Shaofan Li

Bio: Shaofan Li is an academic researcher from University of California, Berkeley. The author has contributed to research in topics: Finite element method & Peridynamics. The author has an hindex of 50, co-authored 261 publications receiving 9630 citations. Previous affiliations of Shaofan Li include Northwestern University & Harbin Engineering University.

Meshfree and particle methods and their applications

Abstract: Recent developments of meshfree and particle methods and their applications in applied mechanics are surveyed. Three major methodologies have been reviewed. First, smoothed particle hydrodynamics ~SPH! is discussed as a representative of a non-local kernel, strong form collocation approach. Second, mesh-free Galerkin methods, which have been an active research area in recent years, are reviewed. Third, some applications of molecular dynamics ~MD! in applied mechanics are discussed. The emphases of this survey are placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics. This review article includes 397 references. @DOI: 10.1115/1.1431547#

Reproducing kernel particle methods for structural dynamics

Abstract: This paper explores a Reproducing Kernel Particle Method (RKPM) which incorporates several attractive features. The emphasis is away from classical mesh generated elements in favour of a mesh free system which only requires a set of nodes or particles in space. Using a Gaussian function or a cubic spline function, flexible window functions are implemented to provide refinement in the solution process. It also creates the ability to analyse a specific frequency range in dynamic problems reducing the computer time required. This advantage is achieved through an increase in the critical time step when the frequency range is low and a large window is used. The stability of the window function as well as the critical time step formula are investigated to provide insight into RKPMs. The predictions of the theories are confirmed through numerical experiments by performing reconstructions of given functions and solving elastic and elastic–plastic one-dimensional (1-D) bar problems for both small and large deformation as well as three 2-D large deformation non-linear elastic problems. Numerical and theoretical results show the proposed reproducing kernel interpolation functions satisfy the consistency conditions and the critical time step prediction; furthermore, the RKPM provides better stability than Smooth Particle Hydrodynamics (SPH) methods. In contrast with what has been reported in SPH literature, we do not find any tensile instability with RKPMs.

Swelling of Graphene Oxide Membranes in Aqueous Solution: Characterization of Interlayer Spacing and Insight into Water Transport Mechanisms

Abstract: Graphene oxide (GO) has recently emerged as a promising 2D nanomaterial to make high-performance membranes for important applications However, the aqueous-phase separation capability of a layer-stacked GO membrane can be significantly limited by its natural tendency to swell, that is, absorb water into the GO channel and form an enlarged interlayer spacing (d-spacing) In this study, the d-spacing of a GO membrane in an aqueous environment was experimentally characterized using an integrated quartz crystal microbalance with dissipation and ellipsometry This method can accurately quantify a d-spacing in liquid and well beyond the typical measurement limit of ∼2 nm Molecular simulations were conducted to fundamentally understand the structure and mobility of water in the GO channel, and a theoretical model was developed to predict the d-spacing It was found that, as a dry GO membrane was soaked in water, it initially maintained a d-spacing of 076 nm, and water molecules in the GO channel formed a semio

Meshfree Particle Methods

Abstract: Meshfree Particle Methods is a comprehensive and systematic exposition of particle methods, meshfree Galerkin and partitition of unity methods, molecular dynamics methods, and multiscale methods Most theories, computational formulations, and simulation results presented are recent developments in meshfree methods They were either just published recently or even have not been published yet, many of them resulting from the authors own research The presentation of the technical content is heuristic and explanatory with a balance between mathematical rigor and engineering practice It can be used as a graduate textbook or a comprehensive source for researchers, providing the state-of-the art on Meshfree Particle Methods

Fast parallel algorithms for short-range molecular dynamics

Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Pattern Recognition and Machine Learning

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Reproducing kernel particle methods

Abstract: A new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time-frequency and space-wave number localization of a window function is developed. This method is motivated by the theory of wavelets and also has the desirable attributes of the recently proposed smooth particle hydrodynamics (SPH) methods, moving least squares methods (MLSM), diffuse element methods (DEM) and element-free Galerkin methods (EFGM). The proposed method maintains the advantages of the free Lagrange or SPH methods; however, because of the addition of a correction function, it gives much more accurate results. Therefore it is called the reproducing kernel particle method (RKPM). In computer implementation RKPM is shown to be more efficient than DEM and EFGM. Moreover, if the window function is C∞, the solution and its derivatives are also C∞ in the entire domain. Theoretical analysis and numerical experiments on the 1D diffusion equation reveal the stability conditions and the effect of the dilation parameter on the unusually high convergence rates of the proposed method. Two-dimensional examples of advection-diffusion equations and compressible Euler equations are also presented together with 2D multiple-scale decompositions.