JPH0395682A - Production of numerical analyzing model - Google Patents

Abstract

PURPOSE:To effectively produce an analyzing model without performing the irregular division of an element by applying a fractionizing operation of a rough element to a necessary element and fractionizing the necessary element included in a roughly divided element. CONSTITUTION:When the rough element is fractionized by an element e1, an element e2 is calculated as a fractionizing candidate element and displayed. A fractionizing pattern and an adaptive pattern are selected for the element e2. Then it is decided whether another fractionizing standard element is available or not in addition to an input fractionizing standard element. If so, an original operation is carried out.

Description

[Detailed Description of the Invention] [Field of Industrial Application] The present invention relates to a numerical analysis method for calculating the distribution of stress, temperature, velocity, etc. in the whole or a part of an object such as a device, and in particular, This invention relates to a method for creating an analytical model in a numerical analysis method in which an object to be analyzed is divided into a plurality of elements and analyzed.

[Conventional technology]

When calculating stress distribution, temperature distribution, etc. of equipment using numerical analysis such as the finite element method or boundary element method, the analytical model is created using the following steps.

For example, the procedure for creating a model for stress analysis when the perforated flat plate shown in FIG. 24 is subjected to tension, which is a two-dimensional problem, is as follows. First, due to the symmetry of the perforated flat plate to be analyzed, a 1/4 part thereof, that is, the part shown in FIG. 7 is modeled as the target for stress analysis. FIG. 7 also shows boundary conditions necessary for analysis. That is, n, n. in FIG. Above, the displacement in the y direction is defined as 0, and on 14rls, the displacement in the X direction is defined as O. Also, nz n. It is specified that a load of magnitude p is acting on the top. Furthermore, n, n. X above
direction, n. n. It is specified that no load is acting on the upper y direction, the X and y directions on n, n4, and ns n+, and especially the y direction on n4n.

Now, the procedure for modeling the part shown in Figure 7 is as follows.
The explanation will be divided into the following two parts: element division and boundary condition setting.

The first task in element division modeling is to define the shape to be analyzed using elements described later, and this task is called element division. When using a numerical analysis method called the finite element method, the shape is defined as a collection of quadrilateral or triangular planes as shown in FIG. This small quadrilateral or triangular area is called a finite element.

In the case of stress analysis, the work of defining a shape using these quadrilateral or triangular elements, that is, the rough guideline for element division, is to divide the stress concentration portion into small pieces. That is,
As shown in Figure 8, the area around the hole is divided into smaller pieces. Similarly, in the case of temperature distribution analysis, it is necessary to divide areas with steep temperature gradients into smaller parts.

Element division using the finite element method has been described above, but there is also a method called the boundary element method that is applied to numerical analysis. The element division in the boundary element method, that is, the definition of the shape of the analysis object, involves representing the outer boundary of the analysis object as a collection of a large number of continuous "lines." At this time, the seventh
Figure 25 shows the outer boundary of the analysis object shown in the figure as a collection of many "lines". In the boundary element method, "lines" are used to represent the outer boundaries of the analysis object. are called elements (boundary elements). Tables 1 and 2 show finite elements and boundary elements for two-dimensional analysis.

Margins below Table 1 As shown in Tables 1 and 2, the shape of an element is defined by points called nodes, and depending on the number of nodes, the lines that define the shape of the element may be straight lines or A quadratic curve can be used. These nodes are also used to define the distribution of variables such as displacement and stress within an element. In other words, as shown in Tables 1 and 2, the distribution of variables within an element is approximated by a polynomial such as a linear function or quadratic function depending on the number of nodes that make up each element. It also has the characteristic of doing so. In the finite element method and boundary element method, the shape to be analyzed is expressed as a collection of elements, as described above.
By polynomial approximation of the deformation within the element, the deformation of each part to be analyzed and of the whole is calculated. The deformation and other behaviors of general analysis targets are inherently complex and cannot be accurately expressed using polynomials, but by using a large number of small elements, complex behaviors can be accurately approximated within each element using polynomials. Therefore, in FIGS. 8 and 25, fine elements are arranged around holes where stress concentration, that is, complex deformation occurs.

