CN108830000B - VTK-based carrier rocket structure finite element analysis visualization method - Google Patents
VTK-based carrier rocket structure finite element analysis visualization method Download PDFInfo
- Publication number
- CN108830000B CN108830000B CN201810666476.7A CN201810666476A CN108830000B CN 108830000 B CN108830000 B CN 108830000B CN 201810666476 A CN201810666476 A CN 201810666476A CN 108830000 B CN108830000 B CN 108830000B
- Authority
- CN
- China
- Prior art keywords
- data
- function
- node
- class
- value
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/15—Vehicle, aircraft or watercraft design
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Geometry (AREA)
- General Physics & Mathematics (AREA)
- Computer Hardware Design (AREA)
- General Engineering & Computer Science (AREA)
- Evolutionary Computation (AREA)
- Aviation & Aerospace Engineering (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Computational Mathematics (AREA)
- Automation & Control Theory (AREA)
- Processing Or Creating Images (AREA)
Abstract
The invention discloses a VTK-based carrier rocket structure finite element analysis visualization method, particularly relates to a C # and VTK combined carrier rocket structure finite element modal analysis result visualization method, and belongs to the field of carrier rocket structure finite element analysis visualization. According to the method, relevant data are obtained and stored in corresponding classes by reading a finite element model file and a finite element analysis result file of the launch vehicle, and four coefficients k1, k2, k3 and k4 are set for realizing control of a user on the modal shape animation; then, newly building a canvas or calling a related function to clean all graphs on the canvas, and displaying the modal shape animation by circularly and continuously calling the function for drawing the carrier rocket model and the function for cleaning all the graphs on the canvas until the cycle number reaches a preset value; the method can provide powerful support for the structural design, vibration control, load analysis and other aspects of the carrier rocket structure, and solves the technical problem of actual engineering in the corresponding field.
Description
Technical Field
The invention relates to a finite element analysis Visualization method for a carrier rocket structure, in particular to a Visualization method for a C # and VTK (Visualization Toolkit) combined carrier rocket structure finite element modal analysis result, and belongs to The field of carrier rocket structure finite element analysis Visualization.
Background
The carrier rocket as one kind of aircraft for sending various kinds of space spacecraft into space includes mainly rocket body, power unit system, control system, etc. The rocket body is used as a base body of the carrier rocket, and the importance of the rocket body to the carrier rocket is self-evident. Therefore, a series of analyses for the arrow structure is necessary. Among them, modal analysis is one of the methods for studying the dynamic characteristics of the structure, and is mainly used to analyze the modal parameters such as the natural frequency, the damping ratio, and the modal shape. The main modal characteristics of each order of the carrier rocket structure in a certain frequency range are obtained by using a modal analysis method, and the actual vibration response generated by the carrier rocket structure in the frequency range under the action of various external or internal loads can be predicted. Therefore, modal analysis is important for dynamic design of the structure of the launch vehicle and fault diagnosis of the launch vehicle equipment.
Scientific Computing Visualization (VISC for short) is an important research direction in computer graphics, and is a leading-edge field in graphics science.
The fundamental goal of scientific computational visualization is to convert a large amount of data obtained by experiments or numerical computation into computer images which can be perceived by human vision, and since the images can organically organize a large amount of abstract data and vividly show the contents represented by the data and the interrelations among the contents, people do not need to directly face the situation that the internal rules are difficult to find due to the complex form consisting of boring and tasteless numbers, and people are helped to directly master the complex global situation, so that the rules are better known.
Scientific computational visualization combines graph generation techniques with image understanding techniques, which can understand both the image data fed into a computer and generate graphs from complex multidimensional data. It relates to several fields independent from each other: computer graphics, interactive techniques, computer vision, computer-aided design, image processing, and the like. In fact, current visualization techniques are not only used for displaying intermediate and final results of scientific calculations, but also for displaying engineering calculations and measurement data.
In conclusion, scientific calculation visualization provides great convenience for scientific research work in many fields, not only changes the working modes of people in related fields, but also effectively improves the working efficiency and the working quality, so that the scientific research work is changed in all directions.
Scientific calculation visualization is a process with a flow characteristic, and comprises several important links such as filtering, mapping, drawing and feedback.
Although the basic process of scientific computational visualization mainly comprises the four links, in practical application, the process needs to be iterated repeatedly, for example, information to be extracted in a filtering link, an optimal mapping relation in a mapping link, and the like need to be iterated for many times to be determined.
Finite element methods have been used in the aerospace field to solve the computational problems of related structures since the beginning of the fifties of the twentieth century, and are now widely used by the engineering community. With the development of the finite element analysis result visualization technology and research, and the promotion of a large amount of data generated in the finite element analysis, many researches using the finite element method as an analysis approach generally adopt a scientific calculation visualization method. Some large-scale application-like finite element software also adopts a finite element analysis scientific calculation visualization method, in the aerospace field, the most notable software of the types is NASTRAN software developed by the national aerospace administration (NASA), which is widely accepted by the aspects of extremely high software reliability, excellent software quality, standard input/output format, open structure, software function and problem solving capability, improves the working efficiency of researchers, and the PATRAN serving as a finite element pre-processor and a finite element post-processor of the NASTRAN software is an open and multifunctional three-dimensional MCAE software package.
With the trend of the aerospace industry towards commercialization over the last decade, some aerospace enterprises seek further research into relevant research and development processes for the purpose of optimizing design and controlling costs. However, at present, there is no scientific calculation visualization method research only aiming at finite element analysis of a carrier rocket structure, even though a PATRAN software package can meet visualization of finite element analysis of the carrier rocket structure, rendering effect of the PATRAN software package on a finite element model is rough, and due to limited transportability of the PATRAN software, calling of a software platform on the software is very complicated, and then a series of flexible expansion applications cannot be realized. As an important class of aircraft, the above-mentioned research on launch vehicles is reasonably considered to be of value and applicable to launch vehicle-related engineering practices.
