A Discrete Element Method for Three-Dimensional Arbitrary Convex Polygonal Blocks Based on Distance Potential Function

Abstract

The invention discloses a three-dimensional random convex polygon block discrete element method based on a distance potential function. A research object is discretized into a block element system; carrying out contact detection on all block elements according to a nonuniform block discrete element contact detection method provided by the method; defining the distance potential function and carrying out normal contact force calculation on mutually contacting block elements, thereby obtaining normal contact force acting on each target block element and a torque caused by the normal contact force; on the basis of a tangential contact force direction vector calculation method provided by the method, carrying out calculation to obtain tangential contact force of each block element and the torque caused by the tangential contact force according to increment of tangential relative displacement; solving acceleration and angular acceleration of each block element through a rigid motion equation; and calculating velocity and displacement of each block element through a velocity verlet algorithm and describing deformation and motion state of a whole medium according to motion and relative position of each block element.

Description

technical field [0001] The invention relates to a block discrete element method, in particular to a three-dimensional arbitrary convex polygon block discrete element method based on a distance potential function, and belongs to the technical field of block discrete elements. Background technique [0002] The idea of ​​discrete element method originated from earlier molecular dynamics. In 1971, Professor Cundall P.A. of the United States first proposed a numerical analysis method for simulating the mechanical behavior of discontinuous media. This method divides the research object into a large number of discrete blocks (particles), and each block has a corresponding degree of freedom. Blocks interact with each other through contact force and moment, and apply appropriate force or displacement boundary conditions at the same time. Under the given initial conditions and external force, based on Newton's second law of motion and using the dynamic relaxation method showing time-...

AI Technical Summary

Problems solved by technology

[0006] The technical problem to be solved by the present invention is to provide a three-dimensional arbitrary convex polygon block discrete element method based on the distance potential function, solve the problem of contact force calculation of three-dimensional arbitrary convex polyhedral block discrete elements, and improve the deficiency of the finite discrete element method

The method of the invention solves the technical problems in the prior art that the unit size is uniform, the form is single, the calculation of the unit stiffness and contact force is affected by the unit form, the tangential contact force is not considered, and it cannot be applied to any polyhedral unit.

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