Smoothed Particle Galerkin Formulation for Simulating Physical Behaviors in Solids Mechanics

摘要

Methods and systems for conducting numerical simulation of structural behaviors in solid mechanics using smoothed particle Galerkin formulation are disclosed. A meshfree model representing a physical domain defined by a plurality of particles is received in a computer system. Each particle is configured for material properties of portion of the physical domain it represents. A smoothed displacement field of the physical domain subject to defined boundary condition is obtained by conducting a time-marching simulation using the meshfree model based on smoothed particle Galerkin formulation. The smoothed displacement field is derived from a set of smoothed meshfree shape functions that satisfies linear polynomial reproduction condition. The set of smoothed meshfree shape functions is constructed by convex meshfree approximation scheme and configured to avoid calculation second order derivatives. The set of smoothed meshfree shape functions is a combination of regular meshfree shape function and a displacement smoothing function for the particles.

主权项

1. A method of obtaining a smoothed displacement field of a physical domain based on smoothed particle Galerkin formulation in solid mechanics, the method comprising:
receiving, in a computer system having an application module installed thereon, a meshfree model representing a physical domain, the meshfree model including a plurality of particles, each configured for material properties of a portion of the physical domain, and a set of boundary conditions defined on the physical domain's border, wherein the application module is configured to perform a time-marching simulation based on smoothed particle Galerkin formulation; and obtaining, by the application module, a numerically-simulated smoothed displacement field of the physical domain subject to the set of boundary conditions by conducting the time-marching simulation using the meshfree model, the smoothed displacement field being derived from a set of smoothed meshfree shape functions that satisfies linear polynomial reproduction condition, wherein the set of smoothed meshfree shape functions, constructed by a convex meshfree approximation scheme and configured to avoid calculating second-order derivatives, is created with a combination of a set of regular meshfree shape functions and a set of displacement smoothing functions for the plurality of particles.