JP2011013976A - Analysis system and analysis program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve the efficiency of data creation while maintaining analytical accuracy.SOLUTION: An analysis system includes: a means for creating first mesh data of an analysis target; a means for creating second mesh data only for a structure included in the analysis object; a means for defining two-dimensional elements on a surface to be a physical property boundary of the second mesh data and grouping the two-dimensional elements in each physical property boundary surface; a means for determining a level set function obtained by allocating values with positive and negative signs to all nodes of the first mesh data through the physical property boundary surface; a means for inputting the first mesh data, the level set function and data for defining the structure included in the analysis target, setting a boundary condition and an initial condition and executing analysis using an extended finite element method to obtain analytical result data; a means for calculating the values of nodes of third mesh data for performing post processing by using the analytical result data and an interpolation function used for analyzing the first mesh data; and a means for performing plotting processing of the analytical results.

Description

  The present invention relates to an analysis system and an analysis program using an extended finite element method.

  In underground facility plans such as bedrock oil storage bases and geological disposal of radioactive waste, it is important to understand the groundwater flow field and predict changes in the flow field due to construction. In particular, the existence of internal structures such as highly permeable faults that form water paths and poorly permeable faults that cause rapid head changes may have a significant impact on underground facilities, requiring detailed examination. It becomes. In the groundwater flow field, the three-dimensional hydrogeological model created based on the geological survey is often examined by a numerical analysis method represented by the finite element method (FEM). It takes a lot of time and labor to create an analysis mesh that faithfully represents a fault within a group. In addition, due to the uncertainty of the three-dimensional distribution information of the fault, there may be cases where a case study on the distribution situation is required, or the analysis mesh may need to be changed due to information updates accompanying the progress of surveys and construction. A thin intrinsic structure such as a fault is often replaced with a simple shape and a bold model such as averaging water permeability is used (see, for example, Non-Patent Document 1, Non-Patent Document 2, and Non-Patent Document 3). ).

Kawanishi, et al .: Development of evaluation method for natural barrier performance of geological disposal of high-level radioactive waste (Part 1) -Analysis method of groundwater flow in fractured rock mass-, Report of Central Research Institute of Electric Power, U93054, pp. 1-46, 1994. Katsuyuki Suzuki et al .: Fracture rock mass infiltration flow analysis by multi-scale finite covering method, Proceedings of the lecture on computational engineering, Vol. 7, pp. 545-548, 2002.5 Hideyuki Sakurai et al .: Groundwater seepage flow voxel analysis for underground facility planning, JSCE Proceedings, No. 687, III-56, pp. 155-168, 2001.9

  However, when the averaging method is used, it is known that there is a problem in analysis accuracy particularly when the fault is hardly permeable, and a method for solving these problems is required.

  The present invention has been made in view of such circumstances, and an object of the present invention is to provide an analysis system and an analysis program to which an extended finite element method is applied that can improve the efficiency of data creation while maintaining analysis accuracy. And

  The present invention provides means for creating first mesh data for analyzing the structure of an analysis object by an extended finite element method, and means for creating second mesh data of only the structure inherent in the analysis object. Means for defining a two-dimensional element on a surface that is a physical property boundary of the second mesh data, and grouping for each physical property boundary surface, each group of the two-dimensional element, and a node of the first mesh data Means for calculating a level set function obtained by assigning a value with a sign of positive or negative via the physical property boundary surface to all nodes of the first mesh data; Using mesh data, the level set function, and data defining the structure inherent in the analysis object as input data, set boundary conditions and initial conditions, and use the extended finite element method For performing post-processing using means for obtaining analysis result data by executing analysis, the analysis result data, and the interpolation function of the extended finite element method used when analyzing the first mesh data Means for calculating a value of a node of the third mesh data, means for plotting the analysis result using the value of the node of the first mesh data and the value of the node of the third mesh data It is characterized by comprising.

  The present invention is an analysis program that operates on a computer of an analysis system that performs structural analysis using an extended finite element method, and includes first mesh data for analyzing the structure of an object to be analyzed by the extended finite element method. A step of creating, a step of creating second mesh data of only the structure inherent in the object to be analyzed, a two-dimensional element being defined on a surface serving as a physical property boundary of the second mesh data, and a physical property boundary surface Grouping each step, calculating the distance between each group of the two-dimensional elements and the nodes of the first mesh data, and adding a value with a positive or negative sign via the physical property boundary surface. Obtaining a level set function obtained by assigning to all nodes of one mesh data; the first mesh data; the level set function; Using the data defining the structure inherent in the analysis object as input data, setting boundary conditions and initial conditions, performing analysis using the extended finite element method, and obtaining analysis result data; and Calculating a value of a node of third mesh data for performing post processing using data and an extended finite element method interpolation function used when analyzing the first mesh data; The computer is caused to perform the step of plotting the analysis result using the node value of the first mesh data and the node value of the third mesh data.

