invention. It is an operation conceptual diagram by a load transmitted in a direction perpendicular to a boundary agent which is not subject to displacement constraint with respect to a direction of an input load of a material agent.

 FIG. 6 shows that when a predetermined input load is applied to a two-dimensional material agent in order to display the load transmission displacement of an object according to an embodiment of the present invention, a displacement constraint is applied to the bottom of the material agent. It is an operation | movement conceptual diagram with respect to an input load when the boundary agent which returns as it is is arrange | positioned.

 FIG. 7 is an explanatory diagram showing a target object and a state in which the target object is displayed as an agent using a computer in order to display the movement of the object according to the embodiment of the present invention.

 FIG. 8 is a graph showing a stress comparison between the agent according to the embodiment of the present invention and the stress of the FEM in the X direction and the stress in the y direction. FIG. 9 is an explanatory view showing a result of deformation of a target object by a method for displaying load transfer displacement of an object according to one embodiment of the present invention.

 FIG. 10 shows the stress values in the X and y directions by the method (the agent) for displaying the load transfer displacement of an object (plane) according to an embodiment of the present invention, and the conventional FEM analysis. 6 is a graph showing the ratio of stress values in the X and y directions.

 FIG. 11 is a graph comparing the method of displaying the load transfer displacement of an object (plane) according to an embodiment of the present invention (the agent) with the displacement of a conventional FEM analysis. BEST MODE FOR CARRYING OUT THE INVENTION

Hereinafter, an embodiment of the method for displaying the load transfer displacement of an object according to the present invention will be described. In particular, when a load is applied to an arbitrary position of a target object, the load is generated from the position to the boundary of the object. Using the concept of the material agent in the object and the boundary agent generated at the boundary of the object, the generation The process and the state in which the displacement of the object is displayed from the load transmission process will be described in detail with reference to the drawings.

 FIG. 1 shows that, when a load is applied to an arbitrary position in the object 1 according to the present embodiment, a first agent is virtually generated at that position, and the load is transmitted inside the object 1, FIG. 2 is a schematic diagram showing an outline in which some agents are generated at the boundary of the object 1 and some agents 3a and 3b are generated at the boundary of the object 1, and FIG. FIG. 4 is a load transmission operation diagram showing in more detail how a load is transmitted between these agents.

 In FIG. 1, reference numeral 1 denotes an object which is a target object, reference numeral 2 denotes, for example, a first material agent generated at an arbitrary load position of an elastic body, and reference numeral 3 a denotes a first material agent generated at a boundary of the object 1. A boundary agent that is generated in a boundary that is not subject to displacement constraint from the surroundings; and 3b is an agent that is generated in the boundary of the object 1 and that is in the rigid body that is subject to displacement constraint from the periphery. Is a boundary agent generated in Reference numeral 4 denotes a boundary that is not subject to displacement constraint from the periphery where the target object 1 according to the present embodiment is arranged, for example, air. Reference numeral 5 denotes a boundary around the target object 1 according to the present embodiment. A boundary subject to displacement constraint from, for example, a rigid body.

In other words, it shows how the load applied to the object 1 is transmitted through the object 1 and eventually displaces (deforms) the object 1. In the embodiment, each agent is generated at an arbitrary position of the target object 1 when a load is applied to the position, a first material agent 2 divided into a predetermined virtual solid is generated, and then the agent 1 of the object 1 is generated. Up to the nth nth material agent 2 generated at the boundary is generated. Then, in a state where the object 1 is placed, a boundary agent 3a generated at a boundary in a boundary that is not subjected to displacement constraint from the surroundings, The explanation is made on the assumption that the boundary agent 3b is generated at the boundary in the boundary subjected to the displacement constraint from the enclosure.

 [Premise of agent generation]

 The generation and load transmission of the following agents are described here based on a square two-dimensional structure for convenience, and then a three-dimensional structure using a cube. That is, in the present embodiment, assuming the arrangement, a two-dimensional target object arranged in a predetermined boundary is assumed, and when a load is applied to a certain position of the two-dimensional object, the two-dimensional object The displacement of each part of the target object is attempted based on Figs.

