CN112733415B - Non-grid processing method and device for thin-wall elastomer boundary, terminal equipment and computing medium - Google Patents

Non-grid processing method and device for thin-wall elastomer boundary, terminal equipment and computing medium Download PDF

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CN112733415B
CN112733415B CN202110050997.1A CN202110050997A CN112733415B CN 112733415 B CN112733415 B CN 112733415B CN 202110050997 A CN202110050997 A CN 202110050997A CN 112733415 B CN112733415 B CN 112733415B
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刘勇
陈永焜
方辉
刘晓
王心玉
李爱军
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Abstract

The invention provides a method and a device for processing a boundary of a thin-wall elastomer without grids, terminal equipment and a computing medium. The method comprises the steps of splitting zero-order elastomer particles into multi-level elastomer particles, and acquiring acting force of fluid particles on the split elastomer particles; in the coupling process of the fluid particles and the elastomer particles, the zero-order elastomer particles always serve as boundaries of the fluid particles, so that the fluid particles are partitioned, the relation between each partitioned fluid particle and the zero-order elastomer particle is established, and the movement of the thin-wall elastomer is simulated. The invention can obviously improve the calculation efficiency and save the calculation cost.

Description

Non-grid processing method and device for thin-wall elastomer boundary, terminal equipment and computing medium
Technical Field
The invention belongs to the technical field of elastomer boundary non-grid processing, and relates to a thin-wall elastomer boundary non-grid processing method, a thin-wall elastomer boundary non-grid processing device, terminal equipment and a computing medium.
Background
With the development and utilization of marine resources by human beings, the application of ultra-large floating structures in the sea draws more and more attention. Such structures have less bending stiffness and greater structural deformation in waves due to the very large ratio of span (length, width) to height (thickness); in hydro-elastic analysis, such structures are often assumed to be thin-walled elastomeric boundaries. In recent years, with the continuous maturity of computational fluid dynamics numerical simulation technology and the continuous improvement of accuracy and reliability, numerical simulation gradually becomes an effective means for analyzing the interaction between waves and ocean structures. The smooth particle hydrodynamic method (SPH), an emerging latticeless particle method in the form of lagrange, was originally used to solve the problem of celestial physics in three-dimensional open spaces and has now been applied to ocean engineering. Compared with the traditional grid-based numerical algorithm, the SPH method has great advantages in solving the problem of large deformation of water bodies and structures due to the particle property and the Lagrangian property. The SPH method is therefore well suited to analyze water elasticity problems. However, the SPH method can only be used to process thin-walled elastomer boundaries by increasing the particle resolution, which is too computationally expensive.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method and a device for processing the boundary of a thin-wall elastic body without a grid, terminal equipment and a computing medium, which can obviously improve the computing efficiency and save the computing cost.
The present invention achieves the above-described object by the following technical means.
A method for processing the boundary of a thin-wall elastomer without a grid comprises the steps of establishing a numerical wave water tank, arranging fluid particles in a fluid area, and arranging elastomer particles in the thin-wall elastomer; splitting the zero-order elastomer particles into first-order elastomer particles or further splitting the first-order elastomer particles into highest-order elastomer particles, and obtaining the pressure of the split elastomer particles to obtain the acting force of the fluid particles on the split elastomer particles; in the coupling process of the fluid particles and the elastomer particles, the zero-order elastomer particles always serve as the boundaries of the fluid particles, so that the fluid particles are partitioned, the relationship between each partitioned fluid particle and the zero-order elastomer particle is established, and the motion of the thin-wall elastomer is simulated.
Further, the zero-order elastomer particles are split into first-order elastomer particles, and the pressure of the first-order elastomer particles is as follows:
Figure BDA0002899036960000011
wherein: p is a radical ofjIs the pressure of the fluid particles and,
Figure BDA0002899036960000012
is the value of the nuclear function between the fluid particle and the first-order elastomer particle, VjIs the volume of the fluid particles,
Figure BDA0002899036960000021
indicating the smooth core length of the first order elastomer particles.