Disclosure of Invention
The method aims at the following technical problems in the field of visualization of finite element analysis results of a carrier rocket structure: (1) the rendering effect reality degree of the finite element units in the model is poor; (2) the modal shape animation display effect is too rough, so that the modal shape is not easy to analyze; (3) is not easy to be integrated in a finite element analysis software platform of a launch vehicle structure. The invention discloses a VTK-based finite element analysis visualization method of a carrier rocket structure, which aims to solve the technical problems that: the method for displaying the modal shape animation of each order of the model by taking the carrier rocket model as a drawing entity and taking the finite element model file and the finite element modal analysis result file as input data has the following advantages: (1) the displayed carrier rocket model meets the requirements of engineering specifications from the structural angle, and meanwhile, the method has a more real rendering effect on the nodes, the beam units and the shell units and has more obvious light and shade contrast; (2) the generated vector field animation modal shape animation can be controlled by a user, has fine display effect and can be used for analyzing the modal shape; (3) the method is easy to call and integrate in a finite element analysis software platform of the launch vehicle structure.
The invention discloses a VTK-based finite element analysis visualization method for a carrier rocket structure, which is characterized in that relevant data are acquired and stored in corresponding classes by reading a carrier rocket finite element model file and a finite element analysis result file, and four coefficients k1, k2, k3 and k4 are set for realizing the control of a user on modal shape animation. And then, newly building a canvas or calling related functions to clean all graphs on the canvas, and displaying the modal shape animation by circularly and continuously calling the functions for drawing the carrier rocket model and the functions for cleaning all the graphs on the canvas until the number of circulation times reaches a preset value. The method can provide powerful support for the structural design, vibration control, load analysis and other aspects of the carrier rocket structure, and solves the technical problem of actual engineering in the corresponding field.
The invention discloses a VTK-based finite element analysis visualization method for a carrier rocket structure, which comprises the following steps:
step 1: reading the finite element model file and the finite element analysis result file of the carrier rocket, and acquiring and storing relevant data in corresponding classes.
The specific implementation method of the step 1 comprises the following steps:
the files corresponding to the finite element model of the launch vehicle mainly comprise three data formats due to different model types, wherein the three data formats are respectively a bdf file corresponding to the mass-beam model, a bdf file corresponding to the mass-beam-shell model and a f06 file standard format, and the data in the three formats are respectively a mass-beam launch vehicle model finite element data file, a mass-beam-shell launch vehicle model finite element data file and a modal analysis result file of the finite element model of the launch vehicle. The functions used for respectively placing the three types of format data in the corresponding classes comprise OpenText, Peer, ReadLine, Contains, Substring, int.
The data comprises three types of data, namely node data, beam unit data and beam unit attribute data, and the three types of data are respectively placed in a CGrid class, a CBar class and a CPbarl class. The method for reading the data of the bdf file corresponding to the beam model comprises the following steps:
step 1.1.1: and opening the corresponding data file by using the input file path by using the OpenText function for opening the corresponding file in the C # function library.
Step 1.1.2: this loop is maintained in the while statement by determining the return value of the Peer function for checking whether the read file is finished. In the cycle, firstly, a line of model data is read by using a ReadLine function for reading a current line, and then, a relation or a Substring function for judging characters is used for judging the characters of the first n bits from the left in the currently read line. When the n-bit character contains a node data keyword 'GRID' or a beam unit data keyword 'CBAR', a class corresponding to the class data is instantiated, a Substring function is used for reading the related data in a character string form, and finally the character string type data is put into a class for storing the node data or the beam data through a type conversion function int. If the n-bit character contains a cross-row node data keyword 'GRID' or a beam unit attribute data keyword 'PBARL', firstly, a part of data is read in a character string form by using a method for reading a row of model data by using a ReadLine function, then, the rest data of the next row is read in by using the ReadLine function, then, the data is read in the character string form, all data types are converted and then placed into a corresponding class, namely, circulation is carried out until the tail of the model data file is read.
Step 1.1.3: after the loop operation of step 1.1.2 is finished, namely the data file is closed by using a Close function for closing the currently read file, the reading process is finished.
Step 1.2.1: and opening the corresponding data file by using the input file path by using the OpenText function.
Step 1.2.2: when the left-start m-bit character in the read-in line contains a shell unit data keyword 'CQUAD 4', the class corresponding to the data is instantiated by using the Substructing function, the relevant data is read in the form of a CQuaD, the class corresponding to the data is read in the form of a CQUAD, the relevant data is read in the form of a character string by using the Substructing function, and the CQuaD is put in the class storing the node data or the beam data.
Step 1.2.3: after the loop operation of step 1.2.2 is finished, namely the data file is closed by using a Close function, the reading process is finished.
Step 1.3.1: and opening the corresponding data file by using the input file path by using the OpenText function.
Step 1.3.2: and opening the corresponding data file by using the input file path by using the OpenText function. The loop is maintained in the while statement by determining the Peer function return value. In the cycle, firstly, a line of result data is read by using a ReadLine function, and then characters in the currently read line are judged by using a contacts or Substring function. When the line contains the first-order modal data first character 'NO. 1', reading two lines of data, entering another while statement, judging the first character from the left of the read line in the statement, instantiating the class corresponding to the data when the character is a blank, reading the related data in the form of a character string by using a Substring function, and finally putting the character string type data into the class storing the vibration type data through the int.Parse or double.Parse function conversion type, namely, continuing to circulate. And after the while statement is finished, judging the value of the variable flag, and if the value of the variable flag is 1, continuing to perform the outermost loop. If the value of the variable flag is 0, reading the remaining files after four lines by using the ReadLine function, respectively reading the circle frequency corresponding to the first-order mode for each line in the remaining files after four lines, converting the data type, and putting the converted data type into the instantiated class. And after the circle frequency corresponding to the first-order mode is read in, keeping the value of the variable flag as 1, namely, continuing to perform outermost layer circulation until the end of the result data file is read.
Step 1.3.3: after the loop operation of step 1.3.2 is finished, namely the data file is closed by using a Close function, the reading process is finished.
Step 2: in order to make the generated vector field animation modal shape animation controlled by the user, four coefficients k1, k2, k3, and k4 are set.