 [Operation of Material Agent (Part 1)]

 The material agent 2 virtually divides the inside of the two-dimensional target object by a predetermined shape (for example, “square”), and assumes a virtual shape supposed to display a position with respect to an external force applied to the target object. And generates one material agent 2 (for example, a first material agent 2a) at an arbitrary position of the two-dimensional target object.

When this first material agent 2a is generated, the input load P. Painter Cal direction and the material agent 2 a base of which is the same direction (BOTTOM) 2 a _2, the material agent 2 a and the second material agent 2 b of the same type are produced in the upper side is in contact position.

Further, when the first material agent 2 a is produced, the said first timber fee agent 2 a of one side (LEFT) 2 a _3, the first material Agent 2 a same shape first second material agent 2 c is generated in, the material E Jento 2 a of the other side (RI GHT) 2 a _4, a similar second material E - stringent 2 d is generated.

Figure 3 shows the results when a predetermined input load is applied to the material agent 2a. It is a conceptual diagram of load transmission in the vertical direction, and it is assumed that the following material agents generated in the respective parts perform the following transmission operations. In the present embodiment, the material agent 2 a is formed of a square, and has an input load P. 2 at and the input load P. And bottom (BOTTOM) ₂ a 2 which are transmitted in such a direction the same direction, and one side (LEFT) 2 a _3, consisting of the other side (RI GHT) 2 a ₄ Prefecture.

 For such a material agent 2, the input load P from above. , The first material agent 2a is generated, the load is transmitted immediately below the first material agent 2a, and the second material agent 2b is generated in the direction in which the load is transmitted. You.

For example, assuming that the force received by the upper side (TOP) of the first material agent 2a is the load P i, the load Pi is the input load P. A load P i (P! = 0;! · P ₀ ) obtained by applying a predetermined transfer coefficient _{α ι} to the load P ₂ , where the force received by the upper side (TOP) of the second material agent 2 is load P _{2 2,} the input load P i load is applied is predetermined transfer coefficient monument ₂ [rho ₂ - a _{(Ρ 2 = α 2 Ρ 0} ).

In addition, the material agent 2 receives an input load from the top. When the Ru given, the second material agent 2 c which said first material agent 2 a of one side (LEFT) other side to _{2 a 3 (RI GHT) 2} c 4 are in contact is created (in FIG. 3 left materials agent 2 a), the frictional force between the material E one Gen DOO 2 a of one side (lEFT) 2 a ₃ and the other side of the material agent 2 c (RI GHT) 2 c 4 occurs , Load P. A load in the same direction as the direction in which is transmitted is applied to the upper side (TOP) 2 of the material agent 2c.

At this time, the force applied to the upper side (TOP) of the material agent 2c is the load P. Load P ₃ (P ₃ = Fei ₃ · [rho.) Took a predetermined transfer coefficient monument ₃ and Similarly, a second material agent 2 d having one side (LEFT) in contact with the other side (RI GHT) 2 a ₄ of the first material agent 2 a is generated (in FIG. 3, the material agent 2 d). 2a), the force applied to the top (TOP) 20 ^ of the second material agent 2d is also the load P. Then, a load Ρ ₃ (Ρ ₃ = α ₃ · Ρ.) Obtained by applying a predetermined transmission coefficient α ₃ to the load is obtained.

That is, the input load Ρ is above the target object. Subject, the target object receives an input load Ρ. The first material agent 2a is generated in the transmission direction by transmitting the load P i with a predetermined transmission coefficient applied in the same direction. Then to produce a second material agent 2 b in said transfer direction while transmitting the load weight [rho ₂ that took predetermined transfer coefficient alpha ₂ directly below the said first material agent 2 a. Further, when the upper part of the second material agent 2b receives the load P i, the second material agent 2b transmits the load having a predetermined transmission coefficient directly below the second material agent 2. Then, a third material agent (not shown in FIG. 3) is generated, and is sequentially transmitted by receiving a load having a predetermined transfer coefficient.