Further, the pressure of the highest order elastomer particles is:
Figure BDA0002899036960000022
wherein k represents the grade number of the elastomer particles, l is the distance between the k-grade elastomer particles and the k-1-grade elastomer particles in the direction of the gravitational acceleration g, and rhoWater (W)Is the density of water.
Furthermore, the force of the fluid particles on the elastomer particles after the splitting includes a force of the fluid particles on the first-stage elastomer particles and a force of the fluid particles on the highest-stage elastomer particles, and the forces of the fluid particles on the first-stage elastomer particles are as follows:
Figure BDA0002899036960000023
wherein p isiPressure of zero-order elastomer particles, ViIs the volume of the zero-order elastomer particles,
Figure BDA0002899036960000024
derivative of zero-order elastomer particles, WijIs the value of the nuclear function between the zero-order elastomer particle and the fluid particle, ViVolume of zero order elastomer particles;
the acting force of the fluid particles on the highest-level elastomer particles is as follows:
Figure BDA0002899036960000025
further, in the coupling process of the fluid particles and the elastomer particles, the motion mode of the highest-order elastomer particles is obtained by the following formula:
Figure BDA0002899036960000026
in the formula uaRepresenting the velocity of a certain highest order elastomer particle, g is the gravitational acceleration vector,
Figure BDA0002899036960000027
is the density of the structured particles, PaAnd PbIs the first Piola-Kirchhoff stress tensor,
Figure BDA0002899036960000028
representing the derivative, W, for the initial particle distribution0abIs the initial value of the kernel function between the highest order elastomer particles a and the highest order elastomer particles b, V0bThe initial volume of the highest order elastomer particles b.
Further, the fluid particle partitioning is achieved by: in initially arranging the elastomer particles, the elastomer structure surface particles are identified, then the outer normal vector of the elastomer surface particles is calculated at each time step, a sector area is made by the outer normal vector, and the fluid particles in the sector area are searched.
A thin-walled elastomeric boundary meshless processing device, comprising:
the model building module is used for building a numerical wave water tank;
the elastomer particle splitting module is used for splitting the zero-order elastomer particles into first-order elastomer particles or further splitting the first-order elastomer particles to obtain highest-order elastomer particles;
the highest-level elastomer particle motion mode acquisition module is used for acquiring the motion mode of the highest-level elastomer particles;
the simulation thin-wall elastomer motion module is used for realizing the coupling of fluid particles and elastomer particles: and partitioning the fluid particles, establishing a relation between each partitioned fluid particle and a zero-order elastomer particle, and simulating the movement of the thin-wall elastomer.
A computer device comprising a processor and a memory;
the memory is used for storing a computer program;
the processor is used for executing the computer program and realizing the mesh-free processing method of the thin-wall elastic body boundary when the computer program is executed.
A computer-readable storage medium, in which a computer program is stored, which, when executed by a processor, causes the processor to carry out the above-mentioned method of meshless processing of thin-walled elastomeric boundaries.
The invention has the beneficial effects that: the zero-order elastomer particles are split into first-order elastomer particles or further split into highest-order elastomer particles, the acting force of the fluid particles on the highest-order elastomer particles and the movement mode of the highest-order elastomer particles are obtained, and all the elastomer particles move along with the highest-order elastomer particles; in the coupling process of the fluid particles and the elastomer particles, the fluid particles are partitioned, the relation between each partitioned fluid particle and the zero-order elastomer particle is established, and the movement of the thin-wall elastomer is simulated. The invention obviously reduces the calculation amount when the SPH method is used for processing the boundary of the thin-wall elastic body, improves the calculation efficiency and saves the calculation cost.