  According to the present invention, the mesh of the internal structure is created independently of the mesh of the basic analysis model, so that the mesh division work becomes very simple and significant efficiency can be achieved. It becomes easy to change the shape and position. In addition, the degradation of the solution is much smaller than the conventional method of averaging water permeability. In particular, in the case of a thin poorly permeable layer, the conventional averaging method has a problem in the accuracy of the solution, but the analysis system of the present invention provides a good result. In addition, the analysis system according to the present invention can use conventional FEM pre / post (data construction / plotting) processing software as it is, so that it is not necessary to purchase or develop new pre / post processing software. can get.

It is explanatory drawing which shows an example of analysis model mesh data. It is explanatory drawing which shows an example of the mesh data of a fault. It is explanatory drawing which shows an example of the analysis model mesh data which modeled the fault. It is explanatory drawing which shows an example of the analysis model mesh data which took in the tomographic mesh. It is explanatory drawing which shows an example of mesh data. It is explanatory drawing which shows an example of mesh data. It is explanatory drawing which shows an example of two-dimensional mesh data. It is explanatory drawing which shows an example of the data definition of an internal structure. It is explanatory drawing which shows an example of mesh data. It is explanatory drawing which shows an example of mesh data. It is explanatory drawing which shows the node set enriched with the material boundary surface in an analysis area | region. It is a flowchart which shows the processing operation of the computer on an analysis system. It is a flowchart which shows the processing operation of the computer on an analysis system. It is a flowchart which shows the processing operation of the computer on an analysis system. It is a flowchart which shows the processing operation of the computer on an analysis system. It is a flowchart which shows the processing operation of the computer on an analysis system. It is explanatory drawing which shows the data structure of the data which the computer on an analysis system handles. It is explanatory drawing which shows the data structure of the data which the computer on an analysis system handles. It is explanatory drawing which shows the data structure of the data which the computer on an analysis system handles. It is explanatory drawing which shows the data structure of the data which the computer on an analysis system handles. It is explanatory drawing which shows the data structure of the data which the computer on an analysis system handles. It is explanatory drawing which shows the data structure of the data which the computer on an analysis system handles. It is explanatory drawing which shows the data structure of the data which the computer on an analysis system handles. It is explanatory drawing which shows the data structure of the data which the computer on an analysis system handles. It is explanatory drawing which shows the data structure of the data which the computer on an analysis system handles. It is explanatory drawing which shows the data structure of the data which the computer on an analysis system handles. It is explanatory drawing which shows the data structure of the data which the computer on an analysis system handles. It is explanatory drawing which shows an example of an analysis model. It is explanatory drawing which shows an example of analysis mesh data. It is explanatory drawing which shows an example of an analysis case. It is explanatory drawing which shows the comparison (thin layer: poor water permeability) result of the total head by the difference in an analysis method. It is explanatory drawing which shows the position of an analysis result comparison node. It is explanatory drawing which shows the comparison (thin layer: high water permeability) result of the total head by the difference in an analysis method. It is explanatory drawing which shows the comparison result of the analysis precision by the difference in an analysis method. It is explanatory drawing which shows the result of having plotted the analysis result. It is explanatory drawing which shows the result of having plotted the analysis result. It is explanatory drawing which shows the result of having plotted the analysis result.

  Hereinafter, an analysis system according to an embodiment of the present invention will be described with reference to the drawings. The present invention is an analysis system based on an extended finite element method (X-FEM) that makes it possible to efficiently model an intrinsic structure such as a fault. Regarding the analysis system by X-FEM, the literature “Sukumar, N et al .: Modeling holes and inclusions by level sets in the extended finite-element method, Comput. Methods. Appl. Mech. Engrg. 190, 6183-6200, 2001 ."It is described in. By using this system, it is possible to consider the underlying structure independently of mesh division, which makes it easier to model thin intrinsic structures such as faults, which was a very difficult task in the past. Efficient work can be achieved. In addition, analysis accuracy is maintained as compared with the above-described method of averaging water permeability. Furthermore, since the present invention can create meshes and plot analysis results using pre / post processing software used in conventional FEMs, development and purchase of new pre / post processing software is not necessary. .

