JP6447454B2 - Numerical analysis method of structure using finite element method - Google Patents

Description

  The present invention relates to a numerical analysis technique for mechanical or mechanical characteristics of a structure using a computer, and more particularly to a numerical analysis technique for a structure by a finite element method.

  With the development of numerical computation technology by computer, mechanical or mechanical characteristics of structures such as vehicle bodies, various machine tools and buildings are numerically analyzed by finite element method using computer, etc. The information obtained there is used for designing the structure. According to the analysis method of the mechanical or mechanical characteristics of the structure by the numerical analysis by the computer, whether or not the structure has the required characteristics in the design stage before the actual structure is manufactured. This is advantageous in that it can be grasped. Further, not only isotropic materials but also structures using anisotropic materials such as CFRP (carbon fiber reinforced plastic) are objects of numerical analysis by the finite element method. For example, Patent Document 1 discloses an example in which a finite element method is used for a damping vibration analysis in a composite material plate in which carbon fibers are oriented and embedded in an epoxy resin. In this case, a model of the plate material, that is, a macro structure, is constructed by connecting the microstructure in which the anisotropy direction is orthogonal to the plate material having anisotropy regarding viscoelastic properties, and the finite element method is used. A simulation of vibration damping characteristics has been performed.

JP2015-32295A

  By the way, a structure using a material having anisotropy in mechanical or mechanical properties such as CFRP (a material whose mechanical property value such as Young's modulus varies depending on the direction, hereinafter referred to as “anisotropic material”) is finite. When performing numerical analysis by the element method, the structure to be analyzed includes a curved surface shape, especially when the direction of anisotropy in mechanical or mechanical properties is curved. The problem is how to set the coordinate system for.

  In the numerical analysis of the mechanical properties of the structure by the finite element method, in short, after determining the shape of the structure to be analyzed, the element of the structure is divided and the coordinate system is set. The mechanical properties such as the Young's modulus and Poisson's ratio of the body material are set and / or the external force is set, and numerical calculations to calculate the deformation, stress distribution, strain distribution, etc. of the structure according to the finite element method Executed. In such a series of processes, typically, one orthogonal coordinate system is applied to the entire structure as the coordinate system of the structure, and the material assumed in the structure is an anisotropic material. The direction of anisotropy of the mechanical or mechanical properties of the material (the direction in which the mechanical property value is larger or smaller than the other directions, hereinafter referred to as “anisotropic direction”) is the curved surface of the structure. When extending along the shape, the anisotropic direction of the material differs depending on the position of the part in the structure, that is, for each element. The direction does not match, and it is necessary to set a mechanical characteristic value for each element (configuration of a characteristic value matrix including the mechanical characteristic value as a component). However, in that case, the number of man-hours is enormous, and the configuration of the characteristic value matrix becomes very complicated, so that it may be difficult to set the mechanical characteristic values with high accuracy. Therefore, conventionally, at least one orthogonal coordinate system is typically used for the entire structure so that at least the configuration of the characteristic value matrix is simplified and the setting of the mechanical characteristic values is achieved with higher accuracy. Instead of setting, a process of setting the coordinate system is performed for each element, that is, individually. When one orthogonal coordinate system is used for the entire structure, one of the axes of the coordinate system (for example, the X axis) is projected on the bottom surface constituting the element. In the case of a certain structure, since the orientation of the bottom surface changes for each element, depending on the element, the bottom surface may be orthogonal to the axis of the coordinate system and may not be projected. It is necessary to set one for each element.

  As described above, in the numerical analysis of the structure by the finite element method, when the material of the structure is not an isotropic material but an anisotropic material, the anisotropic direction of the material depends on the shape of the structure. Different coordinate systems will be set for each element depending on the number of elements, and when the number of elements in the structure reaches thousands, the user can specify the anisotropic direction of the material individually for each element. Considering this, the process of setting the coordinate systems one by one is enormous and requires a lot of labor and labor. Therefore, if the coordinate system is different for each element depending on the anisotropic direction of the material, at least for each group of a certain number of elements, and more preferably, for a group of elements of substantially the entire structure. It would be advantageous to have an algorithm that can be set at least partially using a computer in a lump, because it saves a lot of user effort and labor.

  Thus, one problem of the present invention is that when a numerical analysis of the mechanical properties of a structure is performed by a finite element method using a computer, the structure to be analyzed is made of an anisotropic material and includes a curved surface shape. Even if the user does not perform the process of setting the axis of the coordinate system individually for each element, considering the anisotropic direction of the structure and / or the direction of the curved surface In order not to complicate the structure of the characteristic value matrix, at least a certain number of groups of elements, more preferably, a group of substantially entire groups of elements, It is to provide an algorithm that can set the coordinate system of.