The step 2 specific implementation method comprises the following steps:
step 2.1: four coefficients k1, k2, k3, k4 are defined.
The k1 coefficient is used to normalize the displacement vector data, and its value is determined by the maximum value of all node displacement vector data corresponding to a certain order mode. The value of the k1 coefficient is the inverse of the maximum value.
Since the value of the k2 coefficient depends on the values of the k3 and k4 coefficients, the meaning of the latter two coefficients is introduced.
The value of the k3 coefficient is set by the user and represents the ratio of the maximum displacement displayed in the animation relative to the size of the launch vehicle.
The value of the k4 coefficient is the launch vehicle size mentioned in interpreting the meaning of the k3 coefficient. In determining the mode shape of each order, the coefficient value of k4 is set as the characteristic length of the launch vehicle.
The value of the k2 coefficient is the product of the coefficients k3 and k 4. The actual amplitude is converted into the amplitude displayed in animation by setting four coefficients k1, k2, k3, k 4.
Step 2.2: four coefficients k1, k2, k3 and k4 are provided.
Traversing all data in the CModal class to obtain the maximum value r of the displacement vector data in each node according to the displacement vector data obtained in the step 1maxFurther, the value of the coefficient k1 is obtained as shown in equation (1).
Meanwhile, in the traversal cycle, square and root operation is carried out on three displacement vector data corresponding to the same node, the maximum displacement value corresponding to the node is calculated, and the maximum displacement values of all the nodes are compared to obtain the maximum displacement value R of all the nodesmax。
Step 2.2: and obtaining the values of the coefficients k3 and k4 according to the proportion set by the user and the characteristic length of the launch vehicle obtained in the step 2.1, and further calculating the value of the coefficient k 2.
Namely, setting of four coefficients k1, k2, k3 and k4 is completed.
And step 3: newly creating a canvas or calling related functions to clean all graphics on the canvas.
The function used for newly building the canvas is a New function in the vtkRenderer class, and the function used for cleaning all the graphs on the canvas is a function named RemoveAllViewProps in the renderer class.
And 4, step 4: and continuously calling a function for drawing the carrier rocket model and a function for clearing all graphs on the canvas to display the modal shape animation by circulation until the circulation times reach a preset value.
Because the essence of the animation is the continuous refreshing of the data stream, all images on the current canvas are removed by using a RemoveAllViewProps function along with the refreshing of the data stream, and then the image corresponding to the new data is displayed on the canvas. In order to make the data flow and the graph on the canvas refresh continuously, the operations of clearing the image corresponding to the original data, drawing the image corresponding to the new data and the like are placed in the loop, and the progress of the animation playing is controlled by the four coefficients k1, k2, k3 and k4 set in the step 2 and the variable t which is set in the loop and increases continuously along with the progress of the loop.
The step 4 specific implementation method comprises the following steps:
step 4.1: all data in the CCbar class, CGrid class, and CModal class is traversed and nodes and beam elements are drawn on the canvas.
In the function named generatoccott, which is used to draw a launch vehicle model, all data in the CCbar class is first traversed, and within this traversal loop, all data in the CGrid class is traversed to find the ID data in the CGrid class that is identical to the firstgridd data in the CCbar class. After finding the corresponding node number, traversing all data in the CModa class in a cycle of traversing all data in the CGrid class, and finding the number data corresponding to the ID data in the CGrid class in the CModa class. Then, the displacement value of the node at this time is calculated according to the displacement vector data corresponding to the node number and the value of the variable t in the for loop at this time. The formula for calculating the real-time position of each node is shown in formula (2).
Wherein, newpositionx, newpositiony and newpositionz on the left side of the equal sign are projections of the real-time displacement of the node on an X, Y, Z axis in sequence;
the modal.v, modal.w to the right of the equal sign correspond to the above description of class and data members, representing the modal shape displacement component of the node along the X, Y, Z axis, respectively.
And (3) adding the value on the right side of the equal sign in the formula (2) with the three coordinate data of each node to obtain the real-time coordinate position of the node. And (3) observing the formula (2), namely displaying each order mode vibration mode of the carrier rocket in a simple harmonic vibration mode on a data layer by utilizing a trigonometric sine function term multiplied in a formula for calculating the projection value of the real-time displacement value.
Subsequently, a node is placed using the calculated new coordinates, and the displacement value is taken as the attribute data of the node. Similarly, the second end of the beam unit is determined. In addition, in order to display the displacement value of each node as the attribute data of each node in the subsequent steps by using a cloud graph, after each node is placed, the displacement value of each node needs to be calculated, and the node is associated with the attribute data corresponding to the node by using an InsertTuple1 function of the associated attribute data and the geometric data.
In the loop of traversing all data in the CCbar, after the positions of two end points of the beam element are determined, the two end points are connected by a line to construct the beam element.
Step 4.2: traverse the relevant data and draw the shell element on the canvas.
And after drawing a beam unit by using a traversal loop, traversing the data in the Cquad class, continuously traversing all the data in the CGrid class in the traversal loop, and finding the ID data in the CGrid class corresponding to the first data, second data, third data and fourth data in the Cquad class in the traversal layer. After finding the corresponding node number, traversing all data in the CModa class in a cycle of traversing all data in the CGrid class, and finding the number data corresponding to the ID data in the CGrid class in the CModa class. Then, the displacement value of the node at this time is calculated according to the displacement vector data corresponding to the node number and the value of the variable t in the for loop at this time. Subsequently, a node is placed with the new coordinates, and the displacement value is taken as the attribute data of the node. After placing the four vertices of the shell element using the traversal described above, the operation continues in a loop that traverses all the data in the Cquad class. The operation content is that four vertexes are connected in sequence to form a quadrangle, and the shell unit is represented in a form of a space quadrangle.
Furthermore, similarly to step 4.1, for each of the four vertices of the shell element, the displacement value of each node is calculated, and the vertices are associated with their corresponding attribute data by using the InsertTuple1 function.
Step 4.3: and displaying the color cloud picture by taking the real-time displacement data of each node as attribute data.
