JP2012190444A - Mesh model creation method and analysis method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a suitable technique for obtaining mesh models obtained by reconstructing and successively connecting mesh models on boundary faces when mesh models sink in each other to interfere.SOLUTION: An interference determination part determines interference between a first mesh model and a second mesh model, and extracts an element interfering with the first mesh model and an element interfering with the second mesh model as interference elements. An element deletion part deletes the interference elements, a polygon extraction part extracts a polygon for connecting the first and second mesh models having the interference elements deleted, and an element filling part 13 fill the polygon with elements.

Description

  The present invention relates to a method for automatically reconstructing a mesh model when mesh models interfere with each other.

As a numerical calculation method for handling a free surface, a calculation method using a method of capturing an interface in the Euler coordinate system is often used. Focusing on the grid fixed in the Euler coordinate system, it is a method to numerically solve the entry / exit, storage, etc. In this method, since the lattice is fixed, complicated deformation of the interface can be handled. On the other hand, since the lattice is simple such as an orthogonal lattice, the interface cannot be clearly shown. Further, even when calculating the behavior of a fluid having a high viscosity relative to air, it is necessary to calculate the air portion around the fluid.

On the other hand, a calculation method (ALE method) in an ALE (Arbitrary Lagrangian Eulerian) coordinate system is known as a method for avoiding element distortion caused by the movement of the interface. In the ALE method, since the movement of the substance particles and the mesh model can be handled separately, the mesh model can be reconstructed when the element is distorted due to the movement of the interface. In this method, the interface can be clearly expressed, and it is not necessary to calculate the air portion in the above case.

In the conventional technique using the ALE method, it is possible to handle only when there is one interface which is a free surface, and it is impossible to calculate a phenomenon in which two objects are combined. Similarly, it was not possible to calculate that one interface was deformed and bonded.
For example, let us consider a case where two objects come into contact with each other when a temporal change in motion of two objects that move independently is calculated for each short time step. In the calculation, each object has no effect on the other objects. Therefore, even if two objects are in geometric contact, each object continues to move as if there was nothing.

In order to consider the influence of the movement of each contacted object on the movement of multiple interfaces and the movement of other objects, each object is continuously measured at the contacted interface in the time step calculation. Need to connect to. That is, it is necessary to correct the discontinuity of the mesh model at the interface.
As a method for generating a single continuous mesh model by correcting and combining a plurality of mesh models, a method disclosed in Patent Document 1 is known.

JP-A-2005-216038

As described above, in the calculation in the ALE method, a plurality of objects contact in a time step. The step size of the time step has a certain size in order to reduce the calculation time realistically. For this reason, two objects are not just in contact with each other, and indentation often occurs.
However, in the method of Patent Document 1, only a correction in the case where a plurality of mesh models are in contact with each other and have a common interface can be performed, and it is not possible to cope with the indentation between mesh models.

  The present invention has been made in view of the above problems, and when a mesh model is indented and interferes with each other, a suitable method for reconstructing the mesh model and obtaining a mesh model continuously connected at the interface is provided. The purpose is to provide.

A first aspect of the present invention is a mesh model creation method for restructuring a mesh model when mesh models interfere with each other in a finite element method,
An acquisition step in which a computer acquires coordinate values of nodes of each of the first mesh model and the second mesh model;
An interference determining step in which a computer determines interference between the first mesh model and the second mesh model, and extracts an element interfering with the first mesh model and an element interfering with the second mesh model as interference elements;
An element deletion step in which the computer deletes the extracted interference element;
A polygon extraction step of extracting a polygon for connecting the first and second mesh models from which the interference elements have been deleted;
An element filling step in which the computer fills the extracted polygon with elements;
An output step of outputting, as a new mesh model, a first mesh model and a second mesh model connected to each other by polygons filled with elements to the output unit;
In the interference determination step, an element having a node existing inside another element or on a node or a side is extracted as an interference element.

  According to a second aspect of the present invention, there is provided an analysis method in which a computer analyzes a behavior of an object having a free surface by numerical calculation by a finite element method, wherein the computer applies a mesh model of the object obtained by the numerical calculation. The analysis method is characterized in that a mesh model is reconstructed using the mesh model creation method according to the first aspect of the present invention.