  According to the present invention, the above-described problem is a numerical analysis method for mechanical properties of a structure by a finite element method using a computer, which determines the shape of the structure and executes element division of the structure The process of setting the coordinate system of each element in the structure, the process of setting the mechanical property value for each element set in the coordinate system, and the structure with the mechanical property value set The process of setting the coordinate system for each element in the structure, based on the shape of the structure and / or the anisotropic direction of its mechanical properties. Setting the Z-axis relative to the structure in the direction specified by the user, setting the R-axis orthogonal to the Z-axis and toward the center of each element in each element, A process of setting a θ-axis orthogonal to the Z-axis and the R-axis in each; In each element, specified by the user based on the anisotropy direction of the shape of the structure and / or its mechanical properties among the Z-axis, R-axis, and θ-axis with respect to the bottom surface of the element The angle specified by the user based on the anisotropy direction of the shape of the structure and / or its mechanical properties around the H axis, which is the normal to the bottom surface of the element, and the P axis obtained by projecting one The process of setting the Q-axis obtained by rotating in step S, the process of setting the S-axis orthogonal to the H-axis and the Q-axis in each element, and the H-axis set in each of the elements The process of setting the Q-axis and the S-axis as the coordinate system of each element is achieved by the method executed.

  In the above configuration, the “structure” may be a structure such as a vehicle body, various mechanical devices, buildings, or arbitrary members constituting them. The “finite element method” may be performed according to any arithmetic algorithm known in the art. As is known to those skilled in the art, for a structure in which a process of performing element division in the shape of the structure determined to be analyzed and a mechanical property value are set. The process of executing the calculation by the finite element method is automatically executed by the calculation process of the computer (however, in the process of dividing the element, depending on the state of the divided element or particularly precisely If there is a part to be analyzed, the user may manually change the position of the nodes, add or delete partly.) In the numerical analysis by the finite element method, the deformation of the structure, the stress distribution, the strain distribution and the like with respect to the external force are calculated.

  In the method of the present invention described above, in short, in various mechanical or mechanical numerical analyzes of structures using the finite element method, which may be performed using a computer in the usual manner. If the structure is made of anisotropic material and includes a curved surface, a different coordinate system must be set for each element of the structure. The coordinate system of each element is set according to the process defined above. In the process of setting the coordinate system, as will be understood from the above description, the user determines the Z-axis for the structure based on the shape of the structure and / or the anisotropic direction of the mechanical properties. Setting, selecting one of the Z-axis, R-axis, and θ-axis projected onto the bottom surface of each element, and selecting one of the Z-axis, R-axis, and θ-axis The rotation angle of the Q axis obtained by rotating the P axis, which is projected on the bottom of the element, around the H axis, which is the normal of the bottom surface of the element, is specified. It is automatically executed by the process. In the coordinate system set according to the above process, if the selection process and the designation process in the setting of the user's coordinate system are appropriate, the structure of the characteristic value matrix is not complicated. The mechanical property value of each element can be set for a group of a certain number of elements, more preferably for a group of elements of almost the entire structure. It becomes possible. Thus, compared to the case where the user sets the coordinate system for each element of the structure in consideration of the mechanical characteristics in each element and the orientation of the element surface, The man-hour to do will be reduced significantly. The above-described method of the present invention is effective when the structure is made of an anisotropic material and includes a curved surface shape, but the structure (isotropic property) is not. It may be applied to a structure made of a material, a structure made of an anisotropic material and not having a curved surface shape, and the like.

  Thus, according to the present invention described above, when the mechanical characteristics of a structure made of an anisotropic material and including a curved surface shape are numerically analyzed by the finite element method, the elements in the structure are The user's effort and labor when setting the coordinate system for the user, the user considers the mechanical properties in each element and the orientation of the element surface for each element of the structure. As compared with the case where the coordinate system is set, it is greatly reduced. In addition, the mechanical characteristics in the element are expressed not in one orthogonal coordinate system for the entire structure, but in a coordinate system selected so that the characteristics having material anisotropy are not so complicated for each element. Therefore, it is expected that the calculation accuracy is secured. Further, when the structure has a curved surface shape (whether or not it is made of an anisotropic material), according to the coordinate system setting process in the method of the present invention described above, the case of one orthogonal coordinate system As described above, depending on the element, it is possible to avoid a state in which the bottom surface cannot be projected perpendicularly to the axis of the coordinate system.

  Other objects and advantages of the present invention will become apparent from the following description of preferred embodiments of the present invention.

