力学系与湍流国家重点实验室学术报告3.19( 报告人： Prof. Jiun-Shyan (JS) Chen)
发布时间: 2010-03-16 10:43:00
SEMINAR SERIES
北京大学工学院 ![]()
力学与空天技术系
力学与空天技术系 湍流与复杂系统国家重点实验室
报告题目
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1. Galerkin and Collocation Meshfree Methods: From Continuum to Quantum |
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2. Multiscale Modeling in Biomechanics |
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3. Multiscale Modeling in Mechanics and Materials |
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报告人 Prof. Jiun-Shyan (JS) Chen |
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Chancellor's Professor, Professor & Chair, Civil & Environmental Engineering Department, UCLA |
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主持人：袁明武 教授 |
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时 间：3月19日（周五）下午2:30 |
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地 点：力学楼434会议室 |
欢迎广大师生光临！
报告内容摘要：
报告一:
Mechanics at different length scales exhibit diverse characteristics that require proper regularity in the construction of numerical formulation. Strong and weak discontinuities, topological change in geometry, and singularities are a few examples that render difficulty in the construction of approximation functions with desirable regularity in solving mechanics problems at different length scales. We first review a few finite element and meshfree approximation methods to address these issues. Through three classes of problems at continuum macro-scale, meso-scale, and quantum-scale, we demonstrate the convergence properties of Galerkin meshfree approach and how it can be constructed to alleviate the numerical difficulties associated with the standard finite element methods. The examples include large deformation and fragment impact problems, modeling of microstructure evolution, and solution of Schrodinger equation in quantum mechanics. We then discuss the possibility of introducing meshfree approximation under the strong form collocation framework, including the local moving least squares reproducing kernel and the nonlocal radial basis collocation methods. We show how to combine the advantages of radial basis function and reproducing kernel function to yield a local approximation that is better conditioned than that of the radial basis collocation method, while at the same time offers a higher rate of convergence than that of Galerkin type reproducing kernel method.
报告二:
In this presentation, challenges and issues in computational biomechanics are first addressed, and several mathematical and computational methods for multiscale modeling of biological systems from atomistic and continuum scales are presented. We first introduce wavelet based multisale method that does not require periodicity a priori. We propose a multiscale coarse graining method and multilevel homogenization formulation for numerical simulation of DNA subjected to complex forms of deformation. We develop wavelet-based multiscale formulation for the first level homogenization of potential function for representation of superatoms. Based on superatom molecular structures, we introduce the second level homogenization by constructing an equivalent continuum strain energy density function of the DNA to yield a continuum hyperelastic multi-scale beam formulation for continuum modeling of DNA molecules. The effectiveness of the proposed methods is validated by comparing the predicted DNA stretching load-displacement curves, DNA loop formation mechanisms, DNA-repressor interactions, and DNA translocation through a nanopore. Another major issue in computational biology is the complexity in constructing good quality finite element mesh from medical images. We introduce an image-based discretization method based on Reproducing Kernel approximation and level set functions. The application to modeling of skeletal muscles further demonstrates that the bridging of continuum mechanics and chemical kinetic laws is essential in understanding the passive and active behavior in many biological systems. In this example we also show how computational mechanics can help provide answers to some of the long standing puzzles in muscle mechanics.
报告三:
In this presentation, multi-scale computational methods for continuum mechanics are first introduced. In particular, the “reproducing kernel” and the “wavelet” based multi-scale numerical methods as well as an energy based consistent asymptotic expansion formulation will be presented. Methods for bridging physics on different scales and the corresponding computational techniques for solving coupled problems will then be discussed. Model problems include coupling of coarse and fine scale responses in continua, bridging of continuum and meso scales, multi-scale wavelet projection method for continuum-meso and molecular structures, and adaptive partition of unity method in quantum calculation. Several examples will be given to demonstrate the proposed multi-scale methods. This include modeling of damage and fragment processes, grain structure evolution in polycrystalline materials, wrinkling formation in sheet metals, coupling of meso-scale dislocation and continuum mechanics, and multiscale approach for quantum mechanics.
报告人简介：
J. S. Chen received PhD from Northwestern University in 1989. He is now the Chancellor’s Professor & Department Chair of Civil & Environmental Engineering Department at UCLA. He is also Professor of Mechanical & Aerospace Engineering Department and Professor of Mathematics Department at UCLA. He is the Vice President (July 2008 - June 2010) and President elect (July 2010 – June 2012) of US Association for Computational Mechanics. His research activities include development of finite element and meshfree methods for large deformation and contact mechanics, multiscale materials modeling, computational biomechanics, and computational quantum mechanics. He has received numerous awards, including GenCorp Technology Achievement Award, The Faculty Scholar Award, UCLA Chancellor’s Professor Endowed Chair, Fellow of US Association for Computational Mechanics, Fellow of International Association for Computational Mechanics, Outstanding Alumnus of National Central University, Taiwan, etc. He is the Editor-in-Chief of Interactional and Multiscale Mechanics, and is serving as Associate Editor or on Editorial Board of 8 other international journals. Three of his papers have been cited for more than 100 times (ISI).