Also, the input load P received by the upper part of the first material agent 2a. For example, a second material agent 2c and a second material agent 2d are generated adjacent to the first material agent 2a in the load transfer direction, and these second material agent 2c and the second material Due to the frictional force generated between the second material agent 2c and the second material agent 2d, an input load P is applied to the upper side of the second material agent 2c and the second material agent 2d. Load Weight [rho ₃ which took predetermined transfer coefficient alpha ₃ is load.

Then, the second agent 2 c, 2 d is to load P ₃ and the input load, and transfer loads multiplied by the E shed predetermined transfer coefficient on the load P _3, the second agent 2 c, 2 d the following materials agent produced immediately below of the load predetermined transfer coefficient load heavy P ₃ where (¾ ₂ is applied are sequentially transmitted. Thus the input load p. For the input load p. The value that is considered to be effective for the next transfer of the load transmitted in the same direction as the above, that is, the load is transmitted until the load becomes less than or equal to a predetermined threshold value a, and the direction area in which the transmitted load is generated (In the same direction as the input load P.), the generation of the material agent is repeated.

 [Operation of Material Agent (Part 2)]

' Po, ひ 伝 達係数） がかかる方向に対して直角方向に伝達する。 これは、 第一の材 料エージェント 2 aにかかる荷重により、 該第一の材料エージェント 2 aが押しつぶされようとしたときに入力荷重 P。の分力 P iがかかる方 向に対して直角方向に広がろうとする荷重がかかることによる。 Next, FIG. 4 shows a predetermined input load P to the material agent 2. , The input load P. FIG. 8 is a conceptual diagram of an operation by a load transmitted in a direction perpendicular to the input direction of the two-dimensional object, and generates a first material agent 2a at an arbitrary position of the two-dimensional target object, similarly to the material agent 2 described above. After the first material agent 2a is generated, the first material agent 2a has an input load P. Component of Pi

'Po, the transmission coefficient) is transmitted in a direction perpendicular to the direction in which it is applied. This is the input load P when the first material agent 2a is about to be crushed by the load applied to the first material agent 2a. This is because a load is applied to spread in the direction perpendicular to the direction in which the component force Pi is applied.

The first material agent 2a is, like the above, made of a square, and has an input load P _Q on the upper side (TOP) and an input load P. The base (BBTT〇M) 2 a ₂ that transmits the load in the same direction as the direction in which the component force Pi is applied, and the input load P. One side of the component force P Interview to transfer loads in a direction perpendicular to such direction (LEFT) and 2 a _3, input load P. The component force P E in respect consuming direction consists other side (RI GHT) 2 a ₄ Metropolitan to transfer loads at right angles, one side of the first material agent 2 a (LEFT) 2 a ₃ When the load is transmitted, a second material agent 2 c of the same type as the first material agent 2 a is generated, and the other side (RI GHT) 2 a _{4 of} the first material agent 2 a is generated. When the load is transmitted to the Is done.

In FIG. 4, for the first material agent 2a, the input load P. When affect the synchronization, distortion by facing the load surface by component force P i (Fig. 2 a ₂ surface in 4) to temporarily restrain, Hooke's law (the distortion of the elastic body such thing as proportional to the stress) ( ε), resulting in an input load Ρ. The input force P shrinks in the same direction as the direction in which the component force P i is applied. In the direction perpendicular to the direction in which the component force Pi is applied, based on the Poisson's ratio (レ).

That is, for the first material agent 2a, the input load P is applied to one side (LEFT). When a load perpendicular to the component force P i is transmitted, the second material agent 2 c is generated in contact with one side (LEFT) 2 a ₃ of the first material agent 2 a. A second material agent 2 d is generated in contact with the other side (RI GHT) 2 a ₄ .

By generating the second material agent 2c and the second material agent 2d, the input load P is obtained. The material agent 2 a receives the distortion (ε _χ = 1 β · _r · ε _y (β: transfer coefficient)) on one side (LEFT) 2 a ₃ and the other side (RI GHT) 2 a _4. The minute is about to spread.