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FIG. 1 is a diagram of the mode of elastomer particle fragmentation according to the present invention;
FIG. 2 is a schematic illustration of the elastomer particles of the present invention breaking into secondary elastomer particles;
FIG. 3 is a graph of the relationship between the zoned fluid particles and zero-order elastomer particles according to the present invention;
FIG. 4 is a schematic diagram of the fluid particle acquisition process of the present invention;
FIG. 5 is a schematic view of a numerical water tank employed in the present invention;
FIG. 6 is a graph of the numerical simulation results of the present invention when t is 0.361 s;
FIG. 7 is a graph of the result of the fluid zone partitioning when t is 0.361s according to the present invention;
fig. 8 is an enlarged view of the circled portion of fig. 6 and 7.
Detailed Description
The invention will be further described with reference to the following figures and specific examples, but the scope of the invention is not limited thereto.
A method for processing the boundary of a thin-wall elastomer without grids specifically comprises the following steps:
step (1), a numerical wave water tank is established, fluid particles are arranged in a fluid area, and elastomer particles are arranged in a thin-wall elastomer in the water tank, wherein the size of the elastomer particles is the same as that of the fluid particles.
Step (2), one elastomer particle i (called zero-order elastomer particle) is split into 4 first-order elastomer particles, marked as i, in the manner shown in FIG. 1j(j ═ 1, 2, 3, 4); where Δ x is the initial spacing of the zero-order elastomer particles.
In order to ensure the conservation of mass, the initial value of the physical quantity of the newly generated first-stage elastomer particles is determined as follows:
Figure BDA0002899036960000041
Figure BDA0002899036960000042
Figure BDA0002899036960000043
wherein: m represents the particle mass, ρ represents the particle density, and h represents the smooth core length.
The pressure of the first stage elastomer particles is obtained from the interpolation of the fluid by:
Figure BDA0002899036960000044
wherein: p is a radical ofjIs the pressure of the fluid particles and,
Figure BDA0002899036960000045
is the value of the nuclear function between the fluid particle and the first-order elastomer particle, VjIs the volume of the fluid particles.
In thin-walled elastomers, if smooth lengths of fluid particles are used, the fluid particles must be partitioned, and for simplicity, the smooth core length of the first-order elastomer particles is used.
When the first stage elastomer particles acquire density and pressure, the calculation of the force of the fluid particles on the first stage elastomer particles is started. In the prior art, the formula for calculating the acting force of the fluid particles on the first-stage elastomer particles is as follows:
Figure BDA0002899036960000046
wherein: p is a radical ofiPressure of zero-order elastomer particles, WijDenotes the value of the nuclear function, V, between the zero-order elastomer particle and the fluid particleiIs the volume of the zero-order elastomer particles,
Figure BDA0002899036960000047
the derivative of the zero order elastomer particles is shown.
To solve this problem, equation (5) is modified according to step (3) because thin-walled elastomers do not apply to equation (5) and the first-order elastomer particles and the fluid particles have different smooth core radii, so that equation (5) cannot be directly applied to the calculation.
And (3) changing the formula (5) into a formula (6) according to a Lagrange function, and calculating the acting force of the fluid particles on the first-stage elastomer particles:
Figure BDA0002899036960000048
the smooth length of the first-order elastomer sub-particles being that of the fluid particles
Figure BDA0002899036960000049
Thus, only if the fluid particles are in contact with the first-order projectile is regulatedWhen the somatic particles influence each other, equation (6) can be applied.
A step (4) of splitting the first-order elastomer particles into second-order elastomer particles (see fig. 2) or higher-order splits, the specific process being the same as the way of splitting the first-order elastomer particles, the main difference being in the interpolation method; during the splitting of the first-order elastomer particles, the pressure and density of the first-order elastomer particles are calculated (the relationship between the density ρ and the pressure, p, is B)2(ρWater (W)-ρWater 0) B is the bulk modulus of water, rhoWater 0Is the initial density of water, pWater (W)Is the current density of water) is interpolated from the fluid by a smooth kernel whose smooth length is the first order elastomer particle; calculating the acting force of the fluid particles on the first-stage elastomer particles and using a smooth kernel function with the smooth length being the first-stage elastomer particles; wherein the smooth length of the first-stage elastomer particles is the smooth length of the fluid particles
Figure BDA0002899036960000051
If the pressure of the multistage elastomer particles is calculated by the equation (4), the smooth length of the n-stage elastomer particles is equal to that of the fluid particles
Figure BDA0002899036960000052
This rapidly reduces the number of fluid particles in the support domain of the n-stage elastomer particles, resulting in a reduction in calculation accuracy. To avoid this, the pressure of the multistage elastomer particles and the force of the fluid particles on the multistage elastomer particles in this embodiment are obtained by the following interpolation method:
Figure BDA0002899036960000053
Figure BDA0002899036960000054
wherein k represents the number of elastomer particles, and l represents the number of elastomer particles and the number of elastomers in k-1 orderDistance, rho, of particles in the direction of gravitational acceleration gWater (W)Is the density of water.