The third aspect of the present invention is a mesh model creation device that reconstructs a mesh model when mesh models interfere with each other in the finite element method,
An acquisition unit for acquiring coordinate values of nodes of each of the first mesh model and the second mesh model;
An interference determination unit that determines interference between the first mesh model and the second mesh model, and extracts an element that interferes with the first mesh model and an element that interferes with the second mesh model as an interference element;
An element deletion unit for deleting the extracted interference element;
A polygon extraction unit for extracting a polygon for connecting the first and second mesh models from which the interference element is deleted;
An element filling unit for filling the extracted polygon with elements;
An output unit for outputting the first and second mesh models connected to each other by polygons filled with elements as a new mesh model, and
The interference determination unit is a mesh model creation device that extracts, as an interference element, an element having a node existing inside another element or on a node or a side.

  A fourth aspect of the present invention is a program that causes a computer to execute each step of the mesh model creation method according to the first aspect of the present invention.

  According to the present invention, when mesh models are indented and interfere with each other, the mesh models can be reconstructed to obtain a mesh model continuously connected at the interface.

The figure which shows the hardware constitutions of an analysis apparatus and a mesh model creation apparatus. The functional block diagram of an analysis apparatus and a mesh model creation apparatus. The flowchart of a mesh model creation process. The figure explaining interference determination. The figure explaining the interference in one mesh model. The figure explaining element deletion. The figure explaining polygon extraction. The figure which shows the initial shape of the mesh model used for calculation of an Example. The figure which shows the calculation result of an Example. The figure explaining element deletion when interference arises in a plurality of places. The figure explaining polygon extraction when interference arises in a plurality of places.

<Device configuration>
FIG. 1 is an apparatus configuration diagram illustrating a hardware configuration of an analysis apparatus and a mesh model creation apparatus according to an embodiment of the present invention. This analysis device is a device that analyzes the behavior of an object having a free surface by numerical calculation using a finite element method, and is used for simulations such as fluid calculation and structure calculation. The mesh model creation device is a function that forms part of the analysis device, and reconstructs the mesh model in consideration of the indentation between mesh models for the mesh model of the object obtained by numerical calculation by the finite element method. Is what you do.

  Reference numeral 1 denotes an input unit, for example, a mouse or a keyboard. The input unit 1 is used to input necessary data, create a necessary data file, and start execution of a program when a user performs calculations using the apparatus. Reference numeral 2 denotes a calculation unit, which includes a central processing unit (CPU) 4 and a memory 3. A storage medium 5 stores a program code. Functions and processes of an analysis apparatus and a mesh model creation apparatus described later are realized by loading a program from the storage medium 5 into the memory 3 and executing the program by the CPU 4. Reference numeral 6 denotes a storage unit composed of a hard disk or the like, which is a storage medium for storing an input data file used for calculation, a data file output by calculation, and an intermediate data file created by calculation. The program code can be stored in the storage unit 6. Reference numeral 7 denotes an output unit composed of a display, a printer, or the like, which outputs a calculation result. This apparatus can be configured by installing necessary program code in a general-purpose computer.

<Functional configuration>
FIG. 2 is a functional block diagram of the analysis device and the mesh model creation device. These functions are realized by a program as described above, but may of course be realized by dedicated hardware such as a logic circuit.

式１と式２において、ｖ、ｐ、ｆ、ρ、ａ、η、Ｉ、Ｄはそれぞれ速度、圧力、体積力、密度、加速度、粘性係数、単位テンソル、変形速度テンソルである。
なお、支配方程式はこれに限らず、他の方程式を用いることもできる。 8 is a governing equation calculation unit. The governing equation calculation unit 8 obtains a solution of the governing equation by the finite element method of the ALE method. In addition, the governing equation calculation unit 8 has a function of remeshing with respect to the strain of the element accompanying the deformation of the interface in order to maintain accuracy. In this embodiment, the governing equation of the incompressible Newtonian viscous fluid consisting of the law of conservation of mass (Formula 1) and the law of conservation of momentum (Formula 2) is used. This governing equation can also be used in the deformation of an elastic body.

In Equations 1 and 2, v, p, f, ρ, a, η, I, and D are velocity, pressure, body force, density, acceleration, viscosity coefficient, unit tensor, and deformation rate tensor, respectively.
The governing equation is not limited to this, and other equations can also be used.

  Reference numeral 9 denotes a mesh model correction unit. The mesh model correction unit 9 acquires information such as the coordinate values of the nodes of each mesh model as the calculation result of the governing equation calculation unit 8. And based on this information, from the process which determines whether mesh models interfere, from the process which rebuilds the mesh model connected continuously is performed. The mesh model correction unit 9 includes an interference determination unit 10, an element deletion unit 11, a polygon extraction unit 12, an element filling unit 13, and a node deletion unit 14, and controls their operations. In the present embodiment, the mesh model correction unit 9 corresponds to the acquisition unit of the present invention.