Then, the other side (RI GHT) side of the second material agent 2 c 'is the load P ₄ (P ₄ = (1-β)-V · ε _ν · Α ₃ · Ε (Α ₃ : 2 a ₃ sectional area of the surface, E: receiving a Young's modulus of the)), one side (LEFT) side of the second material agent 2 d is the same and the load P ₄ of the second material agent 2 c receives In the opposite direction, a load P ₄ (P ₄ = (1—] 3) · · · ε _y · Α ₄ · E is applied.

And the input load P. , The input load P. The transmission of the load and the generation of the material agent and the transmission of the load in the direction in which the load is generated (the vertical direction) are repeated until the load transmitted at a right angle to the predetermined threshold "T" or less. [Boundary agent operation without displacement constraint]

FIG. 5 shows that when a predetermined input load is applied to the material agent 2, for example, when the object 1 is placed in a boundary that is not subject to displacement constraint from the surroundings, the object 1 This is a schematic representation of what is affected by this, and the side 2 a _{4 of} the second material agent 2 generated at the boundary of the object 1 is in contact with, for example, air 4). FIG. 9 is a conceptual diagram showing the operation of the boundary agent 3a to show what kind of load is transmitted and the amount and direction of the load with respect to the input load by the side (RI GHT).

5, in contact with the material agent 2 sides (RI GHT) 2 a ₄ to the load of the vertical direction is applied the material agent 2 sides (RI GHT) 2 a _4, boundary agent 3 a is generated while being, the load P ₅ applied from the side (RI GHT) 2 a ₄ of the materials agent 2, is returned to the wood charge agent 2 a by the boundary agent 3 a as a load [rho ₅ 'of the same size the same direction It will be.

At this time, the load transmitted to the material agent 2 a ₄ is the case of the following predetermined to listen Nea, boundary agent 3 a is not generated, load is not reached Den.

 [Boundary agent operation under displacement constraint]

FIG. 6 shows that when a predetermined input load is applied to the material agent 2, when the material agent 2a is, for example, in contact with the rigid body 5, the boundary agent 3b generated there It is an operation | movement conceptual diagram which shows what kind of load is transmitted with respect to load, and the amount and direction of the load. In Fig. 6, the input load P. Base materials Agent 2 a having received the (6 not shown) (B ΟΤΤΌΜ) input load P. from 2 a ₂ When a load P ₆ is transmitted in the same direction as In the present embodiment, a square boundary agent 3b is generated. And, the load P ₆ transmitted from the boundary agent 3 b of the upper (TOP), the load [rho ₆ of the load P ₆ equal amount 'is returned from the boundary agent 3 b in the material agent 2 a. This is because the position where the boundary agent 3b is generated is due to the rigid body 5, and no distortion is caused by the load received from the material agent 2a. Also, the same, the material agent 2 load was reached transferred to a ₂ is in the case of less than a predetermined threshold value §, boundary agent 3 b is not generated, load is not transmitted.

 Thus from material agent 2, input load P. In the same direction as the load is applied, or the input load P. In the material agent 2 sequentially generated in a direction perpendicular to the direction, the transmitted load is reduced based on a predetermined transmission coefficient. For example, assuming an elastic body such as rubber, when a predetermined input load is applied to a part of the upper surface of the rubber (elastic body), the position where the input load is applied greatly dents (distortion), and the input load As the distance from the position increases, the dent (strain) becomes smaller, and if the rubber (elastic body) generated by this material agent is placed on a rigid body (boundary agent 3) such as a concrete table, for example, However, the load transmitted from the rubber (elastic body) is applied to the concrete base (rigid body) and the load is returned to the rubber (elastic body), and the concrete base (rigid body) does not cause any distortion.

 Next, as to the method of displaying the movement of each agent of the two-dimensional target object described above, a state in which the movement of the two-dimensional target object is actually calculated by a computer and displayed on a screen will be described.