The color cloud picture drawing is based on color mapping in the VTK, the color mapping in the VTK is used for coloring an object according to a certain attribute value of the object, and colors in a color Lookup Table (Lookup Table) are mapped to points or units during drawing by establishing the Lookup Table and setting a plurality of colors in the Lookup Table. Meanwhile, the cloud picture can be generated by the aid of the cloud picture generation algorithm in the vtkLookupTable only by calling a function named Build in the vtkLookupTable.
Step 4.3 is specifically realized by the following steps:
step 4.3.1: a color look-up table is established.
The SetTableValue function is used to set p colors in the color lookup table, which in turn correspond to node displacement values from small to large. Meanwhile, the color lookup table is set to accord with mainstream commercial finite element post-processing software, and the rule of color change from small to large corresponding displacement value is blue, green, yellow and red. In addition, the number of the series of colors and the number of the color types set by the color lookup table are also adjusted according to the use habits of the user.
Step 4.3.2: and (4) carrying out interpolation by combining the variation range of all node displacement data and a Build function, and drawing a color cloud picture on the current carrier rocket model.
According to R obtained in step 2.1maxAnd (3) determining the upper limit of the displacement value of all the nodes of the model by using a SetScalarRange function for determining the attribute data range corresponding to the color lookup table, wherein the upper limit and the lower limit of the displacement value correspond to the color lookup table in the step 4.3.1.
And then, performing interpolation calculation on the color corresponding to each node by using the build function and taking the displacement data of each node as attribute data, acquiring the color corresponding to each node, and drawing the color cloud picture on the current carrier rocket model.
Step 4.4: and (4) continuously calling a function for drawing the carrier rocket model and a function for clearing all the graphs on the canvas by circulating the steps 4.1 to 4.3 until the circulation times reach a preset value, so as to form the carrier rocket model modal shape animation.
Further comprising the step 5: obtaining the modal shape animation of each order corresponding to the carrier rocket model after finite element analysis according to the steps 1 to 4, providing powerful support for the application of structural design, vibration control, load analysis and the like of the carrier rocket structure, and solving the technical problem of actual engineering in the corresponding field.
Has the advantages that:
1. compared with the related module of the current mainstream finite element post-processing software, the VTK-based carrier rocket structure finite element analysis visualization method disclosed by the invention has the advantages that the rendering effect of a carrier rocket model, particularly a mass-beam-shell model, is more vivid by using the visualization toolkit, and the potential of further improving the observation visual angle and the light source position is realized.
2. According to the VTK-based finite element analysis visualization method for the structure of the launch vehicle, the four coefficients k1, k2, k3 and k4 are set, so that a user can more comprehensively control the modal shape animation of the launch vehicle model, and convenience is brought to the research of the modal shape from the engineering perspective.
2. Compared with a mainstream finite element post-processing software module, the carrier rocket structure finite element analysis visualization method based on the VTK has strong transportability and easier integration and calling by adopting a C # language programming method, and can be used as a part of a related software platform to support the visualization of a finite element analysis result.
Drawings
FIG. 1 is a general flow chart of a VTK-based visualization method for finite element analysis of a launch vehicle structure;
FIG. 2 is a sample finite element model data file format corresponding to a mass-beam-hull launch vehicle model in an exemplary embodiment;
FIG. 3 is a sample format of a result file obtained from a finite element software modal analysis of a launch vehicle model in an exemplary embodiment;
FIG. 4 is a flowchart corresponding to reading node and beam unit data files in an embodiment;
FIG. 5 is a flowchart corresponding to reading a shell element data file in an embodiment;
FIG. 6 is a flowchart corresponding to reading a finite element analysis results data file in accordance with an embodiment;
FIG. 7 is a diagram of UML classes corresponding to classes and their data members used to store data obtained from a read in an exemplary embodiment;
FIG. 8 is a flow chart corresponding to the coefficients set in step 2 in a specific embodiment;
FIG. 9 is a flowchart illustrating the operation of step 4.1 in accordance with certain embodiments;
FIG. 10 is a flowchart of the operation of step 4.2 in accordance with certain embodiments;
FIG. 11 is a model of a mass-beam-shell launch vehicle constructed using the method of the present embodiment;
FIG. 12 is an enlarged view of a portion of a shell element of a mass-beam-shell launch vehicle model constructed using the method of the present invention in accordance with an exemplary embodiment;
FIG. 13 is a modal shape animation generated using the method of the present embodiment, where 13a) through 13f) are intermittent screenshots of the shape animation;
FIG. 14 is a mass-beam-shell launch vehicle model plotted using PATRAN software in a particular embodiment;
FIG. 15 is an enlarged partial view of a mass-beam-shell launch vehicle model shell element depicted using PATRAN software in accordance with an exemplary embodiment;
FIG. 16 is a modal shape animation generated using PATRAN software in an embodiment, where 16a) through 16f) are intermittent screenshots of the shape animation.
Detailed Description
For a better understanding of the objects and advantages of the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.
Example 1:
the mass-beam-shell launch vehicle model used in this embodiment includes nodes, beam elements, and shell elements, and the launch vehicle model and shell elements are enlarged as shown in fig. 11 and 12.
The finite element analysis visualization method of the carrier rocket structure based on VTK disclosed by the embodiment comprises the following specific implementation steps,
step 1: reading the finite element model file and the finite element analysis result file of the carrier rocket, and acquiring and storing relevant data in the class.
In this embodiment, the finite element analysis software used for the modal analysis of the mass-beam-shell launch vehicle model is NASTRAN software, the format of the finite element model file is a. bdf file, and the format of the finite element analysis result file is a.f 06 file, corresponding to the second and third data formats described in the foregoing, respectively, and specific format examples thereof are shown in fig. 2 and 3, respectively.
The flows of reading the node and beam unit data in the model file, reading the shell unit data in the model file, and reading the result file data are respectively shown in fig. 4, 5, and 6.
The UML class diagram corresponding to the class and its data members involved in step 1 is shown in FIG. 7.
By the method, the data required in the file is read and stored in the corresponding class.