The interference determination unit 10 determines whether a plurality of mesh models interfere with each other due to deformation of the interface.
FIG. 4 is a diagram illustrating the function of the interference determination unit 10. FIG. 4 shows that the first mesh model 20 and the second mesh model 21 interfere with each other. For ease of viewing, the components and nodes of the mesh model 20 are indicated by broken lines, and the components and nodes of the mesh model 21 are indicated by solid lines. Further, the nodes painted in gray as in 22 are nodes that have been embedded in the other mesh model.
The interference determination unit 10 extracts all elements having nodes embedded in the mesh model (hereinafter referred to as “interference nodes”, and elements having interference nodes as “interference elements”). A node of an element E1 (in FIG. 4, all the elements are primary triangular elements, and the element has three nodes) exists inside the other element E2, or on the node or side of the element E2. In this case, it becomes an interference node (if it is on a node or on a side, it is regarded as a contact node). An element E1 having one or more interference nodes is extracted as an interference element.

Here, the interference determination unit 10 performs the determination of the convolution with respect to a certain node N among all the elements not including the node N. This is because if all the elements including the node N are added to the determination target, all the elements correspond to the interference elements.
As shown in FIG. 4, when only the reverberation (interference) can occur between different mesh models, the reverence determination target for the node N of the mesh model 20 is limited to only elements constituting the other mesh model 21. You can also This is because the mesh model 21 does not include the node N.
However, as shown in FIG. 5, there are cases where interference occurs in a single mesh model 200. In this example, interference occurs in a portion 201 by deformation of the mesh model 200 (elements are omitted). When such a case may occur, the determination target for the indentation with respect to the node N needs to be all elements that do not have the node N.

  The above interference determination is performed for both elements of the mesh models 20 and 21. That is, the interference determination unit 10 extracts interference elements on the mesh model 21 that interfere with the mesh model 20 and extracts interference elements on the mesh model 20 that interfere with the mesh model 21.

The element deletion unit 11 deletes interference elements in the mesh models 20 and 21. All the interference elements extracted by the interference determination are deleted. FIG. 6 shows the mesh models 20 and 21 after the interference elements are deleted.

The polygon extraction unit 12 has a function of extracting a polygon for connecting (continuously combining) the two mesh models 20 and 21 from which the interference elements have been deleted.
FIG. 7 is a diagram for explaining polygon extraction. The polygon connecting mesh models 20 and 21 is a closed loop (closed circuit) indicated by 31. A method of extracting the polygon 31 will be described with reference to FIG.

Reference numeral 24 denotes a node group in which constituent nodes of sides (free edges) that are not shared by a plurality of elements are rearranged in order counterclockwise without overlapping in the mesh model 21 before the interference element is deleted. In the mesh model 21 after the interference element has been deleted, if the constituent nodes of the node group 24 are traced two by two in order, there are places where the two nodes are not connected. That is node 25 in FIG. Further, there are places where two nodes are connected again after a place that is not connected continues. That is node 26 in FIG. The nodes 25 and 26 are a start point and an end point of an open loop (open circuit) 27 constituted by free edges newly formed in the mesh model 21 after the interference element is deleted. In other words, the open loop 27 is a set of a plurality of sides that are free (no longer shared by two elements) due to the deletion of the interference element.
Similarly, the open loop 28 and its start point 29 and end point 30 are also obtained for the mesh model 20. By connecting the nodes 26 and 30 and the nodes 25 and 29 obtained in this way, a polygon (closed loop) 31 connecting the open loops 27 and 28 can be created.

  Here, when the distance between the end points is very close, for example, when the nodes 26 and 30 are at substantially the same position, the two nodes may be made identical to connect them. To determine whether the distance between the two endpoints to be connected is very close, it is necessary to provide a certain tolerance (threshold value). For example, it is about one-half of the average distance of the nodes of all mesh models. If you set a threshold, you can connect without distorting the element.

  Next, a method for extracting a polygon when there are a plurality of places where interference occurs as shown in FIG. 10 will be described. 10A is a diagram in which two mesh models interfere with each other, and FIG. 10B is a mesh model after the interference elements are eliminated.