  Hereinafter, an analysis model in which a thin structure such as a fault is three-dimensionally distributed in the analysis region will be taken up as a typical example of modeling of the intrinsic structure, and will be specifically described. In an underground facility construction plan, as shown in FIG. 1, the shape of the underground facility structure is generally given priority when creating an analysis mesh. In addition, it is very difficult to faithfully capture a thin geological structure distributed three-dimensionally like the fault shown in FIG. 2, and usually a model is obtained by changing the physical property value of the element through which the fault passes as shown in FIG. Often used. On the other hand, as shown in FIG. 4, it is very efficient if the analysis can be performed by simply placing the tomographic mesh of FIG. 2 on the analysis mesh of FIG. However, since ordinary FEM (Finite Element Methods) does not allow spatial overlap of elements, the model as shown in FIG. 4 cannot be analyzed. The present invention is an analysis system using an X-FEM that enables analysis even with a mesh as shown in FIG. Hereinafter, taking a simple osmotic flow problem as an example, a data structure for efficiently modeling the underlying structure, a construction method thereof, and a method for plotting an analysis result will be described.

First, an outline of the analysis procedure will be described.
(1) A mesh A (FIG. 5) that does not consider a fault is created.
(2) Independent of mesh A, mesh B (FIG. 6) that models a fault is created.
(3) A two-dimensional element (triangle or quadrilateral) is stretched on the surface of the mesh B which is a physical property boundary with the mesh A, and is grouped for each physical property boundary surface (FIG. 7).
(4) Using the group of two-dimensional elements created in (3), two level set functions (the literature “JA Sethian: Level Set Methods and Fast Marching Methods, Cambridge University Press, 1999”) are generated. That is, the distance between each group of the physical property boundary surface of FIG. 7 and the nodes of the mesh A is calculated, and a value (level set function value) with a positive or negative sign through the physical property boundary surface is set to all the nodes of the mesh A. assign.
(5) A unique ID is assigned to each level set function obtained in (4). For example, F1 and F2. The level set function becomes zero at the physical property boundary position, but here, as shown in FIG. 8, the two level set functions (λ ⁽¹⁾ and λ ^{(2) in} FIG. 8) both pass through the physical property boundary. Negative values on the left and positive values on the right.
(6) In this analysis system, the above level set function is used as input data, and the intrinsic structure (for example, ID1 as ID) is defined as follows.
INC1, + F1, -F2 ... (input data 1)
This means that the intrinsic structure INC1 is defined by two level set functions of F1 and F2, and F1 is positive and F2 is negative. This data format does not depend on the number of boundary surfaces that define the underlying structure. One boundary surface that bisects the analysis region or a closed region such as a sphere (boundary surface is one spherical surface) included in the analysis region can be defined. In addition, an intrinsic structure surrounded by three or more boundary surfaces can be similarly defined.
(7) Mesh A, two level set functions of F1 and F2 and defining internal structure (input data 1) are set as input data, appropriate boundary conditions and initial conditions are set, and analysis is performed by X-FEM To do.
(8) A mesh C is prepared by stretching the surface of the mesh B as shown in FIG. Using the mesh A and the analysis result, the value at the node of the mesh C is calculated using the interpolation function of the extended finite element method used when analyzing the mesh A.
(9) As shown in FIG. 10, the plotting process is performed using the mesh A and the mesh C simultaneously. Thus, continuous contour display can be performed.

  Next, X-FEM will be described. The present invention can be applied to other than osmotic flow analysis. Moreover, although there is no restriction | limiting in the thickness of an internal material structure, it demonstrates for the thin internal structure which can utilize the effectiveness of this invention most here.

In X-FEM, a function called an enrichment function is locally added to a discrete approximation expression of a conventional FEM to express discontinuities such as a material boundary surface independently of mesh division as shown in FIG. be able to. The discrete approximation φ ^h (x) for the scalar potential φ (x) by X-FEM is a general finite expression expressed by the node degree of freedom φ _I and the local coordinate system ζ (x) at an arbitrary point x in the region. Using the shape function L _I (ζ (x)) of the element method and the enrichment function f _I , it can be described as in equation (1).
Here, N is a set of all nodes, and a _I is an additional degree of freedom of node I.