Similarly, when approximating the distribution of variables within an element, more accurate results can be obtained by using higher-order polynomials, such as using a quadratic formula rather than a quadratic formula, or a cubic formula rather than a quadratic formula. It will be done. Therefore, in recent years, it has become common to use elements that can define the distribution of variables using high-order polynomials.

Setting boundary conditions The next task after modeling is setting the boundary conditions necessary for analysis. That is, in the case of stress analysis of a perforated flat plate, it is necessary to define information such as the direction and magnitude of the load shown in FIG. 7, the position of its action, or the position and direction of restraining displacement. Information regarding the settings of these boundary conditions is defined as node information. In other words, the seventh
At the node on nn2 in the figure, the displacement in the y direction is defined as O,
At the node on n4 ns, the displacement in the X direction is defined as O. Also, n! A load of magnitude p/ (length of nzn3) is defined at the node above n=. Furthermore, n, n.
X direction of upper node, n. n. y direction of the upper node, n=n4
and n, n, the X and y directions of the nodes on, and na n
A load of size O is defined in the y direction of the upper node s.

As explained above, an analytical model can be created by dividing elements and setting boundary conditions.

Now, among the creation of these analytical models, in the analytical model shown in FIG. 8, which is an analytical model based on the finite element method, the task of combining fine element division and coarse element division is a task that requires a great deal of effort. In other words, the coarse element division part and the fine element division distribution are regular divisions, so the coarse element division part is treated as coarse element division, and the fine element division part is treated as fine element division by using a computer. element division can be performed mechanically. However, element division at the part where the distribution of coarse element division and the part of fine element division are joined is irregular element division, so element division cannot be performed mechanically. You need to create an element. This manual element division requires a lot of experience, as it requires a thorough knowledge of various element division patterns to connect coarse element division and fine element division.
Creating an analytical model often requires a large amount of time. On the other hand, in order to avoid this manual creation of an analysis model, there is a method of mechanically dividing the entire analysis model into fine elements, but in that case, the number of elements and nodes that need to be examined in the analysis model is significantly large. Become. Since the calculation time for analysis increases in proportion to the square to the cube of the number of nodes,
The method of dividing the whole into smaller parts is extremely uneconomical when considering the usage time of the calculator or the usage fee.
This is not a very practical method. Therefore, the development of an element division method that mechanically joins coarse element division parts and fine element division parts is eagerly awaited. Above, we have explained how to create an analytical model using the finite element method and the boundary element method using the two-dimensional tensile problem of a flat plate with holes as an example.

The procedure for creating an analytical model for a three-dimensional problem is the same as for a two-dimensional problem. Here, a method for creating a three-dimensional analytical model will be explained using the tensile problem of a notched prism shown in FIG. 26 as an example.

Due to the symmetry of the shape and load conditions, it is 1/8 as shown in Figure 27.
The part is modeled.

Element division using the finite element method in a three-dimensional problem is performed using three-dimensional elements (finite elements) as shown in Table 3. In this case as well, element division is performed such that the stress concentration area near the notch is finely divided and the other parts are coarsely divided. For 3D problems, manual element division takes into account the depth of the elements.
It is necessary to perform element division as shown in FIG. 28, which combines fine element division and coarse element division, and this work can only be performed by a highly skilled person. Therefore, although the calculation time is usually long and the computer usage fee is enormous, calculations are performed using an analytical model in which the whole is divided into fine elements as shown in FIG. 29.

Margins below Also, in the boundary element method, element division is performed to define the outer boundary shape of the analysis target using planar elements (boundary elements) as shown in Table 4. In the case of analytical models using the boundary element method, since the elements are planar, it is easier to join fine element divisions and coarse element divisions compared to the finite element method.
Even so, skillfully combining fine element division and coarse element division requires considerable skill, and the reality is that this method cannot be said to be fully practical.

[Problem to be solved by the invention]

The above-mentioned conventional technology does not take into consideration the two purposes of simultaneously establishing two objectives: to easily perform element division and to reduce the number of nodes in order to shorten calculation time. In other words, if you try to do it mechanically, you will have to divide the entire analytical model into small elements,
Therefore, the number of nodes increases unnecessarily and calculation time increases. In addition, if element division is performed with sparse density to shorten the calculation time, irregular element division parts will occur to connect coarse element division parts and fine element division parts, which causes element division to become difficult. There was a problem that it became complicated and could only be handled by an experienced person.