  FIG. 11A illustrates an open loop extraction method. Reference numeral 124 denotes a node group in which constituent nodes of sides (free edges) that are not shared by a plurality of elements are rearranged in order counterclockwise without overlapping in the mesh model 121 before the interference element is deleted. In the mesh model 121 after the interference element has been deleted, if the constituent nodes of the node group 124 are traced two by two in order, there are places where the two nodes are not connected. That is node 125. Further, there are places where two nodes are connected again after a place that is not connected continues. That is the node 126. The nodes 125 and 126 are the start point and end point of the open loop 127 composed of new free edges in the mesh model 121 after the interference elements are deleted. In other words, the open loop 127 is a set of a plurality of sides that are free (no longer shared by two elements) due to the deletion of the interference element.

FIG. 11B illustrates a method of extracting a polygonal closed loop (closed circuit). In the present embodiment, the nodes 125 and 126 that are the end points on both sides of the open loop (open circuit) 127 of the mesh model 121 are connected to one of the nodes on the open loop (open circuit) of the other mesh model 120, respectively. Thus, a closed loop is formed. At this time, the connection destination of the end point 125 is the end point 125 among the nodes constituting the interference elements (130a, 130b, 130c) on the mesh model 120 that are deleted as interfering with the element having the end point 125 as a node. The one with the closest distance is selected. The node to which the end point 126 is connected is also selected in the same manner.

  This will be described in more detail. In FIG. 11 (b), nodes 128 and 129 are nodes to which nodes 125 and 126, which are the end points of the above-described open loop 127, are connected via a free edge before the interference element is deleted. Elements 130a, 130b, and 130c filled in gray are elements that have been deleted as interference elements in the mesh model 120, and are elements that intersect a line segment 131 connecting the node 128 and the node 125. Of the nodes that constitute the elements 130a, 130b, and 130c and that are not interference nodes, 132, which is the node closest to the node 125, is set as a connection candidate for the node 125. Similarly, since the element 133 is an element that intersects the line segment 134 connecting the node 126 and the node 129, among the nodes that constitute the element 133 and that are not interference nodes, the node 135 that is the node closest to the node 126 is the node. 126 as connection candidates. An open loop 127 and an open loop when the free edge on the mesh model 120 is traced from the node 135 to the node 132 are represented by a line segment connecting the nodes 125 and 132 and a line segment connecting the nodes 129 and 135. If connected, a polygonal closed loop 145 is obtained.

  FIG. 11C illustrates the polygon extraction described above performed from the free edge and open loop 136 side of the mesh model 120. The connection candidates of the start point 137 and the end point 132 of the open loop are the nodes 138 and 125 of the mesh model 121, respectively. As a result, a polygonal closed loop 146 is obtained. It can be seen that the closed loop 145 obtained in FIG. 11B and the closed loop 146 obtained in FIG. The polygonal closed loop to be finally adopted is determined so that the number of nodes constituting the closed loop is reduced by using the extraction results of these temporary connection candidates. The open loop start point candidate on the mesh model 121 side is 125, and the end point candidate is 126 or 138. On the other hand, the open loop start point candidate on the mesh model 120 side is 132, and the end point candidate is 135 or 137. Here, the open loop constituting the closed loop to be finally extracted is selected so that the length connecting the start point and the end point along the free edge in each mesh model is the shortest. That is, the start point and end point of the open loop on the mesh model 121 side are 125 and 126 (shorter than 125 and 138), and the start point and end point of the open loop on the mesh model 120 side are 132 and 135 (shorter than 132 and 137). ). Finally, the open loop extracted along the free edge from the nodes 125 to 126 and the open loop extracted along the free edge from the nodes 132 to 135 are divided into the line segments of the nodes 125 and 132, and the nodes 126 and 135. By connecting with the line segment, it is possible to extract a polygonal closed loop. In this case, as a result, 145 in FIG. 11B becomes a polygonal closed loop.

  FIG. 11D shows a method for extracting a polygonal closed loop in the same manner for all open loops. Starting from the node 126, which was the end point of the open loop 127 of the mesh model 121, when the nodes of the node group 124 are traced in order, there are nodes that are not connected to each other. In addition, there is a node where two nodes are connected again after a part that is not connected continues. An open loop having the respective nodes as the start point and the end point is indicated by 151 in FIG. A polygon closed loop 147 is obtained by performing polygon extraction by the same process as the open loop 127. In this way, all open loops created by deleting the interference elements are extracted along the free edges, and all mesh models are combined by creating a polygonal closed loop for the open loops. be able to.

