CN114065599A - 'key type' near field dynamics method based on 'particle pair' integral form - Google Patents
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Abstract
The invention belongs to the technical field of numerical simulation based on a non-grid method, and particularly relates to a key-type near field dynamics method based on a particle pair integration form. Aiming at the problem domain, the target object is dispersed into a plurality of object points with a certain volume; performing neighborhood particle search on discrete material points in a certain near field domain, and forming ordered 'particle pairs' of all the material points and the material points in the neighborhood; performing particle energy density integral solution through a particle pair action mode, and performing surface correction on the reduction of material rigidity caused by near field domain truncation; finally, within the time integration cycle, the near field force solution is performed in the form of 'particle pairs'. The method is based on the key-type near-field dynamics method, the traditional neighborhood particle full-pairing mode is replaced by the particle pair mode to carry out near-field force solution, the problem of computing repeatability of the traditional method is solved, and the effects of reducing the calculated amount, obviously improving the computing efficiency and reducing the time cost are achieved.
Description
Technical Field
The invention belongs to the technical field of numerical simulation based on a non-grid method, and particularly relates to a key-type near field dynamics method based on a particle pair integration form.
Background
As a non-grid method, the near-field dynamics method has natural method advantages in crack propagation and fracture damage treatment, and is widely applied to rock and soil, sea ice, ceramics and other materials. At present, the numerical calculation by using a 'bond type' near field dynamics method mainly comprises the following steps: first, the object is discretized into a volume of several object points, each of which is represented by a point located in the center of the volume. After dispersing the solid material, performing neighborhood substance point search on the dispersed substance points in a certain near field area, and recording neighborhood sea ice substance points corresponding to each substance point one by one. And then, performing material surface correction on the reduction of the rigidity of the material due to the truncation of the near field domain. Finally, a time integration cycle is performed, and the near field dynamics equation is solved based on the dynamic state or the static state.
At present, because the 'key type' near field dynamics method meets the angular momentum conservation, the force density of object points is equal in magnitude and opposite in direction. Therefore, when performing neighborhood material point integral calculation on a discrete material point, all material points in the neighborhood are calculated one by one based on the material point number, and the process has almost half of repeated calculation and influences the execution efficiency of subsequent material strain energy density, surface correction and near field force calculation at each time step. In the numerical solving process of the near-field dynamics method, the calculation time of the near-field force integral at each time step is large, and the time consumption is huge when large-scale calculation is carried out. Therefore, a method for overcoming the problem of calculation repeatability of the method is urgently sought.
Disclosure of Invention
The invention aims to provide a 'bond type' near field dynamics method based on a 'particle pair' integration form.
A method of "bond-type" near field dynamics based on a form of "particle pair" integration, comprising the steps of:
step 1: aiming at the problem domain, dispersing a target object into a plurality of substance points with a certain volume, wherein parameters such as volume, position, speed and the like of each substance point are carried by a point positioned in the center of the volume;
step 2: neighborhood substance point searching is carried out on the discrete substance points in a certain near field domain, and the neighborhood particle searching process is stored in a 'particle pair' form; for a material point with a certain number, considering that the mutual near-field forces of two material points are equal in magnitude and opposite in direction, all material points with a larger number are required to be traversed in the neighborhood from small to large in sequence, and the material points with the smaller number are not required to be repeated, so that the material points with the number and the material points in the neighborhood form a particle pair, and the information of all the material points and the neighborhood material points is stored;
and step 3: performing particle energy density integral solution in a particle pair mode, and performing surface correction on reduction of material rigidity and the like caused by truncation of a near field region;
and 4, step 4: carrying out time integration, and solving a near field dynamics equation based on dynamic or static state; during the time integration cycle, the near-field force solution is carried out in the form of 'particle pair', and it is noted that the force directions of the two end point object particles of the 'particle pair' are opposite.
The invention has the beneficial effects that:
aiming at the problem domain, the target object is dispersed into a plurality of object points with a certain volume; after dispersion, neighborhood particle search is carried out on discrete material points in a certain near field area, a central material point and neighborhood material points with numbers larger than that of the central material point are paired and numbered in a particle pair mode, material point numbers at two ends of the particle pair are recorded at the same time, the material points with numbers smaller than that of the particle pair in the neighborhood do not need to be repeatedly paired, finally, all the material points and the material points in the neighborhood form ordered particle pairs, and all the material points and neighborhood material point information are stored; on the basis, the particle density integral solving is carried out through a particle pair action mode, and the surface correction is carried out on the reduction of the rigidity of the material caused by the truncation of the near field area. Finally, within the time integration cycle, the near field force solution is performed in the form of 'particle pairs'. The method is based on the key-type near-field dynamics method, the traditional neighborhood particle full-pairing mode is replaced by the particle pair mode to carry out near-field force solution, the calculation repeatability problem of the traditional method is solved only by simply changing the calculation program of the traditional method, and the effects of reducing the calculation amount, obviously improving the calculation efficiency and reducing the time cost are achieved.