Step 2: the four coefficients k1, k2, k3 and k4 set in the method are processed, and data required in the subsequent steps are acquired, so that the mode shape of each order is easier to study.
Step 2.1: four coefficients k1, k2, k3 and k4 are defined.
Step 2.2: values for k1, k2, k3, k4 are set. In this embodiment, according to the maximum normalization method, the value of the coefficient k1 defaults to the reciprocal of the maximum value of all node displacement vector data, which is 121; the coefficient k3 is set to 0.1, which corresponds to a maximum displacement of one tenth of the value of the coefficient k4 in the mode-shape animation; the coefficient k4 was set to the full length of the rocket body of the launch vehicle model, which was 53; the coefficient k2 is the product of k3 and k4, and has a value of 5.3.
The processing flow of the coefficients in step 2 is shown in fig. 8.
In addition, in order to display the real-time displacement values of the nodes of the launch vehicle model in the subsequent step by using the color cloud chart, the maximum value R of the displacement values of the nodes serving as attribute data is also determined in the stepmax。
And step 3: in the embodiment, a New function in the vtkRenderer class is used for newly building the canvas, so that preparation is made for drawing and generating the subsequent carrier rocket modal shape animation.
And 4, step 4: and continuously calling a function for drawing the mass-beam-shell carrier rocket model and a function for clearing all graphs on the canvas to display the modal shape animation by circulation.
Step 4.1: in this embodiment, all data in the CCbar class, CGrid class, and CModal class is traversed and nodes and beam elements are drawn on the canvas.
In the function named generatoccount for drawing the launch vehicle model, the related data is determined through the traversal process described above, and the displacement value of the node at this time is calculated according to the displacement vector data corresponding to each node number and the value of the variable t in the for cycle at this time. The formula for calculating the real-time position of each node is shown in formula (3).
Wherein the coefficient k1 is a maximum value normalization coefficient in the present embodiment; k2 is the product of k3 and k 4. Namely, the mode shape of each order of the carrier rocket can be displayed in a simple harmonic vibration mode on the data level.
Subsequently, the method node described above is utilized, and the displacement value is taken as the attribute data of the node. After each node is placed, the displacement value of each node is calculated and the node is associated with its corresponding attribute data using a function named InsertTuple 1.
Finally, after the positions of the two end points of the beam unit are determined, the two end points are connected by using a line to construct the beam unit of the launch vehicle model, and the flow corresponding to the step 4.1 is shown in fig. 9.
Step 4.2: in this embodiment, the shell elements occupy a lower proportion of the entire model but the step of drawing the shell elements is still critical to the modal shape animation. The method will traverse the relevant data and draw the shell element on the canvas.
The method described above is used to traverse the data in the CQuad class, continue traversing all the data in the CGrid class in the traversal loop, and find the ID data in the CGrid class corresponding to the data in the CQuad class in the traversal loop. The numbering data in the CModal class corresponding to the ID data in the CGrid class is found by traversing all the data in the CModal class. Thereafter, the displacement value of the node at this time is calculated, the node is placed with the new coordinates, and the displacement value is used as the attribute data of the node. After the four vertices of the shell element have been placed using the traversal described above, the shell element is represented in the form of a spatial quadrilateral in the manner described above, and the vertices are associated with their corresponding attribute data using a function named InsertTuple 1.
The corresponding flow of step 4.2 is shown in fig. 10.
Step 4.3: and displaying a color cloud picture on the mass-beam-shell carrier rocket model by taking the attribute data as a basis.
Step 4.3.1: a color look-up table is established.
In an embodiment, a function named SetTableValue is used to set the default 15 colors of the method, wherein the 15 colors correspond to node displacement values from small to large in sequence, and the color change rule corresponding to the displacement values from small to large is blue-green-yellow-red.
Step 4.3.2: and (4) carrying out interpolation by combining related data, and drawing a color cloud picture on the current carrier rocket model.
In a particular embodiment, according to the known data RmaxDetermining the upper limit of displacement values of all nodes of the model, using a SetScalarRange function to enable the upper limit and the lower limit of the displacement values to correspond to the color lookup table, then using a build function to perform interpolation calculation on the color corresponding to each node, obtaining the color corresponding to each node, and then drawing the color cloud picture on the current carrier rocket model.
For the mass-beam-shell launch vehicle model, although the color cloud is finally drawn on the beam elements and shell elements of the model, the attribute data on which the color cloud is drawn is still associated with each node and cannot be associated with the beam elements or shell elements.
Step 4.4: and (4) continuously calling a function for drawing the carrier rocket model and a function for clearing all graphs on the canvas by circulating the steps 4.1 to 4.3 to form a fifth-order modal shape animation of the carrier rocket model until the circulation times reach a preset value.
For the fifth order mode of the launch vehicle model, the vector field animation generated using the method described above is shown in FIG. 13.
Comparing fig. 11, fig. 12, and fig. 13 drawn by the method disclosed by the present invention with fig. 14, fig. 15, and fig. 16 drawn by the existing finite element post-processing software PATRAN, it can be seen that rendering effect of the VTK-based finite element analysis visualization method of the launch vehicle structure disclosed by the present invention on the launch vehicle model, particularly the mass-beam-shell model, is more realistic.
The modal shape animation corresponding to the mass-beam-shell carrier rocket model is obtained according to the steps 1 to 4, so that powerful support can be provided for the application of the carrier rocket in structural design and analysis, and the method has wide application prospect and benefit.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention, and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (7)
1. A VTK-based carrier rocket structure finite element analysis visualization method is characterized in that: comprises the following steps of (a) carrying out,
step 1: reading a finite element model file and a finite element analysis result file of the carrier rocket, and acquiring and storing related data in corresponding classes;
step 2: in order to make the generated vector field animation modal shape animation controlled by the user, four coefficients k1, k2, k3 and k4 are set;
and step 3: newly building a canvas or calling a related function to clean all graphs on the canvas;
the function used for newly building the canvas is a New function in the vtkRenderer class, and the function used for cleaning all the graphs on the canvas is a function named RemoveAllViewProps in the renderer class;
and 4, step 4: continuously calling a function for drawing a carrier rocket model and a function for clearing all graphs on the canvas to display the modal shape animation in a circulating manner until the circulating times reach a preset value;
because the essence of the animation is the continuous refreshing of the data stream, all images on the current canvas are removed by using a RemoveAllViewProps function along with the refreshing of the data stream, and then the image corresponding to the new data is displayed on the canvas; in order to enable the data stream and the graph on the canvas to be refreshed continuously, the operation of clearing the image corresponding to the original data and drawing the image corresponding to the new data is placed in a loop, and the progress of the animation playing is controlled by the four values of the coefficients k1, k2, k3 and k4 set in the step 2 and the variable t which is set in the loop and continuously increases along with the progress of the loop.