And (5) calculating the following constitutive equation of the highest-level elastomer particles according to the split elastomer particles obtained in the step (4), wherein the constitutive equation (generalized Hooke's law) of the elastomer particles is as follows, wherein a and b represent two highest-level elastomer particles:
Figure BDA0002899036960000055
in the formula uaRepresenting the velocity of a certain highest order elastomer particle, g is the gravitational acceleration vector,
Figure BDA0002899036960000056
in order to be able to determine the density of the structured particles,
Figure BDA0002899036960000057
representing the derivative, W, for the initial particle distribution0abIs the initial value of the kernel function between the highest order elastomer particles a and the highest order elastomer particles b, V0bIs the initial volume of the highest elastomer particle b, PaAnd PbFor the first Piola-Kirchoff stress tensor, P can be solved by the following equation:
P＝FS (10)
Figure BDA0002899036960000058
Figure BDA0002899036960000059
Figure BDA0002899036960000061
Figure BDA0002899036960000062
wherein F is a deformation tensor, S is a Piola-Kirchoff stress tensor of the second type, K is a volume modulus, G is a shear modulus, I is an identity matrix, E represents a Green-Lagrange strain tensor, X represents the position of the particle at the current moment, M is an intermediate quantity, and X represents the position of the particle at the initial moment; the shear modulus G is obtained by generalized hooke's law E ═ 2G (1+2 ν) ═ 3K (1-2 ν), where E denotes young's modulus and ν denotes poisson's ratio, both of which can be obtained by laboratory measurements.
Step (6), all the elastomer particles move along with the highest-level elastomer particles, that is, all the elastomer particles except the highest-level elastomer particles obtain movement information through the highest-level elastomer particles, and in order to ensure the regularity of the zero-level elastomer particle arrangement, the embodiment uses a shepard interpolation mode in a complete lagrange form to characterize the movement process:
Figure BDA0002899036960000063
wherein:
Figure BDA0002899036960000064
denotes the velocity, u, of any elastomer particle except the highest elastomer particlemRepresenting the velocity of any highest order elastomer particle,
Figure BDA0002899036960000065
is the initial value of the kernel function between any elastomer particle and any highest order elastomer particle,
Figure BDA0002899036960000066
is a smooth core length of any elastomer particle, V0mIs the initial volume of any highest order elastomer particle.
Step (7), in the coupling process of the fluid particles and the elastomer particles, the zero-order elastomer particles always serve as the boundaries of the fluid particles; the zero-order elastomer particles belong to a thin-wall structure, so that the fluid particles need to be partitioned, and then the motion of the thin-wall elastomer is simulated; as shown in FIG. 3, A-BP, B-BP and C-BP represent three types of zero-order elastomer particles, and A-BP obtains fluid information from interpolation in the first region and only interacts with the fluid particles in the first region; B-BP obtains fluid information from interpolation in the second region and only interacts with fluid particles in the second region; C-BP obtains fluid information by interpolation from the first region, the second region and the third region, and interacts with fluid particles in the first region, the second region and the third region; the fluid particles in region one and region two do not interact.