The computer used in the present embodiment is a personal computer having a memory of 128 MByte and a CPU of Celelon 400 MHz manufactured by Intel (Inte 1), and the software is manufactured by Sun Microsystems. J AVA language (Ver.1.1.7) with Swingl. 1 and Visua 1 Cafe Ver3.0c made by Symantec were used. '-Fig. 7 is an explanatory diagram showing how a two-dimensional target object is agentized using a computer and the load transmission displacement of the object is displayed.

 At this time, in the method of displaying the load transmission displacement of the object of the present invention, the program of the display method may be recorded in a computer-readable recording medium in advance, and the program may be read from the recording medium.

First, as a virtual object information, a computer uses a flat plate with a width of 200 mm, a height of 200 mm, and a thickness of 2 mm. 6 GPa, Poisson's ratio 0.3, input load 2N from above, α = 0.5, ₂ = 0.5, ₃ = 0.25, and / 3 = 0.5, and the threshold value = 1 0 3—3.

 When the above-mentioned conditions of the target object (material agent) are input to the computer, and an input load (for example, the above-mentioned 2 mm load) is applied to an arbitrary position of the target object from top to bottom, the transmitted load is Generates material agent 2 when the value is larger than the threshold value, and performs deformation and load transmission of material agent 2.

 Deformation of all generated agents until they become smaller than a predetermined threshold value. ・ After calculating the transmitted load, the results are displayed on, for example, a display device connected to the computer or a printer. Then, the motion of the 2D target object is displayed.

 The condition of the target object (material agent) may be input for each target object, but the conditions of a plurality of target objects may be input in advance, stored in a database.

FIG. 8 shows a method for displaying the movement of an object (plane) according to the present invention (the above-described method). Fig. 9 is a graph showing the ratio of the stress values in the x and y directions according to the conventional FEM analysis and the stress values in the x and y directions according to the conventional FEM analysis. This is a stress comparison graph comparing the stress in the y direction and the stress in the y direction. In each of the graphs, the trends are almost the same, and especially in the X direction of the stress comparison graph (see Fig. 9). ing.

 Fig. 10 is an explanatory view showing the result of deformation of the target object, and Fig. 10 (a) shows the result obtained by the conventional FEM when the input load is applied to the target object. (B) shows the deformation (distortion) of each agent when an input load is applied to the target object, and the general trend is expressed in almost the same form.

 At this time, according to the display method of the present application, for a portion where no external force acts on the target object, the agent is not generated and the load is not transmitted, and the initial state is displayed as it is.

 FIG. 11 is a graph comparing the displacement of the method of displaying the movement of the object (plane) according to the present invention (the agent) with a conventional FEM analysis. In this graph, the tendency of both is the same. .

 In this way, when represented by a matrix of the same size as the conventional FEM, there is roughness, but the calculation is simple and fast, so the target object is made smaller and the transfer coefficient is adjusted, so that the FEM In almost the same way as the display, the movement of the object can be sufficiently displayed.

 Then, for the agent described above, the input weight is, for example, 0.

By repeatedly displaying up to 2 N in 1 N increments, it is possible to display the movement of this target object as it deforms.

So far, the material agent 2 and the boundary agent 3 have been described in two dimensions. Next, as a second embodiment, the motion of the object according to the present invention will be described. 'Describe how to display material agent 2 and boundary agent 3 in three dimensions.

 FIG. 2 described above is a load transfer operation diagram of the three-dimensional target object (agent) according to the present embodiment, where reference numeral 12 is a material agent, and 13 is a boundary agent.

For example, an input load P at a predetermined position of the material agent 12. Then, in the present embodiment, for example, a cubic material agent 12a is generated, and when the material agent 12a is generated, the input load P is calculated based on a predetermined transfer coefficient. The load P i is transmitted in the same direction as that of the input load P i, and the input load P is applied to the bottom surface of the material agent 12 a in the same direction as the input load P i based on a predetermined transmission coefficient ₂ . A transmitted load P ₂ of the same direction, the material agent 1 2 b of the same shape having an upper surface in contact with the transfer Direction region (materials agent 1 2 a of the bottom surface) is generated, the input load P. In the same direction, the material agent 12 is generated and transmits the load until the material agent 12 falls below the predetermined threshold value or reaches the material agent 12h.