SUMMARY OF THE INVENTION An object of the present invention is to provide an element division method that allows not only experts but also non-experts to easily create an analysis model in which elements are divided into elements with density depending on the situation of the object to be analyzed.

[Means to solve the problem]

The above purpose is to mechanically perform regular coarse element division on the entire analytical model using a computer, then display the rough element division diagram on a display using the computer, and Among them, select the element that needs to be divided into fine elements, and select the appropriate element from among the subdivision patterns created in advance and stored in the database that are also displayed on the display. Select interactively, automatically calculate elements that need to be subdivided adjacent to the subdivided element, display the automatically calculated subdivision candidates on a graphic display, and display the same elements on the display. This is achieved by interactively selecting an appropriate subdivision pattern from among the subdivision patterns displayed above to sequentially and interactively subdivide the elements that require subdivision.

For example, in the case of element division of a perforated flat plate shown in FIG. 8, the irregular element division that joins the fine element division around the hole, which is the stress concentration area, and the coarse element division in other parts, is Manual creation is a major obstacle, making element division difficult. For this reason, as a starting point for the element division in Figure 8, we created the overall coarse regular element division model shown in Figure 4, and the element division in Figure 4 was made as shown in Figures 9 to 14. The element division shown in FIG. 8 can be obtained by mechanically subdividing in the following order. The object of the present invention is to provide a means by which not only an expert but also an unskilled person can easily perform appropriate element division of a model to be analyzed by mechanical subdivision.

[Effect]

In the analytical model creation method of the present invention, by interactively subdividing the overall coarse element division that has been mechanically created using a computer in advance, fine element division and coarse element division can be freely combined. Appropriate element divisions can be created interactively. Therefore, it is no longer necessary for the person creating the analytical model to perform element division at the part where fine element division and coarse element division are joined by the conventional complicated manual work. Even a non-skilled person with little experience can easily create an analysis model of appropriate element division by freely combining fine element division and coarse element division.

In other words, it is no longer necessary to manually perform irregular element segmentation, which is time-consuming, and it is now possible to create an analytical model that has been segmented into elements with appropriate sparsity and density to obtain accurate solutions in a short amount of time. can be created.

〔Example〕

The method for creating a numerical analysis model according to the present invention will be explained below with reference to the drawings, but first the overall structure will be explained.

FIG. 1 is a flowchart showing one embodiment of the present invention. In FIG. 1, at 1, an element division diagram of the analytical model is displayed. At the first stage of the subdivision operation, an element division diagram that is coarsely divided mechanically and regularly is displayed (for example, FIG. 4). 2, one element (
For example, element e in FIG. ) is selected using an input device such as a keyboard, mouse, or light pen. 3, the second
The subdivision pattern created in advance as shown in the figure is displayed on the display, and the subdivision pattern intended by the creator of the analysis model is selected.

Here, the pattern of subdivision created in advance is
Stored as a database on magnetic disks or computer memory.

In step 4, for example, if pattern C in FIG. 2 is selected in step 3, which of the patterns shown in FIG. will be displayed.

In other words, the subdivision pattern is a subdivision pattern for how to subdivide the target element, and the adaptation pattern is a pattern for applying the selected subdivision pattern to the target element, for example, in what direction. be. 5
Now, it is determined whether the subdivision patterns selected in steps 3 and 4 match the intention of the creator of the analytical model. 6 connects (adjacent) to elements subdivided in 3-5
Calculate elements that need to be subdivided (subdivision candidate elements). In step 7, it is determined whether or not subdivision candidate elements have been calculated in step 6. When a subdivision candidate element is calculated in 7, the subdivision candidate element is displayed in 9, and is subdivided by the operations 3 to 5 in the same manner as described above. In step 8, it is determined whether or not to end the subdivision operation. To continue the subdivision operation, display the element division diagram again in step 1, input the subdivision reference element in step 2, and perform the operations from step 3 onwards.

Hereinafter, the mutual relationship between each structure or part will be explained in detail.

In Figure 1, an element division diagram is displayed at l, but in this case, in a three-dimensional problem, the element division diagram when the analytical model is viewed from a direction where it is easy to select the reference elements for subdivision is used to create the analytical model. displayed by the person.