The method of extracting such a polygon (closed loop) does not need to strictly follow the processing method shown here, and uses a new open loop created by deleting interference elements to combine two mesh models. It suffices if a closed loop can be created. Further, when connecting the end points, in order to more faithfully reproduce the shape of the original mesh model, for example, a node located on the shape of the original mesh model may be added between the nodes 26 and 30. .

  The element filling unit 13 has a function of filling the polygon 31 extracted by the polygon extraction unit 12 with elements. As a method of filling the polygon 31 with elements, a Delaunay division method with boundary conditions can be used. The boundary condition is a method of connecting nodes by Delaunay algorithm so as not to destroy the original polygonal shape. The method of filling a polygon with elements is not limited to Delaunay division, and other algorithms such as an advanced front method are known, and an appropriate method may be used.

  The node deletion unit 14 deletes unnecessary nodes. The unnecessary nodes are the nodes 22 filled with gray in FIGS. 4, 6, and 7.

  Reference numeral 15 denotes an overall control unit. The overall control unit 15 performs data input, execution control of each function described above, non-stationary time repetitive processing, various determination processes, data output, and the like.

<Mesh model creation process>
FIG. 3 is a flowchart for explaining mesh model creation processing.
The overall control unit 15 first inputs data in S1. In S <b> 1, the user inputs an initial mesh model file through the input unit 1. The mesh model file is electronic data in which nodes and elements constituting the mesh model are defined. A node has a unique number and coordinate value data, and an element has a unique number of a group of nodes. In S1, calculation data for determining the behavior of the fluid is input. This is used when finding the solution of the governing equation, and is a physical property value such as a viscosity coefficient or a boundary condition. The calculation data depends on the governing equation. When the governing equation changes, it is necessary to input data corresponding to the governing equation. For example, in the case of viscoelasticity, relaxation time is required in addition to viscosity.

  In S2, the governing equation calculation unit 8 obtains a solution of the governing equation by numerical calculation based on data such as the initial condition acquired in S1. As a result, the speed and pressure of all nodes of the mesh model are obtained. Furthermore, when the deformation of the interface becomes larger than the initial deformation, the total number of nodes and elements and coordinate values change due to remeshing.

  In S3, the interference determination unit 10 extracts interference elements based on the mesh model obtained as a result of S2. The overall control unit 15 secures a 1-byte storage area as deletion element determination information for all elements, and stores the element flags extracted by the interference determination unit 10. The determination process of the interference determination unit 10 is as described above.

  In S4, the overall control unit 15 rearranges the constituent nodes of the free edge in the counterclockwise order without duplication in each mesh model, and obtains information on the total number of nodes of the loop and the number of the node after the rearrangement. Remember. This information is used in the next step S5. The element deletion unit 11 deletes all interference elements based on the deletion element determination information.

  In S5, the polygon extraction unit 12 extracts a polygon that joins the interference portions. The processing is as described above. As a result, the total number of polygons, the number of constituent nodes of each polygon, and an array in which the constituent node numbers of the polygons are arranged in order counterclockwise are created and stored as polygon information.

  In S6, the element filling unit 13 fills all polygons with elements based on the polygon information. Thereafter, unnecessary nodes that are no longer shared by any element are deleted by the node deletion unit 14.

If the calculation is completed until a desired time, data is output to the storage unit 6 in S7. The calculation result is also output to the output unit 7 such as a display or a printer.
If the calculation is not finished, the overall control unit 15 updates the time step in S8. In S <b> 8, the overall control unit 15 gives speed and pressure information to newly generated nodes and moved nodes. This is because this information is required for the calculation of the next time step. It should be noted that the velocity and pressure of a newly generated node or a moved node may be obtained by interpolating the values of previous time steps in surrounding elements (nodes). Thereafter, S2 to S6 are performed again.

<Example>
The example which calculated by crushing the state where the spherical resin was piled up with a rigid body is shown. The spherical resin assumes toner particles in an electrophotographic image forming apparatus, and calculates the state in which the toner particles are crushed and deformed. FIG. 8 is a mesh model of an initial shape used for the calculation. The calculation was performed in a two-dimensional coordinate system of x-axis (horizontal direction) and y-axis (vertical direction). That is, the resin can be said to be cylindrical.
Here, the resin 40 had a diameter of 6 μm and a viscosity coefficient of 100,000 poise (= 10 MPa · sec). The toner is actually a viscoelastic body and is a substance whose viscosity changes with temperature. Here, the toner is a viscous fluid having a constant viscosity. When the toner is handled as a viscoelastic body, the viscous stress term in Equation 2 may be expressed using an appropriate viscoelastic constitutive equation. Further, the temperature dependence may be expressed using a WLF rule (Williams-Landel-Ferry rule) or the like.