Drawings
Fig. 1(a) is a schematic view of load application of a square column uniaxial compression calculation model in an embodiment of the present invention.
Fig. 1(b) is a schematic diagram of a square column uniaxial compression model of the sea ice material after the dispersion in the embodiment of the invention.
FIG. 2 is a schematic diagram of the object particles in the center i +3 and i +4 regions to be searched and integrated (conventional method).
FIG. 3 is a schematic diagram of the "particle pair" pair of the center particle point i +3 to be calculated (in "particle pair" form).
FIG. 4 is a schematic diagram of the "particle pair" pair of the center particle point i +4 to be calculated (in "particle pair" form).
FIG. 5 is a graph comparing the two methods for calculating the behavior of the square prism uniaxial compression process.
FIG. 6 is a graph showing the time consumption of two methods for calculating the total number of particles of different substances at 10000 time steps for square column uniaxial compression.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The invention aims to solve the problem that a 'bond type' near field dynamics method is repeatedly calculated in the process of performing neighborhood substance point integration on discrete substance points, and provides a 'bond type' near field dynamics method based on which the substance point strain energy density integration and the substance point near field force integration solution in each time step are performed in a 'particle pair' mode instead of the traditional neighborhood particle full-pairing mode. Compared with the traditional method, the method can achieve the aims of reducing the calculated amount, improving the calculation efficiency and saving the time cost when carrying out numerical simulation based on the key type near field dynamics method.
The purpose of the invention is realized as follows:
And 2, after the object is dispersed, performing neighborhood material point search on the dispersed material points in a certain near field area, wherein the neighborhood particle search process is stored in a 'particle pair' form, and for a material point with a certain number, considering that the mutual near field forces of the two material points are equal in magnitude and opposite in direction, only all the material points with the number larger than that of the material point are required to be sequentially traversed from small to large in the neighborhood, and the material points with the number smaller than that of the material point are not required to be duplicated. The numbered material points and material points in their neighborhood will form individual "particle pairs" that store information about all material points and their neighborhood.
The difference here from the traditional "bond-type" near-field dynamics approach is: the neighborhood particle searching process is stored in a 'particle pair' mode, for a certain number of object particles, considering that the mutual near-field forces of the two object particles are equal in magnitude and opposite in direction, all the object particles with the numbers larger than that of the object particles are required to be sequentially traversed from small to large in the neighborhood, and the object particles with the numbers smaller than that of the object particles are not required to be duplicated. The material points of the number and the material points in the neighborhood of the material points form a particle pair, and the particle pair established after the searching stores the information of all the material points and the material points in the neighborhood.
And 3, performing particle energy density integral solving through a particle pair form, and performing surface correction on reduction of material rigidity and the like caused by truncation of a near field region. Since the above is recorded based on the form of "particle pair", the surface correction is also performed in this section by the form of "particle pair", so that the repetitive calculation can be effectively avoided and the calculation amount can be reduced.
And 4, carrying out time integration, and solving a near field dynamics equation based on dynamic or static. During the time integration cycle, the near-field force solution is carried out in the form of 'particle pair', and it is noted that the force directions of the two end point object particles of the 'particle pair' are opposite.
According to the method, neighborhood particle search is stored in a 'particle pair' form in a 'key type' near field dynamics method framework, and the problem of repeated calculation of neighborhood particles in the process of performing strain energy density and near field force integral calculation in the traditional 'key type' near field dynamics method is solved. The invention performs strain energy density calculations in the form of "particle pairs" in the framework of a "bond-type" near-field dynamics method. Near-field force calculations are performed in the time integral in the form of "particle pairs" in the "bond-type" near-field dynamics method framework.