Also, when this material agent 1 2a is generated, the input load P. Takes the same direction, i.e. it takes friction force to the four sides of the material agent 1 2 a, as in the first embodiment, based on a predetermined transmission coefficient monument _3, input load P. The load P ₃ in the same direction is transmitted, the material agent 1 2 a of the same shape of materials agent 1 2 c, 1 2 d, 1 2 e, 1 2 f is generated.

That is, in Fig. 2, the material agent 12a is on the right front side of the material agent 12a, and the material agent 12d is on the left front side of the material agent 12a. The material agent 1 2 e is generated on the side of, and the material agent 12 f force is generated on the right rear side. And, like the agent formation and load transmission described above, the material agent 12a receives the input load P. The component ε is crushed by receiving the component force P i, and the strain ε tends to spread laterally, and is perpendicular to each side surface (4 directions in the present embodiment) (with respect to the input load Ρ).荷重₄ (Ρ ₄ = (1-) 3) · V · ε _y · A · Ε (Α: cross section of one side of material agent 2a, E: Young's modulus of material)) Is transmitted.

Then, each material agent 1 2 c, 1 2 d, 12 e, 12 ί, a load [rho _eta in - - - is transmitted, until the load becomes a predetermined threshold value §, there have materials agent 1 Generate material agent 12 and transmit load until it reaches 2 g, and then generate and transmit material agent (not shown in Fig. 2) in contact with the side of material agent 12b.

Then, as described above, if one side of the material agent 12 g is a boundary where displacement is not restricted (for example, in the air), a boundary agent 13 a is generated in contact with one side of the material agent 12 g together with the material agent 1 2 load P ₅ applied from one side to be returned to g is applied to the boundary agent 13 a as its or until the load P ₅ '.

Also, input load P. The input load P from the bottom surface of the material agent 1 2h, which transmitted the load by receiving the component force P i. When a load P _{6 in the} same direction as that is transmitted, a cubic boundary agent 13 b is generated at the boundary (for example, rigid body) that is constrained by displacement, and the load P ₆ transmitted from the upper surface of the boundary agent 13 b is the same amount of load [rho ₆ 'is returned from the border agent 1 3 b in the material E one Gen Bok 12 h and the load P _6.

 In this way, for a three-dimensional object, as in the case of the two-dimensional structural object described above, each agent can generate and transmit a load, and the state of displacement can be easily calculated.

In the above embodiment, the shape of each agent is square or Although described as a cube, the shape may be a regular polygon or a regular polyhedron (for example, regular hexagon or regular hexahedron). In particular, if agents of the same shape are generated adjacently without any gap, The shape is not limited.

 In the above embodiment, the boundary agent that is not subject to displacement constraint is described as being in air, but may be in water (in a liquid), in a vacuum, or in a specific type of gas, and the components of the boundary agent are not particularly limited.

 In the above embodiment, the boundary agent subject to the displacement constraint is described as a rigid body, but may be an object having another transfer coefficient in addition to the rigid body. Calculations (with different transfer coefficients) may be performed by the method. Industrial applicability

 According to the method for displaying the load transfer displacement of an object according to the present invention, a first agent is generated for a load on a target object, and the agent is sequentially generated from the agent based on a predetermined transfer coefficient. In the field of computer graphics, it can be easily incorporated into application programs such as games, and the deformation of displayed objects can be easily applied to physics, especially in the field of material mechanics. Computer graphics animation for displaying the status can be easily realized. This eliminates the need to learn and use the finite element method that requires specialized knowledge, and also simplifies the program, which reduces the computation time (object) of the computer that executes it. (The time required to display the displacement).

