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Material information mapping method for material point method for large deformation response of structure

An information mapping and material point technology, which is applied in the material information mapping field of the material point method, achieves the effect of overcoming the shortcomings of complex interpolation algorithms, avoiding the complexity of solving algorithms, and avoiding the non-conservation of mass and momentum

Active Publication Date: 2019-11-15
JIANGXI UNIV OF SCI & TECH
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0005] Aiming at the deficiencies of the prior art, the present invention provides a material information mapping method for the material point method used for the large deformation response of the structure. The momentum and mass of the background grid nodes are conserved, which can effectively eliminate the grid crossing error of the material point method when solving the large deformation problem of the structure, and improve the solution accuracy of the material point method to analyze the dynamic response of the large deformation of the structure

Method used

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  • Material information mapping method for material point method for large deformation response of structure
  • Material information mapping method for material point method for large deformation response of structure
  • Material information mapping method for material point method for large deformation response of structure

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Embodiment 1

[0025] A material information mapping method for the material point method of the large deformation response of the structure, comprising the following steps:

[0026] Step 1. Based on the discrete problem domain of Lagrangian material points, initialize the material information of each material point such as mass, momentum, density, stress-strain, and deformation gradient; at the same time, arrange a set of regular Euler-type background grids to realize The solution of the governing equation and the interaction and connection between each material point;

[0027] Step 2. Determine the current volume domain of each material point through the deformation gradient of the material point;

[0028] At time t, the volume domain of material point p can be expressed as:

[0029]

[0030] in: is the deformation gradient of material point p at time t; and Respectively represent the volume domain of the material point p at the initial time and time t.

[0031] Step 3. Determin...

Embodiment 2

[0076] This embodiment takes a one-dimensional rod as an example to specifically illustrate the application of the method of the present invention;

[0077] Such as image 3 As shown, a one-dimensional rod with initial velocity and fixed at both ends will produce a dynamic response along the axial direction due to the effect of the initial velocity. Utilize the material point method and the present invention to analyze the vibration response of this one-dimensional rod respectively, and the calculation parameters are selected as follows: modulus of elasticity E=50Pa, density ρ=25kg / m 3 , model length L=1m, v 0 =0.1m / s, the grid size is 6.25mm, 4 material points are arranged in each background grid, and the time step is 0.5μs. Figure 4 The distribution of displacement and stress along the rod axis and the corresponding L 2 error.

Embodiment 3

[0079] This embodiment takes a two-dimensional free beam as an example to specifically illustrate the application of the method of the present invention;

[0080] Such as Figure 5 As shown, a straight beam with constant section with length L=0.06m and height H=0.01m, where point a is the center point of the beam, the elastic modulus of the beam is E=318GPa, density ρ=1845kg / m3, Poisson’s ratio v= 0.054. At the initial moment t=0, each point in the beam is distributed with a first-order free beam bending vibration modal velocity; when t>0, the beam vibrates in a free state, respectively using the material point method and the present invention for this two-dimensional free beam The vibration response is simulated, where the background grid size is dx=dy=6.25×10 -4 m, time step dt=0.001 μs, and 4×4 material points are arranged in each grid. Figure 6 The normal stress contour of the beam in the x direction calculated by the material point method and the present invention is ...

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Abstract

The invention provides a material information mapping method of a material point method for large deformation response of a structure. The material information mapping method comprises the following steps: establishing a topological relation between a material point volume domain and a background grid by tracking the change of the material point volume domain in the large deformation process of the structure; dividing the volume domain of the material point into a plurality of volume sub-domains by the background grid node, respectively arranging virtual mapping material points in the centersof the volume sub-domains of the material point, and directly determining the material information on the virtual mapping material points by the material information on the material points; and mapping of mass, momentum, physical strength, surface force, stress and other material information of the background grid nodes is realized based on the virtual mapping material points. The material information mapping method can accurately give the material point method, can effectively eliminate the grid crossing error of the material point method when solving the large deformation problem of the structure, and solves a problem that the solving precision of the material point method is not high enough when solving the large deformation dynamic response of the structure.

Description

technical field [0001] The invention relates to the technical field of structural dynamics, in particular to a material information mapping method of a material point method used for large deformation responses of structures. Background technique [0002] The material point method is a particle-type gridless algorithm, which consists of a series of Lagrangian material points to discretely solve the domain, and uses the Euler background grid to cover the entire solution domain; among them, the material points carry all the material information of the material, It includes historical variables such as position, velocity, momentum, stress and strain, and moves with the movement of objects; the linear interpolation shape function in the finite element method is used to realize the information exchange between each material point and the background grid node, and then the information is exchanged on the background grid. The solution of spatial derivatives and governing equations ...

Claims

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Application Information

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IPC IPC(8): G06F17/50
CPCY02T90/00
Inventor 孙政周晓敏
Owner JIANGXI UNIV OF SCI & TECH
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