Here, a level set method is used in order to define a free surface shape to be a material boundary surface. The level set method is a numerical calculation method for tracking a free surface shape that changes every moment. In X-FEM, the level set function is introduced to represent the discontinuous surface in the region, so that all information is defined on the nodes and the shape processing is simplified. It is advantageous. In the level set method, the free surface shape is implicitly defined by an isosurface where the level set function value is zero. When the distance from each node I to the free surface is calculated, and a value λ _I signed through the free surface is assigned to each node, a signed distance function from the material boundary surface at any point x in the region ( The level set function) can be expressed as in equation (2) using the FEM shape function.

Since the free surface is represented by an isosurface where λ (x) = 0, it can be defined independently of the element division. When there are a plurality of free surfaces, the equation (2) corresponding to each may be determined. At the material interface, the physical quantity of interest is continuous and its differentiation is discontinuous. Several enrichment functions corresponding to this have been proposed, but the function shown in Equation (3) designed so that the condition number of the final coefficient matrix does not deteriorate and the solution does not deteriorate is used. .

  This function is a ridge function that forms a ridge along the material boundary surface, and the value is always 1.0 on the material boundary surface, and the value is zero for elements that do not cross the material boundary. M is a set of nodes to be enriched, and is a set of nodes having the elements crossed by the material boundary (see FIG. 11).

Assuming that the number of material boundary surfaces is K, an approximate function of X-FEM can be written as in equation (4).

  A final algebraic equation can be obtained in the same manner as a normal FEM procedure, except that the equation (4) is used as an approximation function and the node degree of freedom is partially increased.

The following three-dimensional steady saturated osmotic flow problem will be described.
Here, φ is the total head, ∇ is a linear differential operator, K (bold) is the hydraulic conductivity tensor, and V is the analysis region. The subscript ^ represents a known amount, n is a unit normal vector set at the boundary of the region V, and q is a flux. S _φ and S _n each represent a boundary where the boundary condition is defined.

The functional Π corresponding to this problem is

By substituting equation (4) into equation (11), the following linear algebraic equation can be obtained from the stationary condition of equation (11).
Here, N is the total number of all nodes, and M ^(K) is the number of nodes to be enriched.

  Next, an operation for processing the above-described analysis procedure by a computer will be described. 12 to 16 are flowcharts showing the processing operation of the analysis program. A computer that executes the processing operations shown in FIGS. 12 to 16 includes an external storage device such as a hard disk drive, an input device such as a keyboard and a mouse, and a display device such as a liquid crystal display device.

  First, the computer reads the FE model for analysis (see FIG. 5) stored in the external storage device (step S1). Here, physical property data, node data, element data, and boundary condition data read from the external storage device are shown in FIGS. Each data shown in FIGS. 17 to 20 is created by an analyst using model creation software or the like and stored in advance in an external storage device.

  Next, the computer reads the internal structure boundary surface data (two-dimensional mesh data shown in FIG. 7) stored in the external storage device (step S2). Here, the node data and element data of the two-dimensional mesh shown in FIG. 7 read from the external storage device are shown in FIG.

  Next, the computer calculates a level set function value (signed distance between all nodes of the analysis FE model and the two-dimensional mesh) based on the read data (step S3). In step S3, as shown in FIG. 13, the process of calculating the level set function values for all nodes is repeated for the number of level set functions (step S3-1). The computer stores the calculation result calculated here in an external storage device. FIG. 23 shows an example of data stored in the external storage device by calculating the level set function values of all nodes.

  Next, the computer reads the intrinsic structure definition data stored in advance in the external storage device (step S4). Here, FIG. 24 shows an example of the intrinsic structure definition data read from the external storage device.

  Next, the computer adds a degree of freedom to the nodes to be enriched (step S5). In step S5, as shown in FIG. 14, it is determined whether the positive and negative of the level set function are mixed (whether there is a physical property boundary surface) for the constituent nodes of each element (step S5-1). If the positive and negative of the level set function are mixed, it is determined whether the constituent node has already been enriched for the level set function (step S5-2). If the result of this determination is that it has not already been enriched, one degree of freedom is added (enriched) to that constituent node (step S5-3). The computer repeats this process as many times as the number of element constituent nodes, and further repeats as many times as the number of all elements and the number of level set functions.

  Next, the computer constructs the equation (12) (step S6), substitutes boundary condition data for the constructed equation (12), and solves the simultaneous linear equations (step S7). And a computer performs the process of the X-FEM discrete approximation formula with respect to an enriched node (step S8). In step S8, as shown in FIG. 15, it is determined whether the node is enriched (step S8-1). If the result of this determination is that the node is enriched, the total head of the node is expressed by equation (4). A value is calculated (step S8-2). The computer repeats this process for all nodes.