FIG. 1A is a diagram schematically showing a computer that performs numerical analysis of mechanical characteristics of a structure according to the finite element method according to the present invention. FIG. 1B is a flowchart showing the numerical analysis process according to the present invention in the form of a flowchart. FIG. 2 is a diagram showing an example of the shape of a structure to be analyzed on a monitor of a computer device. In the structure of the figure, element division is executed. 3A to 3E are diagrams schematically showing a process of setting an element coordinate system in the shape of a structure to be analyzed. FIG. 4A is an enlarged view of a part of the shape of the structure displayed in FIG. 2, and is an illustration in which an element coordinate system (Q axis) set for each element is displayed by an arrow. FIG. 4B is a diagram showing the element coordinate system indicated by arrows in the structure shown in FIG.

DESCRIPTION OF SYMBOLS 1 ... Computer body 2 ... Computer terminal 3 ... Monitor 4 ... Keyboard, mouse (input device)

Outline of Computer Device Configuration and Numerical Analysis Processing Process The numerical analysis of the mechanical properties of the structure according to the finite element method according to the present invention is illustrated in FIG. 1 (A) in the form normally used in this field. As described above, it may be realized by the operation of a computer program in the computer apparatus 1. The computer apparatus 1 is equipped with a CPU, a storage device, and an input / output device (I / O) connected to each other by a bidirectional common bus in a normal manner, and the storage device is used in the calculation of the present invention. A memory storing each program for executing the arithmetic processing, and a work memory and a data memory used during the calculation. In addition, the display and output of instructions, calculation results, and other information to the computer device 1 by the practitioner are performed through the computer terminal device 2 connected to the computer device 1. The computer terminal device 2 is provided with an input device 4 such as a monitor 3 and a keyboard and a mouse in a normal manner. When the program is started, the practitioner inputs according to the display on the monitor 3 according to the program procedure. It is possible to perform various instructions and inputs to the computer apparatus 1 using the apparatus 4 and to visually check the calculation state and calculation result from the computer apparatus 1 on the monitor 3. Note that the computer device 1 and the computer terminal device 2 may be equipped with other peripheral devices (not shown) (printer for outputting results, storage device for inputting / outputting calculation conditions and calculation result information, etc.). Should be understood. When various processes or operations described below are executed using the computer apparatus 1, programs necessary for the various processes or calculations are started in a normal manner, and the practitioner can connect the computer terminal apparatus 2 to the computer terminal apparatus 2. Then, in accordance with the input procedure prepared in the program, data necessary for calculation, calculation conditions at the time of calculation, and other various settings are input, and calculation is started. Then, during or after the execution of the calculation, the calculation result can be output through the computer terminal device 2 as appropriate.

  In the computer apparatus 1 described above, generally, the numerical analysis of the mechanical characteristics of the structure according to the finite element method is performed in a process as shown in FIG. With reference to the figure, first, formation of the shape of the structure to be analyzed is executed (step 1). In forming the shape of such a structure, typically any CAD system or software may be used to form the desired shape of the user. Here, the shape of the structure may be configured in a virtual space in which coordinates are defined by an xyz orthogonal coordinate system. When the shape of the structure is formed, division of the elements (mesh) of the shape of the structure is executed as illustrated in FIG. 2 (step 2). Such element division processing may be automatically executed using an arbitrary computer program for element division. In addition, depending on the element division state obtained automatically, or when there is a part to be analyzed particularly precisely, the arrangement, addition, or deletion of the nodes may be manually performed by the user. . When the element division processing is performed, the setting of the coordinate system (element coordinate system) of each element is executed according to the teaching according to the present invention described later in detail (step 3), and then in each element. Input of mechanical characteristic values, typically characteristic values representing mass, rigidity, and viscosity (step 4) and setting of conditions such as external force applied to the structure (step 5) is made by the user, and thereafter The calculation according to the finite element method, for example, calculation of the deformation amount, the stress distribution, and the strain distribution is executed using a computer program (step 6). The calculation result may be displayed graphically or numerically on the monitor 3 as described above.

Setting of element coordinate system As described in the “Summary of Invention” section, in the numerical analysis of the mechanical properties of the structure by the finite element method as described above, the structure to be analyzed is anisotropic such as CFRP. Assuming that the structure is formed of a material having a property (a state in which mechanical properties such as elasticity and rigidity in a specific direction are larger or smaller than those in other directions), and the structure is curved or curved. If the material has a shape and the anisotropic direction of the material is along the curved surface shape or the curved shape, the anisotropic direction is different for each element. In that case, if one orthogonal coordinate system is used for the entire structure, the structure of the matrix representing the mechanical property values in each element becomes complicated, and the numerical operation cannot always be performed accurately, Depending on the direction of the curved surface or the curved surface, it may be difficult to give coordinates appropriately. Therefore, when a structure formed of an anisotropic material and having a curved surface shape or a curved shape is an object to be analyzed, it is preferable that the calculation of the finite element method in the anisotropic material is relatively performed for each element. For example, the element coordinate system is preferably set so that the axis of the coordinate system is along the anisotropic direction of the material so that the characteristic value matrix having a simple configuration can be executed with higher accuracy.