For example, in the case of an analytical model of a cylindrical shell with a nozzle as shown in (A) in Figure 30, there is a view from the inside (1/4 model view) as shown in (B) in the same figure, and (C) in the same figure. ) As seen from the outside (1/4 model diagram), in three-dimensional problems, there are visible and invisible places depending on the viewing direction, so it is easy to select reference elements for subdivision (or ) Displays a diagram of the analysis model viewed from the direction. In 2,
Use the keyboard, mouse,
Select using an input device such as a light ben.

At this time, the selected element can be distinguished from other elements by, for example, changing its color.

In step 3, the pattern for subdividing the element selected in step 2 is retrieved from the subdivision pattern database and displayed on the screen, and the creator of the analysis model selects the intended dividing pattern.

In step 4, a suitable pattern for applying the subdivision pattern selected in step 3 to the element selected in step 2 is selected. For example, if pattern C in Figure 2 is selected as the subdivision pattern in step 3, pattern C is selected as element e1 in Figure 4.
There are four matching patterns as shown in Figure 5. Therefore, the compatibility pattern intended by the creator of the analytical model, for example (a), is selected from Fig. 5,
display on the display. It is determined in step 5 whether the pattern thus displayed is appropriate. Also,
In 4, after selecting a suitable pattern, [option] functions can be specified. That is, the image shown in FIG. 6 is displayed on the screen, and detailed data for subdivision can be input.

For example, in addition to dividing the length of the side of an element into two, fine-grained subdivision can be performed such as subdivision into 1:2 or 1:3. However, general default values are set in the analytical model creation method of the present invention. For example, the numerical values displayed in FIG. 6 are representative examples. Here, the default value (default Vague)
is a standard value that is automatically set by a computer program when data input to the computer is omitted. Figure 6 shows that the standard is to divide the length of the side of an element into two equal parts. ing.

In step 5, if the selection of the subdivision Bakun or matching pattern is different from the intention of the creator of the analysis model, the process can be returned to step 3 and the subdivision work can be performed again. In addition, if you want to temporarily cancel the element subdivision work, select cancel here and proceed to step 8.

In step 6, an element that is connected adjacent to the element selected in step 2, subdivided in steps 3 to 5, and that needs to be subdivided is calculated as a subdivision candidate element. For example, in Figure 4, element e
In the case of subdivision by 1, element e2 is calculated here as a subdivision candidate element, and by 9, element e! It is displayed on the screen that is a subdivision candidate element. Then, in steps 3 and 4, the subdivision pattern and the matching pattern are selected for the element e2. In step 7, it is determined whether or not there are any further elements that can be used as subdivision reference elements in addition to the subdivision reference elements input in step 2. Here, if there is an element that becomes a further subdivision reference element, the process returns to 2 and the operations from 3 onwards are executed.

The embodiments of the analytical model creation method according to the present invention have been described above. The invention will be further explained with examples.

The first example is the element division of a flat plate with holes shown in FIG. 7, which is a two-dimensional problem. First, the element division shown in FIG. 4 is obtained by applying regular coarse element division to the whole using a computer. In the present invention, the element division shown in FIG. 4 can be subdivided in an interactive manner to create the element division shown in FIG.

First, at 1 in FIG. 1, FIG. 4 is displayed. Then, consider the case where element e1 is selected as the subdivision reference element in step 2. The result of selecting pattern C from FIG. 2 in step 3 and selecting pattern A from FIG. 3 in step 4 is shown in FIG. e2 is calculated as 6 and displayed as 9 as a subdivision candidate element connected to element e. FIG. 10 shows the results of selecting e2's subdivision pattern and matching pattern in 3 and 4. Similarly, by sequentially subdividing elements e3, e4, and es, the element division shown in FIG. 1l is obtained. Further, by further subdividing the elements g+, gz, gs generated by subdividing the elements e3%ea, es shown in FIG. 1l, the element division shown in FIG. 12 is obtained. Thereafter, by repeating this operation, the element divisions shown in FIG. I3 and FIG. 14 are successively obtained, and finally the element division shown in FIG.

The second example is the element division of a rectangular parallelepiped as shown in FIG. 15, which is a three-dimensional problem. r1 is 2 as a subdivision reference element
When selected, the subdivision pattern shown in FIG. 16 is displayed as 3. Here, it is assumed that pattern 8 in FIG. 16 is selected. Next, in step 4, the matching patterns shown in FIG. 17 are displayed, and the pattern intended by the creator of the analytical model is selected.