2. The VTK-based finite element analysis visualization method of a launch vehicle structure according to claim 1, wherein: and step 5, obtaining the modal shape animation of each order corresponding to the carrier rocket model after finite element analysis according to the steps 1 to 4, providing powerful support for the application of structural design, vibration control and load analysis of the carrier rocket structure, and solving the technical problem of actual engineering in the corresponding field.
3. A VTK-based visualization method of finite element analysis of a launch vehicle structure according to claim 1 or 2, characterized in that: the specific implementation method of the step 1 comprises the following steps,
the files corresponding to the finite element model of the launch vehicle mainly comprise three data formats due to different model types, wherein the three data formats are respectively a bdf file corresponding to the mass-beam model, a bdf file corresponding to the mass-beam-shell model and a f06 file standard format, and the data in the three formats are respectively a mass-beam launch vehicle model finite element data file, a mass-beam-shell launch vehicle model finite element data file and a modal analysis result file of the finite element model of the launch vehicle; the functions used for respectively placing the three types of format data in the corresponding classes comprise OpenText, Peer, ReadLine, Contains, Substring, int.
4. A VTK-based visualization method of finite element analysis of a launch vehicle structure according to claim 3, wherein: the data comprises three types of data, namely node data, beam unit data and beam unit attribute data, which are respectively placed in a CGrid class, a CBar class and a CPbarl class; the method for reading the data of the bdf file corresponding to the beam model comprises the following steps,
step 1.1.1: opening a corresponding data file by using an OpenText function for opening a corresponding file in the C # function library and using an input file path;
step 1.1.2: the loop is maintained in while statement by judging the return value of the Peer function for checking whether the read file is finished; in the cycle, firstly, reading a line of model data by using a ReadLine function for reading a current line, and then judging the front-left n-bit characters in the currently read line by using a relations or Substring function for judging the characters; when the n-bit character contains a node data keyword 'GRID' or a beam unit data keyword 'CBAR', instantiating a class corresponding to the class data, reading in related data in a character string form by using a Substring function, and finally putting the character string type data into a class for storing the node data or the beam data through a type conversion function int. If the n-bit character contains a cross-row node data keyword 'GRID' or a beam unit attribute data keyword 'PBARL', firstly reading a part of data in a character string form according to a method for reading a row of model data by using a ReadLine function, then reading the rest data in the next row by using the ReadLine function, then reading the data in the character string form, converting all data types and then placing the converted data types into corresponding classes, namely circulating until the tail of a model data file is read;
step 1.1.3: after the loop operation of the step 1.1.2 is finished, namely closing the data file by using a Close function for closing the currently read file, and finishing the reading process;
step 1.2.1: opening a corresponding data file by using an OpenText function and an input file path;
step 1.2.2: judging a return value of a function by using a while statement to maintain the circulation, when a left n-bit character in a read-in line respectively contains 'GRID', 'CBAR', 'GRID' or 'PBARL', instantiating a class corresponding to the class data by using a Substring function, reading related data in a character string form by using a Substring function, finally, converting the character string type data into the class storing node data or beam data by using a type conversion function int.Parse or double.Parse function, when a left m-bit character in the read-in line contains a shell unit data keyword 'CQUAD 4', instantiating the class corresponding to the class data by using a CQuad, reading the related data in the character string form by using the Substring function, and finally, converting the character string type data into the class by using the double or double.Parse function, namely, continuing the circulation until a model data file tail is read;
step 1.2.3: after the loop operation of the step 1.2.2 is finished, namely closing the data file by using a Close function, and finishing the reading process;
step 1.3.1: opening a corresponding data file by using an OpenText function and an input file path;
step 1.3.2: opening a corresponding data file by using an OpenText function and an input file path; the loop is maintained by judging the return value of the Peer function in the while statement; in the cycle, firstly, a line of result data is read by using a ReadLine function, and then characters in the currently read line are judged by using a contacts or Substring function; when the line contains a first-order modal data first character NO.1, reading two lines of data, entering another while statement, judging the first character from the left of the read line in the statement, instantiating a class corresponding to the data when the character is a blank, reading related data in a character string form by using a Substring function, and finally putting the character string type data into the class storing vibration type data through int.Parse or double.Parse function conversion types, namely continuously circulating; after the while statement is finished, judging the value of a variable flag, and if the value of the variable flag is 1, continuing to perform outermost-layer circulation; if the value of the variable flag is 0, reading four lines of residual files by using a ReadLine function, respectively reading circle frequency corresponding to a first-order mode for each line of the four lines of residual files, converting the data type, and putting the converted data type into an instantiated class; after the circle frequency corresponding to the first-order mode is read in, the value of the variable flag is recorded as 1, namely, the outermost layer circulation is continued until the end of the result data file is read;
step 1.3.3: after the loop operation of step 1.3.2 is finished, namely the data file is closed by using a Close function, the reading process is finished.