Partitioning is mainly realized by the following modes: in initially arranging the elastomer particles, the elastomer surface particles are first identified, then the outer normal vector of the elastomer surface particles is calculated at each time step, and then a sector area is made by the outer normal vector, as shown in fig. 4, and the fluid particles in the sector area are searched. The method for calculating the external normal vector n of the surface particles t of the elastic body is as follows:
Figure BDA0002899036960000067
wherein: intermediate volume
Figure BDA0002899036960000071
Intermediate volume
Figure BDA0002899036960000072
r represents the position of the particle, WqValue of the nuclear function of any elastomer particle, VqIs the volume of any elastomer particle.
Through the process, the simulation of the thin-wall elastic body structure boundary in the non-grid method is realized, and the calculation cost is saved.
In this example, a numerical water tank as shown in fig. 5 was selected to test the non-grid processing method of the present invention, and the young's modulus E of the thin-walled elastomer was 5.8 × 106The poisson ratio ν is 0.4, the thickness of the thin-walled elastomer is 0.032m, and Δ x is 0.008 m. Fig. 6 shows the simulation results when t is 0.361s, and fig. 7 shows tFig. 8 shows the calculation result of the outer normal vector of the elastomer structure surface particle at the circled portion of fig. 6 and 7, which is the result of the fluid particle partition at 0.361 s.
A non-grid processing device for the boundary of a thin-wall elastomer comprises a model establishing module, an elastomer particle splitting module, a highest-level elastomer particle motion mode acquiring module and a thin-wall elastomer motion simulation module;
the model building module is used for building a numerical wave water tank and arranging fluid particles and elastomer particles;
the elastomer particle splitting module is used for splitting the zero-order elastomer particles into first-order elastomer particles or splitting the first-order elastomer particles into second-order elastomer particles until the first-order elastomer particles are split into the highest-order elastomer particles;
the highest-level elastomer particle motion mode acquisition module is used for acquiring the motion mode of the highest-level elastomer particles, and all the elastomer particles move along with the highest-level elastomer particles;
the simulation thin-wall elastomer motion module is used for realizing the coupling of fluid particles and elastomer particles: and partitioning the fluid particles, establishing a relation between each partitioned fluid particle and a zero-order elastomer particle, and simulating the movement of the thin-wall elastomer.
The above-mentioned mesh-free processing means of the thin-walled elastomer boundary may be implemented in the form of a computer program which can be run on a computer device, which may be a server or a terminal. The server can be an independent server or a server cluster; the terminal can be an electronic device such as a mobile phone, a tablet computer, a notebook computer, a desktop computer, a personal digital assistant and a wearable device.
The computer device comprises a processor, a memory and a network interface which are connected through a system bus, wherein the memory can comprise a nonvolatile storage medium and an internal memory; the non-volatile storage medium may store an operating system and a computer program. The computer program includes program instructions that, when executed, cause a processor to perform any one of the methods for meshless processing of thin-walled elastomeric boundaries. The processor is used for providing calculation and control capability and supporting the operation of the whole computer equipment. The memory provides an environment for execution of a computer program in a non-volatile storage medium, which when executed by the processor, causes the processor to perform any of the thin-walled elastomer boundary mesh-free processing methods. The network interface is used for network communication, such as sending assigned tasks.
It should be understood that the Processor may be a Central Processing Unit (CPU), and the Processor may be other general purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs) or other Programmable logic devices, discrete Gate or transistor logic devices, discrete hardware components, etc. Wherein a general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The embodiment of the application also provides a computer readable storage medium, the computer readable storage medium stores a computer program, the computer program comprises program instructions, and the processor executes the program instructions to realize the mesh-free processing method of the thin-wall elastic body boundary.
The computer-readable storage medium may be an internal storage unit of the computer device described in the foregoing embodiment, for example, a hard disk or a memory of the computer device. The computer readable storage medium may also be an external storage device of the computer device, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), and the like provided on the computer device.
The present invention is not limited to the above-described embodiments, and any obvious improvements, substitutions or modifications can be made by those skilled in the art without departing from the spirit of the present invention.