A velocity of −0.02 cm / sec in the y-axis direction was given as a boundary condition to the contact portion between the resin 40 and the rigid body 41. Similarly, a speed of 0 cm / sec is applied to the contact portion between the resin 40 and the rigid body 42. 43 is a periodic boundary condition.
The calculation results are shown in FIG. (A), (b), (c), and (d) in FIG. 9 are the mesh model and velocity vector after 6 msec, 15 msec, 25 msec, and 30 msec, respectively. It can be seen that the mesh models of the toner particles are coupled to each other and the calculation can be performed without any defect of the mesh model.

  7: output unit, 8: governing equation calculation unit, 9: mesh model correction unit, 10: interference determination unit, 11: element deletion unit, 12: polygon extraction unit, 13: element filling unit

Claims (10)

A mesh model creation method for reconstructing a mesh model when mesh models interfere with each other in the finite element method,
An acquisition step in which a computer acquires coordinate values of nodes of each of the first mesh model and the second mesh model;
An interference determining step in which a computer determines interference between the first mesh model and the second mesh model, and extracts an element interfering with the first mesh model and an element interfering with the second mesh model as interference elements;
An element deletion step in which the computer deletes the extracted interference element;
A polygon extraction step of extracting a polygon for connecting the first and second mesh models from which the interference elements have been deleted;
An element filling step in which the computer fills the extracted polygon with elements;
An output step of outputting, as a new mesh model, a first mesh model and a second mesh model connected to each other by polygons filled with elements to the output unit;
In the interference determination step, an element having a node existing inside another element or on a node or a side is extracted as an interference element.   The mesh model creation method according to claim 1, wherein in the element deletion step, all the interference elements extracted in the interference determination step are deleted.   In the polygon extraction step, a plurality of sides that are no longer shared by the two elements due to the deletion of the interference element in the first mesh model, and two elements that are deleted by the interference element in the second mesh model. The mesh model creation method according to claim 1 or 2, wherein the polygon is created by a closed path including a plurality of sides that are no longer shared by elements.   In the polygon extraction step, end points on both sides of the open circuit composed of a plurality of sides that are no longer shared by the two elements due to the deletion of the interference element in the first mesh model are respectively set to the second mesh model. The closed circuit is formed by connecting to any node on an open circuit composed of a plurality of sides that are no longer shared by two elements due to the deletion of the interference element in claim 1. 3. A mesh model creation method according to 3.   In the polygon extraction step, the nodes connected to the end points of the open circuit in the first mesh model are deleted as a plurality of nodes on the open circuit in the second mesh model because they interfere with elements having the end points as nodes. The mesh model creation method according to claim 4, wherein a node that constitutes the interference element is selected and a node closest to the end point is selected. In the polygon extraction step,
A closed circuit formed so as to connect an end point of the open circuit in the first mesh model to a node on the open circuit in the second mesh model, and an end point of the open circuit in the second mesh model is a node on the open circuit in the first mesh model Each of the cycles formed to connect to
6. The mesh model creation method according to claim 4, wherein when two obtained cycles are different from each other, a cycle having a smaller number of nodes constituting the cycle is selected. In an analysis method in which the computer analyzes the behavior of an object having a free surface by numerical calculation by the finite element method,
The computer executes reconstruction of a mesh model using the mesh model creation method according to any one of claims 1 to 6, with respect to the mesh model of the object obtained by the numerical calculation. Analysis method.   The analysis method according to claim 7, wherein the object is toner. A mesh model creation device that reconstructs a mesh model when mesh models interfere with each other in the finite element method,
An acquisition unit for acquiring coordinate values of nodes of each of the first mesh model and the second mesh model;
An interference determination unit that determines interference between the first mesh model and the second mesh model, and extracts an element that interferes with the first mesh model and an element that interferes with the second mesh model as an interference element;
An element deletion unit for deleting the extracted interference element;
A polygon extraction unit for extracting a polygon for connecting the first and second mesh models from which the interference element is deleted;
An element filling unit for filling the extracted polygon with elements;
An output unit for outputting the first and second mesh models connected to each other by polygons filled with elements as a new mesh model, and
The said interference determination part extracts the element which has the node which exists in the inside of another element, or on a node or a side as an interference element, The mesh model production apparatus characterized by the above-mentioned.   A program that causes a computer to execute each step of the mesh model creation method according to any one of claims 1 to 6.

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