If pattern D is selected here, the element division shown in FIG. 18 will be obtained. Next, r2 is calculated as a subdivision candidate element connected to element r1 at 6, and by subdividing f2 by pattern selection, the element division shown in FIG. 19 is obtained. As described above, by using the analytical model creation method according to the present invention for three-dimensional problems, it is possible to easily create an analytical model that divides elements with density.

Another embodiment of the invention is shown in FIG. This embodiment is based on the same idea as the embodiment shown in FIG. 1, but differs in that at least two or more elements to be subdivided are input in step 2. Further, in step 10, the number of subdivision reference elements input in step 2 is calculated, and in step 11, steps 3 to 12 are repeated by the number of subdivision elements. However, in step 12, if the unsubdivided elements input in step 2 are the same as the last subdivision pattern, in step l3 all remaining unsubdivided elements are subdivided in the same pattern and the process proceeds to step 6. In this case, when subdividing a large number of elements, it is possible to perform the subdivision work while simultaneously viewing the overall subdivision state, thereby preventing mistakes in the subdivision work due to misunderstandings etc. be able to.

For example, when performing element division as shown in FIG.
If the entire diagram is roughly divided into regular elements, the left part is selected with 2, the subdivision pattern is selected with 3 and 4, and the remaining elements are the same pattern with 12, then the elements in Figure 23 The divisions are obtained all at once, and the subdivision candidate elements at the junction of the fine element division and coarse element division are automatically calculated, so by subdividing the subdivision candidate elements interactively, the second
It is possible to obtain the element division of one figure.

〔Effect of the invention〕

According to the present invention, a problem including a stress concentration part or a problem with a complicated shape can be easily divided into elements using a small number of nodes. Therefore, it is possible to reduce both the time required to create analytical models such as the finite element method and boundary element method, and the analysis time.
Product reliability can be improved through many case studies, case studies for optimal design can be easily conducted, and product costs can be reduced.

Furthermore, in recent years EWS (EngineeringWor
With the rapid development and spread of the K Station), many engineers are involved in numerical analysis using computers, so even users who are not familiar with numerical analysis or creating analytical models can easily learn how to create an analytical model using the present invention. By using this method, there is a great industrial advantage that an appropriate analytical model can be created faster and more reliably with as few nodes as an expert can do than when an expert manually creates an analytical model.

[Brief explanation of drawings]

FIG. 1 is a flow diagram showing an embodiment of the analytical model creation method according to the present invention, FIGS. 2 to 19, and 30A.
Figures 20 to 30C are diagrams for explaining the present invention.
21 to 23 are flowcharts showing other embodiments of the present invention, FIGS. 2l to 23 are diagrams for explaining other embodiments of the present invention shown in FIG. The figure is a diagram illustrating a conventional analytical model creation method.

Claims (2)

[Claims] (1) A method of creating an analytical model used for numerical analysis in which an object to be analyzed is divided into multiple elements and analyzed using a computer, an image display device, and an input device,
A step of dividing the analysis target into a plurality of coarsely divided elements by a computer and displaying the same on an image display device as a coarsely divided model, and a step of selecting an element to be further divided into smaller parts from the displayed model using an input device. , a step of displaying on an image display device a plurality of subdivision patterns that have been input into a computer in advance and compiled into a database;
A step of subdividing the element by selecting and applying a pattern to be applied to the selected coarse element from among the plurality of displayed subdivision patterns, and determining whether or not the above subdivision is appropriate. a step of selecting an element to be subdivided next from among the coarse elements adjacent to the subdivided element if judged appropriate; and applying the same subdivision operation as described above to the coarse element. A method for creating a numerical analysis model, characterized in that the coarsely divided elements are subdivided into necessary elements. (2) In claim (1), if it is determined that the selected coarse element is inappropriate in the step of determining the suitability of subdivision, the subdivision pattern should be applied from a plurality of subdivision patterns stored in a database. A method for creating a numerical analysis model, comprising the steps of reselecting a subdivision pattern, and applying the reselected pattern to coarsely divided elements to perform subdivision again.