According to the method of displaying the load transfer displacement of an object according to the present invention, the portion that is not subjected to a load (below a predetermined threshold) is generated by the agent. Since there is no need to transmit and generate loads, when displaying the partial displacement of an object, it was necessary to calculate the entire state in the past. Since there is no need to perform this, there is an extremely excellent feature and effect that the calculation time for the combination display required for the entire display can be drastically reduced.

 In this way, specialized knowledge is not required and the processing load on the computer can be reduced, so that it can be used for computer games using computer graphics, movie backgrounds (frames), etc. It can be applied to simulations, and can be widely used to calculate the trend of displacement not only in physical properties but also in fluids and display it in a simulation.

 Furthermore, by combining the display method of the present invention for displaying the load transfer displacement of an object with CG program software, the display can be performed in consideration of the deformation of the object itself. When a car turns a curve, natural movements can be realized in the same way as real images (shooting with a video camera or the like), taking into account the power applied to the tires.

Claims

The scope of the claims 1. A method of displaying a load transfer displacement of an object on a rigid body subject to displacement constraint from the periphery in a boundary not subject to displacement constraint from the periphery, wherein the load transfer displacement is virtually given to an arbitrary position of the object. A first material agent having a hexahedron or planar shape generated in the object, and a second material agent having the same shape virtually generated on an adjacent surface other than the surface receiving the load of the first material agent Similarly, the third and fourth virtual agents are sequentially generated in the same manner in the same manner as described above, sequentially to the boundary between the object and the rigid body subject to the displacement constraint and / or the rigid body subject to the displacement constraint. , A 'n' material agent, and a boundary agent of a predetermined shape virtually generated on the contact surface between the object and the boundary not subject to the displacement constraint and the rigid body subject to the displacement constraint or the displacement constraint. And said In the material agent, for the load direction, a predetermined load according to the material characteristics of the upper surface and the lower surface of the object in the load direction, and a distortion characteristic of the object on the surface perpendicular to the load direction. The specified load and the load subjected to the predetermined displacement constraint are transmitted to the upper surface in the load direction of the other material agent adjacent to the material agent, and the load is generated in the boundary where no displacement constraint is applied. In the boundary agent, the load from the adjacent material agent is transmitted in the load direction with the same value, and in the boundary agent generated in the rigid body subjected to the displacement constraint, the load from the adjacent material agent is And transmitting a load having the same value as the load in a direction opposite to the load to display a load transfer displacement of the object. 2. The display method according to claim 1, wherein the first to n-th material agents are generated in a load transmitting direction when a transmitted load is larger than a predetermined threshold. 3. From the surroundings in the boundary where there is no displacement constraint from the surroundings on the computer screen A method for displaying the load transfer displacement of an object on a rigid body subject to a displacement constraint, wherein a hexahedron or plane shape virtually generated in the object at a load position given to an arbitrary position of the object A first material agent of the same shape, and a second material agent of the same shape virtually generated on an adjacent surface other than the surface receiving the load of the first material agent. A third, fourth,..., N-th material agent virtually generated up to a boundary between the object and the boundary that is not subjected to the displacement constraint and / or a boundary between the rigid body that is subjected to the displacement constraint. A boundary agent having a predetermined shape virtually generated on a boundary not subject to displacement constraint and / or a contact surface of a rigid body subject to displacement constraint, wherein the material agent A predetermined load according to the material properties of the upper and lower surfaces of the object in the load direction, and a predetermined load according to the strain characteristics of the object on a surface perpendicular to the load direction, adjacent to the material agent; A boundary agent generated in a boundary that is not subjected to a displacement constraint transmits a load subjected to a predetermined displacement constraint to the upper surface in the load direction of another material agent, and a load from the adjacent material agent is generated. A boundary agent generated in a rigid body subject to the displacement constraint, transmitting a load of the same value in the load direction and having the same value as the load in the opposite direction to the load from the adjacent material agent And a computer-readable recording medium on which a program for transmitting the load transmission displacement of the object is recorded. 4. The program according to claim 3, wherein the first to n-th material agents are generated in a load transmitting direction when a transmitted load is greater than a predetermined threshold. A computer-readable storage medium.