  Next, the computer reads the data of the post model (FIG. 9, mesh C) stored in the external storage device (step S9). Here, the node data and element data of the post-processing model read from the external storage device are shown in FIGS.

  Next, the computer calculates a node value of the post model (step S10). In step S10, as shown in FIG. 16, in which element of the analysis FE model the node of the post model exists is searched (step S10-1), and the local coordinates of the analysis mesh element of the post model node are searched. A value (ξ) is calculated (step S10-2). Then, the interpolated value (solution) of the post model node is calculated from the equation (4) (step S10-3).

  Next, the computer outputs the FE model for analysis and the model node value for post obtained by calculation to the display device. FIG. 27 shows the FE model for analysis and the model node value for post that are output here.

Next, a calculation example will be described with a specific example. A benchmark test was conducted for the 3D steady saturated seepage flow problem. FIG. 28 shows an analysis model in which a rectangular area of 10 m × 6 m × 6 m is divided by 2 m cubic hexahedral elements. As the boundary conditions, the entire head was constrained so that the hydraulic gradient in the x direction was 1.0 on the upper surface of the model, and the other surfaces were impermeable conditions. Some host rock is the analysis region, consider a model in which a thin stratum of thickness are distributed in three dimensions, permeability k _f is compared with impermeable and permeability k ₀ of rocks of the thin layer ( for the case where the high permeability of _{k f = 1 / 100k 0)} (k f = 100k 0), was carried out case study the thickness t of the thin layer. FIG. 29A shows an analysis mesh obtained by dividing a thin layer into elements by a normal FEM. In the case of X-FEM, as shown in FIG. 29 (b), it is not necessary to divide the elements of the thin layer, and the analysis can be performed by giving a boundary surface indicated by a broken line by the level set method.

For comparison, an analysis was also conducted by conventional simple modeling that averages the hydraulic conductivity of the elements through which the thin layer passes. The total volume of the element thin layer passes (hatched in FIG. 29 (c)) divided by the area of the boundary surface of the thin layer and the host rock, converted into a layer of uniform thickness t _v, equivalent water permeation across elements of the hatch This is a method of applying a coefficient. In rocks having an average thickness of t _v, if there is a thin layer having a thickness of t _f, the equivalent hydraulic conductivity, hydraulic conductivity of orthotropic with main shaft orthogonal direction of the in-plane and the plane of the thin layer Can be approximated by equations (20) and (21).
Here, k _vs is the hydraulic conductivity in the direction along the thin layer, and k _vn is the hydraulic conductivity in the direction perpendicular to the thin layer. A list of analysis cases is shown in FIG.

FIG. 31 shows a comparison of x-direction distributions of all the heads when the thin layer is hardly permeable (k _f = 1/100 k ₀ ). Differences in the thin layer thickness t are summarized in three sets of diagrams (a), (b), and (c) in the order of the z coordinate. FIG. 32 shows the node positions where the analysis results are compared.

  The X-FEM result (solid line) is in good agreement with the FEM result (thick line) obtained by dividing the thin layer into elements in each case, and represents an abrupt water head difference before and after the hardly permeable layer. On the other hand, the result of applying the equivalent hydraulic conductivity (dotted line) is significantly different from the FEM result in the vicinity of the fault, and the effect of homogenizing the hydraulic conductivity was noticeable.

FIG. 33 shows a comparison result when the thin layer has high water permeability (k _f = 100 k ₀ ). Even when the thin layer had high water permeability, the result of X-FEM (solid line) agreed well with the result of FEM (thick line) obtained by dividing the thin layer into elements. Although the result of the equivalent hydraulic conductivity (dotted line) shows almost the same distribution as the FEM result, the entire element through which the thin layer passes becomes highly permeable, so the influence of the thin layer becomes stronger and the thin layer becomes the element. The difference from the divided FEM results is large.

FIG. 34 compares the relationship between the thin layer thickness and the analysis accuracy by the difference in analysis method. In the figure, ● is the result of X-FEM, and ▲ is the result of applying the equivalent hydraulic conductivity. The analysis accuracy was based on the difference from the normal FEM analysis result shown in Equation (8) as an index.

As shown in FIG. 34, in the analysis based on the equivalent permeability, it can be seen that the difference between the FEM analysis result E _phi increases particularly when a thin layer is impermeable. On the other hand, in the analysis by X-FEM, it was confirmed that a good solution was obtained regardless of the water permeability and width of the thin layer.