The invention relates to a method for storing a neighborhood particle search process in a 'particle pair' form in a 'bond type' near field dynamics method framework, and performing material point strain energy density integration and material point near field force integration in each time step in the 'particle pair' form. The method is provided for overcoming the problem that a large amount of repeated calculation exists in the neighborhood particle integration calculation process in the traditional 'key type' near field dynamics method. Firstly, the method is used for dispersing a target object into a plurality of object points with a certain volume aiming at a problem domain; after dispersion, neighborhood particle search is carried out on the dispersed material points in a certain near field area, and considering that the mutual near field forces of the two material points are equal in magnitude and opposite in direction, the material points at the center and the neighborhood material points with the numbers larger than that of the material points are only required to be paired and numbered in a 'particle pair' mode, and the material points at the two ends of the 'particle pair' are recorded at the same time, so that the material points with the numbers smaller than that of the material points in the neighborhood are not required to be repeatedly paired. Finally, all the material points and the material points in the neighborhood of the material points form an ordered 'particle pair', and the particle pair stores the information of all the material points and the neighborhood material points. On the basis, the particle density integral solving is carried out through a particle pair action mode, and the surface correction is carried out on the reduction of the rigidity of the material caused by the truncation of the near field area. Finally, within the time integration cycle, the near field force solution is performed in the form of 'particle pairs'. The method is based on a 'key type' near field dynamics method, the traditional neighborhood particle full-pairing mode is replaced by a 'particle pair' mode to carry out near field force solution, the calculation repeatability problem of the traditional method is solved only by simply changing on the basis of the calculation program of the traditional method, and the effects of reducing the calculation amount, obviously improving the calculation efficiency and reducing the time cost are achieved.
Example 1:
the technical implementation method of the invention is described in detail by taking square column uniaxial compression as an example, and the detailed steps are as follows:
And 2, after a plurality of sea ice substance points are formed, searching the sea ice substance points in a certain near field area for neighborhood substance points. The neighborhood particle action mode of the traditional 'key type' near field dynamics method in its neighborhood is solved by integrating the central particle with its neighborhood particle one by one, as shown in fig. 2. The key-type near field dynamics method of the ' particle pair ' action mode adopted by the invention is to store the particle pair ' mode in the neighborhood particle searching process, for a certain numbered material point, all sea ice material points with larger numbers are traversed in the neighborhood from small to large in sequence, and the sea ice material points with smaller numbers are not required to be re-compounded, as shown in fig. 3 and 4. All sea ice material points and sea ice materials with numbers larger than the sea ice material points in the neighborhood are established into a particle pair, so that the problem of repeated calculation in the neighborhood search of the traditional 'key type' near field dynamics method is effectively solved.
And 3, performing particle energy density integral solving in a particle pair mode, and performing surface correction on the reduction of the rigidity and the like of the sea ice material caused by the truncation of the near field region. Since the above is based on the form of "particle pair", this part is also surface-corrected by the form of "particle pair". The surface correction is performed for X, Y, Z three directions one by one for the "particle pair" number pair.
And 4, in the time integration cycle process, solving the near field force by adopting a particle pair mode aiming at the solving of the near field force, wherein the directions of the particle pair and the particle force of the two end points are opposite.
When the method is used for searching the neighborhood particles, the method stores the neighborhood particles by adopting a particle pair mode, and uses the particle pair in the whole process of numerical integration calculation of a key type near field dynamics method. Compared with the traditional method, the method has the advantages that the calculation amount and the calculation speed are obviously improved, and the time cost is reduced. Taking the uniaxial compression of a square column as an example, under the same working condition, numerical simulation is carried out by adopting a particle pair integration mode, and the calculation efficiency is improved by nearly one time. Under the same calculation condition, a 'key type' near field dynamics-based method is developed in a 'particle pair' mode, so that large-scale calculation domain simulation can be realized.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (1)
1. A method of "bond-type" near field dynamics based on a form of "particle pair" integration, comprising the steps of:
step 1: aiming at the problem domain, dispersing a target object into a plurality of substance points with a certain volume, wherein parameters such as volume, position, speed and the like of each substance point are carried by a point positioned in the center of the volume;
step 2: neighborhood substance point searching is carried out on the discrete substance points in a certain near field domain, and the neighborhood particle searching process is stored in a 'particle pair' form; for a material point with a certain number, considering that the mutual near-field forces of two material points are equal in magnitude and opposite in direction, all material points with a larger number are required to be traversed in the neighborhood from small to large in sequence, and the material points with the smaller number are not required to be repeated, so that the material points with the number and the material points in the neighborhood form a particle pair, and the information of all the material points and the neighborhood material points is stored;
and step 3: performing particle energy density integral solution in a particle pair mode, and performing surface correction on reduction of material rigidity and the like caused by truncation of a near field region;
and 4, step 4: carrying out time integration, and solving a near field dynamics equation based on dynamic or static state; during the time integration cycle, the near-field force solution is carried out in the form of 'particle pair', and it is noted that the force directions of the two end point object particles of the 'particle pair' are opposite.
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