Claims (4)

1. A non-grid processing method for the boundary of a thin-wall elastomer is characterized in that a numerical wave water tank is established, fluid particles are arranged in a fluid area, and elastomer particles are arranged in the thin-wall elastomer; splitting the zero-order elastomer particles into first-order elastomer particles or further splitting the first-order elastomer particles into highest-order elastomer particles, and obtaining the pressure of the split elastomer particles to obtain the acting force of the fluid particles on the split elastomer particles; in the coupling process of the fluid particles and the elastomer particles, the zero-order elastomer particles always serve as the boundaries of the fluid particles, so that the fluid particles are partitioned, the relationship between each partitioned fluid particle and the zero-order elastomer particle is established, and the motion of the thin-wall elastomer is simulated;
the zero-order elastomer particles are split into first-order elastomer particles, and the pressure of the first-order elastomer particles is as follows:
Figure FDA0003612317250000011
wherein: p is a radical ofjIs the pressure of the fluid particles and,
Figure FDA0003612317250000012
is the value of the nuclear function between the fluid particle and the first-order elastomer particle, VjIs the volume of the fluid particles,
Figure FDA0003612317250000013
represents the smooth core length of the first order elastomer particles;
the pressure of the highest-order elastomer particles is as follows:
Figure FDA0003612317250000014
wherein k represents the grade number of the elastomer particles, l is the distance between the k-grade elastomer particles and the k-1-grade elastomer particles in the direction of the gravitational acceleration g, and rhoWater (W)Is the density of water;
the acting force of the fluid particles on the elastomer particles after the splitting comprises the acting force of the fluid particles on the first-stage elastomer particles and the acting force of the fluid particles on the highest-stage elastomer particles, and the acting force of the fluid particles on the first-stage elastomer particles is as follows:
Figure FDA0003612317250000015
wherein p isiPressure of zero-order elastomer particles, ViIs the volume of the zero-order elastomer particles,
Figure FDA0003612317250000016
derivative of zero-order elastomer particles, WijIs the value of the nuclear function between the zero-order elastomer particle and the fluid particle, ViVolume of zero order elastomer particles;
the acting force of the fluid particles on the highest-level elastomer particles is as follows:
Figure FDA0003612317250000017
in the coupling process of the fluid particles and the elastomer particles, the motion mode of the highest-level elastomer particles is obtained by the following formula:
Figure FDA0003612317250000018
in the formula uaRepresenting the velocity of a certain highest order elastomer particle, g is the gravitational acceleration vector,
Figure FDA0003612317250000019
is the density of the structured particles, PaAnd PbIs the first Piola-Kirchoff stress tensor, W0abIs the initial value of the kernel function between the highest order elastomer particles a and the highest order elastomer particles b, V0bIs the initial volume of the highest order elastomer particles b;
the fluid particle partition is realized by the following modes: in initially arranging the elastomer particles, the elastomer structure surface particles are identified, then the outer normal vector of the elastomer surface particles is calculated at each time step, a sector area is made by the outer normal vector, and the fluid particles in the sector area are searched.
2. An apparatus based on the method for non-grid processing of the thin-wall elastomer boundary of claim 1, comprising:
the model building module is used for building a numerical wave water tank;
the elastomer particle splitting module is used for splitting the zero-order elastomer particles into first-order elastomer particles or further splitting the first-order elastomer particles to obtain highest-order elastomer particles;
the highest-level elastomer particle motion mode acquisition module is used for acquiring the motion mode of the highest-level elastomer particles;
the simulation thin-wall elastomer motion module is used for realizing the coupling of fluid particles and elastomer particles: and partitioning the fluid particles, establishing a relation between each partitioned fluid particle and a zero-order elastomer particle, and simulating the movement of the thin-wall elastomer.
3. A computer device comprising a processor and a memory;
the memory is used for storing a computer program;
the processor configured to execute the computer program and when executing the computer program to implement the gridless processing method of the thin-walled elastomeric boundary of claim 1.
4. A computer-readable storage medium, wherein the computer-readable storage medium stores a computer program that, when executed by a processor, causes the processor to implement the method for meshless processing of thin-walled elastomeric boundaries of claim 1.
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