  However, when the user sets the element coordinate system for each element in consideration of the anisotropic direction of the material and the shape and orientation of the element one by one, the number of elements reaches several thousand. In this case, the number of man-hours is enormous, and the user needs a lot of labor and labor. Therefore, in the present invention, as described above, a method is proposed that can greatly reduce a great amount of labor and labor for the user in setting the element coordinate system for each element. . According to such a method, it is possible to set the coordinate system of each element in a lump for at least a certain number of element groups, and more preferably for substantially the entire element group of the structure. It becomes.

  Specifically, in the process of setting the element coordinate system in the present invention (step 3 in FIG. 1B), first, as schematically depicted in FIG. The user designates N1 and N2 in the virtual space of the xyz coordinate system where the structure is placed, and sets the direction of N1-N2 as the Z axis. The Z-axis direction refers to the shape of the structure and / or the anisotropic direction of its mechanical properties. For example, the shape of the structure and / or the extending direction of the anisotropy is substantially axisymmetric with respect to the Z-axis. May be determined to be

  Thereafter, as schematically illustrated in FIG. 3B, the R-axis is set in a direction orthogonal to the Z-axis direction and toward the center C of the element, and the direction orthogonal to the Z-axis and the R-axis. Is set to the θ axis. The setting of the R axis and the θ axis is automatically set for each element by referring to the Z axis direction and the center of each element by a computer program.

  Next, in consideration of the respective directions of the Z-axis, R-axis, and θ-axis, and the anisotropic direction of the material assumed in the structure, the user determines the Z-axis, R-axis, and θ-axis. One of them is selected, and the computer program selects the selected axis as the bottom face B (N1′-N2′-N3 ′ plane) of each element as schematically shown in FIG. And the P axis is set. In this case, the bottom surface B may be arbitrarily selected. For example, a surface closest to the Z axis or a surface close to parallel may be selected. In one of the Z axis, R axis, and θ axis projected on the bottom surface B of each element, the user refers to the shape of the structure and the anisotropic direction of the material, for example, The axis in the direction closest to the anisotropy direction of the material is selected for at least some group of elements, and more preferably for a group of elements of substantially the entire structure. . At that time, since the R axis and the θ axis are set for each element, the Z axis direction and the respective directions of the R axis and the θ axis of each element in the group of the target elements are For example, the axis in the direction closest to the anisotropic direction of the material is selected as the axis to be projected onto the bottom surface B. (In FIG. 3C, the R axis is selected as an example, but the θ axis or the Z axis may be selected depending on the shape of the structure and the anisotropic direction of the material.)

  Thus, when the P-axis is set, as schematically illustrated in FIG. 3D, an angle designated with the P-axis within the bottom surface B, that is, around the normal H-axis direction of the bottom surface B. Rotate by δ, set the Q axis, set the S axis in the direction in the bottom surface B perpendicular to the Q axis and the H axis, and set the H axis, Q axis, and S axis as the element coordinate system of each element The Here, the angle δ when the P axis is rotated to obtain the Q axis is arbitrarily set by the user referring to the shape of the structure and the anisotropic direction of the material. For example, the specified angle δ is more preferably at least about a certain number of groups of elements such that the Q-axis substantially coincides with the anisotropic direction of the material. It is set collectively for the entire group of elements. The H-axis is automatically determined when the position and orientation of the bottom surface of the element are determined, and the S-axis is automatically determined when the Q-axis is set. The origin of each element in the HQS axis coordinate system may be an arbitrary position, for example, may be one node of the element as shown in FIG. It may be the center of the bottom surface or the center (C) of the element. When the HQS axis coordinate system of each element is set, the input of the dynamic characteristic value setting (step 4 in FIG. 1B) is executed in the HQS axis coordinate system. Thus, calculation according to the finite element method such as deformation amount, stress distribution, strain distribution and the like is executed using the mechanical characteristic values set for each element. Note that the input of setting conditions such as external force applied to the structure (step 5 in FIG. 1B) is typically performed in the xyz coordinate system, but is not limited to this.