5. The VTK-based finite element analysis visualization method of a launch vehicle structure according to claim 4, wherein: the step 2 specific implementation method comprises the following steps,
step 2.1: defining four coefficients k1, k2, k3, k 4;
the k1 coefficient is used for normalizing the displacement vector data, and the determination of the value depends on the maximum value of the displacement vector data of all nodes corresponding to a certain order mode; the value of the k1 coefficient is the inverse of the maximum value;
since the value of the k2 coefficient depends on the values of the k3 and k4 coefficients, the meaning of the latter two coefficients is introduced first;
the value of the k3 coefficient is set by the user and represents the ratio of the maximum displacement displayed in the animation relative to the size of the launch vehicle;
the value of the k4 coefficient is the launch vehicle size mentioned in interpreting the meaning of the k3 coefficient; setting the coefficient value of k4 as the characteristic length of the carrier rocket when determining the modal shape of each order;
the value of the k2 coefficient is the product of the coefficients k3 and k 4; converting the actual amplitude into the amplitude displayed in the animation by setting four coefficients k1, k2, k3 and k 4;
step 2.2: setting four coefficients k1, k2, k3 and k 4;
traversing all data in the CModal class to obtain the maximum value r of the displacement vector data in each node according to the displacement vector data obtained in the step 1maxFurther obtaining the value of the coefficient k1, as shown in formula (1);
meanwhile, in the traversal cycle, the square and root operation is carried out on the three displacement vector data corresponding to the same node, the maximum displacement value corresponding to the node is calculated, and each node is subjected to square root operationComparing the maximum displacement values of the points to obtain the maximum displacement value R of each nodemax；
Step 2.2: obtaining the values of coefficients k3 and k4 according to the proportion set by the user and the characteristic length of the launch vehicle obtained in the step 2.1, and further calculating the value of the coefficient k 2;
namely, setting of four coefficients k1, k2, k3 and k4 is completed.
6. The VTK-based finite element analysis visualization method of a launch vehicle structure according to claim 5, wherein: the specific implementation method of the step 4 comprises the following steps,
step 4.1: traversing all data in the CCbar class, the CGrid class and the CModal class, and drawing nodes and beam units on a canvas;
in a function named Generaterocket for drawing a launch vehicle model, firstly traversing all data in a CCbar class, and traversing all data in a CGrid class in a traversal loop to find ID data in the CGrid class which is the same as firstGridID data in the CCbar class; after finding out the corresponding node number, traversing all data in the CModa class in a cycle of traversing all data in the CGrid class, and finding out the number data corresponding to the ID data in the CGrid class in the CModa class; then, calculating the displacement value of the node at the moment according to the displacement vector data corresponding to the node number and the value of the variable t in the for cycle at the moment; the formula for calculating the real-time position of each node is shown as the formula (2);
wherein, newpositionx, newpositiony and newpositionz on the left side of the equal sign are projections of the real-time displacement of the node on an X, Y, Z axis in sequence;
the modal.u, modal.v, modal.w to the right of the equal sign correspond to the above descriptions for class and data members, representing the modal shape displacement component of the node along the X, Y, Z axis, respectively;
adding the value on the right side of the middle number in the formula (2) and the three coordinate data of each node to obtain the real-time coordinate position of the node; observing the formula (2), namely displaying each order mode vibration mode of the carrier rocket in a simple harmonic vibration mode on a data layer by utilizing a trigonometric sine function term multiplied in a formula for calculating a projection value of a real-time displacement value;
then, using the calculated new coordinates to place a node, and using the displacement value as the attribute data of the node; similarly, the second end point of the beam unit is also determined; in addition, in order to display the displacement value of each node as the attribute data of each node by using a cloud graph in the subsequent steps, after each node is placed, the displacement value of each node needs to be calculated, and the node is associated with the attribute data corresponding to the node by using an InsertTuple1 function of the associated attribute data and the geometric data;
in the cycle of traversing all data in the CCbar, after the positions of two end points of the beam unit are determined, connecting the two end points by using a line to construct the beam unit;
step 4.2: traversing the related data and drawing the shell unit on the canvas;
after a beam unit is drawn by using a traversal loop, traversing data in the CQuds, continuously traversing all data in the CGrid in the traversal loop, and finding ID data in the CGrid which is the same as the ID data in the CGrid corresponding to the first data, the second data, the third data and the fourth data in the CQuds in the traversal layer; after finding out the corresponding node number, traversing all data in the CModa class in a cycle of traversing all data in the CGrid class, and finding out the number data corresponding to the ID data in the CGrid class in the CModa class; then, calculating the displacement value of the node at the moment according to the displacement vector data corresponding to the node number and the value of the variable t in the for cycle at the moment; then, a node is placed by using the new coordinates, and the displacement value is used as attribute data of the node; after the four vertexes of the shell unit are placed by utilizing traversal, continuously operating in a loop of traversing all data in the CQoad class; the operation content is that four vertexes are sequentially connected to form a quadrangle, and the shell unit is represented in a space quadrangle form;
in addition, for four vertexes of each shell element, calculating the displacement value of each node, and associating the vertex with the corresponding attribute data by using an InsertTuple1 function;
step 4.3: displaying a color cloud picture by taking real-time displacement data of each node as attribute data;
the drawing of the color cloud picture is based on color mapping in the VTK, the color mapping in the VTK is to color an object according to a certain attribute value of the object, and the color in the color Lookup Table is mapped to a point or a unit during drawing by establishing a color Lookup Table and setting a plurality of colors in the Lookup Table; meanwhile, the cloud picture can be generated by an algorithm which is used for generating the cloud picture in the vtkLookupTable class by calling a function named Build in the class;
step 4.4: and (4) continuously calling a function for drawing the carrier rocket model and a function for clearing all the graphs on the canvas by circulating the steps 4.1 to 4.3 until the circulation times reach a preset value, so as to form the carrier rocket model modal shape animation.