  When the analysis result (total head) of X-FEM is plotted using the mesh A used for the analysis, the mesh A has no nodes on the boundary surface of the thin layer. The distribution of cannot be displayed properly. FIG. 36 is a contour diagram of the entire head drawn using mesh A and mesh C simultaneously. As described above, the total head value of the node of the mesh C was calculated from the value of the mesh A by using an X-FEM interpolation function. Compared to FIG. 37, which plots the FEM results in FIG. 29 (a), the contours are partially discontinuous, but the change in the total head distribution due to the presence of a thin layer can be adequately expressed. I understand.

  As explained above, since the mesh of the internal structure is created independently of the mesh of the basic analysis model, the mesh division work becomes very easy and the efficiency is greatly improved. It becomes easy to change the shape and position. In addition, the degradation of the solution is much smaller than the conventional method of averaging water permeability. In particular, in the case of a thin poorly permeable layer, the conventional averaging method has a problem in the accuracy of the solution, but the analysis system of the present invention provides a good result. In the analysis system according to the present invention, since conventional FEM pre / post (data construction / drawing) processing software can be used as it is, it is not necessary to purchase or develop new pre / post processing software.

  Note that a program for realizing the function of the processing unit in FIG. 1 is recorded on a computer-readable recording medium, the program recorded on the recording medium is read into a computer system, and executed to execute the X-FEM. The analysis processing used may be performed. Here, the “computer system” includes an OS and hardware such as peripheral devices. The “computer system” includes a WWW system having a homepage providing environment (or display environment). The “computer-readable recording medium” refers to a storage device such as a flexible medium, a magneto-optical disk, a portable medium such as a ROM and a CD-ROM, and a hard disk incorporated in a computer system. Further, the “computer-readable recording medium” refers to a volatile memory (RAM) in a computer system that becomes a server or a client when a program is transmitted via a network such as the Internet or a communication line such as a telephone line. In addition, those holding programs for a certain period of time are also included.

  The program may be transmitted from a computer system storing the program in a storage device or the like to another computer system via a transmission medium or by a transmission wave in the transmission medium. Here, the “transmission medium” for transmitting the program refers to a medium having a function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication line) such as a telephone line. The program may be for realizing a part of the functions described above. Furthermore, what can implement | achieve the function mentioned above in combination with the program already recorded on the computer system, what is called a difference file (difference program) may be sufficient.

Claims (2)

Means for generating first mesh data for analyzing the structure of the analysis object by an extended finite element method;
Means for creating second mesh data of only the structure inherent in the analysis object;
Means for defining a two-dimensional element on a surface which is a physical property boundary of the second mesh data, and grouping for each physical property boundary surface;
The distance between each group of the two-dimensional elements and the nodes of the first mesh data is calculated, and the values with positive and negative signs are added to all the nodes of the first mesh data through the physical property boundary surface. Means for obtaining a level set function obtained by assigning;
The first mesh data, the level set function, and data defining a structure inherent in the analysis target are input data, boundary conditions and initial conditions are set, and analysis is performed using an extended finite element method To obtain analysis result data by executing
Means for calculating a value of a node of third mesh data for performing post-processing using the analysis result data and the interpolation function of the extended finite element method used when analyzing the first mesh data When,
An analysis system comprising: means for plotting an analysis result using a node value of the first mesh data and a node value of the third mesh data. An analysis program that runs on the computer of an analysis system that performs structural analysis using the extended finite element method,
Creating first mesh data for analyzing the structure of the analysis object by an extended finite element method;
Creating second mesh data of only the structures inherent in the analysis object;
Defining a two-dimensional element on a surface that is a physical property boundary of the second mesh data, and grouping for each physical property boundary surface;
The distance between each group of the two-dimensional elements and the nodes of the first mesh data is calculated, and the values with positive and negative signs are added to all the nodes of the first mesh data through the physical property boundary surface. Obtaining a level set function obtained by assigning;
The first mesh data, the level set function, and data defining a structure inherent in the analysis target are input data, boundary conditions and initial conditions are set, and analysis is performed using an extended finite element method To obtain analysis result data by executing
Calculating a value of a node of third mesh data for performing post-processing using the analysis result data and the interpolation function of the extended finite element method used when analyzing the first mesh data When,
An analysis program causing the computer to perform a step of plotting an analysis result using a node value of the first mesh data and a node value of the third mesh data.