  According to the method for setting the HQS axis element coordinate system described above, as already described, the structure to be analyzed is formed of an anisotropic material, and the structure is curved or curved. Even when the anisotropic direction differs from element to element, it is preferable that at least a certain number of element groups, more preferably, a substantially entire element group of the structure, The HQS axis element coordinate system can be set collectively. FIG. 4A shows the structure (ring) of FIG. 2 in which the anisotropy direction of the mechanical characteristic value (the direction of the white arrow) is slightly axial with respect to the circumferential direction of the ring. FIG. 4 is an enlarged view of a part of the tilted configuration (two-dimensional in the drawing, but actually a structure that is curved with respect to the paper surface), and FIG. 4B shows the structure of FIG. The small arrows in each element (lattice) indicate the Q axis in each element. Also, in FIG. 4A, each axis set in the process described in FIG. 3 is schematically drawn. In this case, in the xyz coordinate system in which the shape of the structure is first arranged, the anisotropic direction is different for each element with respect to the axial direction, and accordingly, the xyz coordinate system. If it is left as it is, the structure of the matrix representing the mechanical characteristic values becomes very complicated, the numerical calculation becomes complicated, and the accuracy may decrease. On the other hand, as schematically shown in FIG. 4A, in the method of setting the HQS axis element coordinate system by the process described in FIG. In some cases, for at least a certain number of element groups, more preferably, with respect to the substantially whole group of elements, the Q-axis or S-axis is approximately in the anisotropic direction of each element. (In the case of FIG. 4, the Q axis substantially coincides with the anisotropy direction).

  In the process of setting the HQS axis element coordinate system described with reference to FIG. 3, the operations performed by the user are the Z axis setting and the axis projected onto the bottom surface of each element. Only the setting of the specified angle δ when obtaining the Q axis from the P axis, and other processes are automatically executed by the computer program, so that the user can select each element of the structure. On the other hand, as compared with the case where the element coordinate system is set, the labor and labor of the user are greatly reduced. In setting the mechanical characteristic value, the anisotropy direction and the HQ- in at least a certain number of elements group, more preferably in a group of elements of almost the whole structure. It is expected that the axial direction of the S-axis element coordinate system is the same. In this case, the setting of the mechanical characteristic value can be executed collectively, and the labor and labor of the user can be reduced. Become.

  It is expected that the range of the analysis target that can set the collective element coordinate system in accordance with the teaching of the present invention is relatively wide. In the case of a structure with a relatively complicated shape, the setting of the collective element coordinate system according to the method of the present invention is applied to each partial (including a plurality of elements) area instead of the entire structure. Good (if the element coordinate system settings according to the invention apply to a group of at least some number of elements). For example, for each region (including a plurality of elements), processing such as selection of an axis projected on the bottom surface of the element and change of the specified angle δ of the Q axis from the P axis may be performed according to the anisotropic direction. The present invention is advantageously used when a structure formed of an anisotropic material and having a curved surface shape or a curved shape is an object to be analyzed. In numerical analysis of other structures by a finite element method. It should be understood that any of these may be utilized and still be within the scope of the present invention.

  Although the above description has been made in relation to the embodiment of the present invention, many modifications and changes can be easily made by those skilled in the art, and the present invention is limited to the embodiment exemplified above. It will be apparent that the invention is not limited and applies to various devices without departing from the inventive concept.

Claims (1)

A numerical analysis method of mechanical properties of a structure by a finite element method using a computer,
Determining the shape of the structure and performing element division of the structure;
Setting a coordinate system for each of the elements in the structure;
A process of setting a mechanical characteristic value for each element set in the coordinate system;
Performing a calculation by a finite element method on the structure in which the mechanical property value is set,
In the process of setting a coordinate system for each of the elements in the structure,
Setting the Z-axis for the structure in a direction specified by the user based on the shape of the structure and / or the anisotropic direction of its mechanical properties;
Setting an R-axis in each of the elements perpendicular to the Z-axis and toward the center of the element;
Setting a θ-axis orthogonal to the Z-axis and the R-axis in each of the elements;
Used in each of the elements based on the shape of the structure and / or the anisotropic direction of the mechanical properties of the Z-axis, the R-axis, and the θ-axis with respect to the bottom surface of the element Based on the shape of the structure and / or the anisotropic direction of its mechanical properties, the P-axis obtained by projecting one designated by the person around the H-axis, which is the normal to the bottom surface of the element Setting a Q-axis obtained by rotating at an angle specified by the user;
Setting an S-axis orthogonal to the H-axis and the Q-axis in each of the elements;
A method in which the H-axis, the Q-axis, and the S-axis are set as a coordinate system of the element in each of the elements.