7. The VTK-based finite element analysis visualization method of a launch vehicle structure according to claim 6, wherein: step 4.3 the concrete implementation steps are as follows,
step 4.3.1: establishing a color lookup table;
setting p colors in a color lookup table by using a SetTableValue function, wherein the p colors sequentially correspond to node displacement values from small to large; meanwhile, the color lookup table is set to accord with commercial finite element post-processing software, and the color change rule corresponding to the small-to-large displacement value is blue-green-yellow-red; in addition, the number of a series of colors and color types set by the color lookup table is also adjusted according to the use habit of the user;
step 4.3.2: performing interpolation by combining the variation range of all node displacement data and a Build function, and drawing a color cloud picture on the current carrier rocket model;
according to R obtained in step 2.1maxValue determination model all node displacement value upper limit, using for determiningThe SetScalarRange function of the attribute data range corresponding to the color lookup table corresponds the upper and lower limits of the displacement value to the color lookup table in the step 4.3.1;
and then, performing interpolation calculation on the color corresponding to each node by using the build function and taking the displacement data of each node as attribute data, acquiring the color corresponding to each node, and drawing the color cloud picture on the current carrier rocket model.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810666476.7A CN108830000B (en) | 2018-06-26 | 2018-06-26 | VTK-based carrier rocket structure finite element analysis visualization method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810666476.7A CN108830000B (en) | 2018-06-26 | 2018-06-26 | VTK-based carrier rocket structure finite element analysis visualization method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108830000A CN108830000A (en) | 2018-11-16 |
| CN108830000B true CN108830000B (en) | 2022-03-15 |
Family
ID=64138743
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810666476.7A Active CN108830000B (en) | 2018-06-26 | 2018-06-26 | VTK-based carrier rocket structure finite element analysis visualization method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108830000B (en) |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109858189B (en) * | 2019-01-09 | 2023-03-31 | 蓝箭航天空间科技股份有限公司 | Carrier rocket load analysis method |
| CN110399692B (en) * | 2019-07-31 | 2021-01-15 | 大连理工大学 | Mode screening method of large-scale bundled rocket |
| CN113256791A (en) * | 2021-05-24 | 2021-08-13 | 南开大学 | Holographic augmented reality assisted human-computer interaction diagnosis and treatment system in surgical operation |
| CN113538687B (en) * | 2021-06-08 | 2024-06-14 | 广州颖力科技有限公司 | Finite element visualization method, system, device and storage medium based on VTK |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103455645A (en) * | 2012-05-31 | 2013-12-18 | 北京宇航系统工程研究所 | Overall-modal extraction method |
| CN105631066A (en) * | 2014-10-31 | 2016-06-01 | 北京临近空间飞行器系统工程研究所 | Modal test result-based finite element three-dimensional model modal adjusting method |
| CN106529055A (en) * | 2016-11-18 | 2017-03-22 | 南京航空航天大学 | Model updating method based on strain modal shape correlation |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8380473B2 (en) * | 2009-06-13 | 2013-02-19 | Eric T. Falangas | Method of modeling dynamic characteristics of a flight vehicle |
-
2018
- 2018-06-26 CN CN201810666476.7A patent/CN108830000B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103455645A (en) * | 2012-05-31 | 2013-12-18 | 北京宇航系统工程研究所 | Overall-modal extraction method |
| CN105631066A (en) * | 2014-10-31 | 2016-06-01 | 北京临近空间飞行器系统工程研究所 | Modal test result-based finite element three-dimensional model modal adjusting method |
| CN106529055A (en) * | 2016-11-18 | 2017-03-22 | 南京航空航天大学 | Model updating method based on strain modal shape correlation |
Non-Patent Citations (3)
| Title |
|---|
| Analysis and research about rocket aeroelasticity;Yun Li等;《 Proceedings of 2011 International Conference on Electronic & Mechanical Engineering and Information Technology》;20110919;第4220-4223页 * |
| 基于有限元的某多管火箭炮模态分析;徐立黄等;《弹箭与制导学报》;20110330;第30卷(第6期);第110-11、115页 * |
| 运载火箭动特性有限元模型修正技术研究;林宏等;《载人航天》;20111125;第17卷(第6期);第30-34、39页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN108830000A (en) | 2018-11-16 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108830000B (en) | VTK-based carrier rocket structure finite element analysis visualization method | |
| CN113593051A (en) | Live-action visualization method, dam visualization method and computer equipment | |
| Sakamoto et al. | KVS: A simple and effective framework for scientific visualization | |
| CN111639426A (en) | Wind characteristic space-time process visualization method | |
| Pang et al. | Fast rendering of diffusion curves with triangles | |
| US8446425B1 (en) | Object transformation for object trees utilized with multiprocessor systems | |
| Stahl et al. | Post-processing and visualization techniques for isogeometric analysis results | |
| Tian et al. | A survey of smooth vector graphics: Recent advances in representation, creation, rasterization and image vectorization | |
| Wang et al. | 3D-TSV: The 3D trajectory-based stress visualizer | |
| US9251548B1 (en) | Object transformation for object trees utilized with multiprocessor systems | |
| Shi et al. | Filling n-sided regions with G 1 triangular Coons B-spline patches | |
| KR20230167746A (en) | Method and system for generating polygon meshes approximating surfaces using root-finding and iteration for mesh vertex positions | |
| CN113434514B (en) | Voxelization index and output method of offshore oil and gas field point cloud model | |
| Mateo et al. | Hierarchical, Dense and Dynamic 3D Reconstruction Based on VDB Data Structure for Robotic Manipulation Tasks | |
| US8514247B1 (en) | Object trees for multiprocessor systems | |
| Panagiotidou et al. | From Intricate to Coarse and Back A voxel-based workflow to approximate high-res geometries for digital environmental simulations | |
| Romanyuk et al. | 3D vector fields visualization using graphics processing units | |
| Mao | Three-dimensional tree visualization of computer image data based on Louvain algorithm | |
| Aristizabal et al. | HARDWARE-ACCELERATED WEB VISUALIZATION OF VECTOR FIELDS-Case Study in Oceanic Currents | |
| CN116363329B (en) | Three-dimensional image generation method and system based on CGAN and LeNet-5 | |
| US11574444B1 (en) | Multi-characteristic remeshing for graphical objects | |
| CN116416409B (en) | Fluid simulation particle self-adaptive resolution surface reconstruction method and system | |
| Penev | Computer Graphics And Geometric Modelling–A Hybrid Approach | |
| CN114937110B (en) | GPU (graphics processing unit) -accelerated drainage wire modeling method, system, equipment and medium | |
| Hua et al. | Dynamic implicit solids with constraints for haptic sculpting |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |