复变量重构核粒子法与有限元法耦合解弹性力学问题

提出了弹性力学的复变量重构核粒子法与有限元法的耦合法(CVRKPM/FEM).采用场量耦合试函数法将弹性力学的复变量重构核粒子法与有限元法进行耦合,详细推导了在整个求解域上的耦合公式.最后通过数值算例证实了本文所提弹性力学的复变量重构核粒子法与有限元的耦合法的有效性.本文的耦合法不仅可以很方便地施加本质边界条件,而且可以充分利用无网格方法和有限元法的优势,弥补各自不足以提高计算效率.     

无限粘弹介质中圆孔时变问题的解析分析

本文推导粘弹介质中圆孔孔径时变时的应力和位移.由粘弹解与弹性解的对应关系得到粘弹时变应力解.用直接解方程法求径向位移,最终归结为求解关于待定函数的l阶非齐次微分方程.将半径时变函数泰勒展开,用幂级数解法得到一般情况下的解.在寻找定解条件时,采用了对待定函数的光滑化处理,认为在t=0的微小邻域内函数仍满足微分方程,通过积分得到与待定系数数目相同的定解条件,从而获得本问题径向位移解析解.对Maxwell粘弹模型的求解证明了该法的可靠性.文中解适用于任意粘弹模型和孔径任意时变的情况.     

蜻蜓翅膀的力学研究进展

本文对蜻蜓翅膀的力学问题研究进展进行了综述.蜻蜓之所以成为自然界最优秀的飞行者之一,是因为其翅膀的特殊结构.翅结和翅痣的作用,是在飞行中平衡翅膀前后两部分和消除翅膀振颤.常用的翅膀模型有四种:概念模型、物理模型、简单分析模型和数值分析模型.其中前三种模型过于简化,数值模型虽然可以进行三维数值模拟,但是忽略了翅膀的材料组成.本文还分析了蜻蜓翅膀的飞行机制和力学特点,认为蜻蜓的飞行力学分析必须考虑非定常流的影响;介绍了翅膀的弹性模量、硬度和抗弯刚度的测量方法,指出翼展方向的抗弯刚度(EI)与翼展长度的三次方(L3)成正比,翼弦方向的抗弯刚度(EI)与翼弦长度的平方(D2)成正比;最后提出了对蜻蜓翅膀力学的研究展望和有待于进一步解决的问题.     

A novel virtual node method for polygonal elements

A novel polygonal finite element method （PFEM） based on partition of unity is proposed, termed the virtual node method （VNM）. To test the performance of the present method, numerical examples are given for solid mechanics problems. With a polynomial form, the VNM achieves better results than those of traditional PFEMs, including the Wachspress method and the mean value method in standard patch tests. Compared with the standard triangular FEM, the VNM can achieve better accuracy. With the ability to construct shape functions on polygonal elements, the VNM provides greater flexibility in mesh generation. Therefore, several fracture problems are studied to demonstrate the potential implementation. With the advantage of the VNM, the convenient refinement and remeshing strategy are applied.     

Numerical simulation of solid tumor angiogenesis with Endostatin treatment： a combined analysis of inhibiting effect of anti-angiogenic factor and micro mechanical environment of extracellular matrix

To investigate the influence of anti-angiogenesis drug Endostatin on solid tumor angiogenesis, a mathematical model of tumor angiogenesis was developed with combined influences of local extra-cellular matrix mechanical environment, and the inhibiting effects of Angiostatin and Endostatin. Simulation results show that Angiostatin and Endostatin can effectively inhibit the process of tumor angiogenesis, and decrease the number of blood vessels in the tumor. The present model could be used as a valid theoretical method in the investigation of anti-angiogenic therapy of tumors.     

Study on magneto–elastic–plastic deformation characteristics of ferromagnetic rectangular plate with simple supports

In this paper, the magnetic-elastic-plastic deformation behavior is studied for a ferromagnetic plate with simple supports. The perturbation formula of magnetic force is first derived based on the perturbation technique, and is then applied to the analysis of deformation characteristics with emphasis laid on the analyses of modes, symmetry of deformation and influences of incident angle of applied magnetic field on the plate deformation. The theoretical analyses offer explanations why the configuration offer- romagnetic rectangular plate with simple supports under an oblique magnetic field is in-wavy type along the x-direction, and why the largest deformation of the ferromagnetic plate occurs at the incident angle of 45°for the magnetic field. A numerical code based on the finite element method is developed to simulate quantitatively behaviors of the nonlinearly coupled multi-field problem. Some characteristic curves are plotted to illustrate the magneto--elastic-plastic deflections, and to reveal how the deflections can be influenced by the incident angle of applied magnetic field. The deformation characteristics obtained from the numerical simulations are found in good agreement with the theoretical analyses.     

Tuning of band gaps for a two-dimensional piezoelectric phononic crystal with a rectangular lattice

In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic-electric coupling. The generalized eigenvalue equation is obtained by the relation of the mechanic and electric fields as well as the Bloch-Floquet theorem. The band structures of both the in-plane and anti-plane modes are calculated for a rectangular lattice by the planewave expansion method. The effects of the lattice constant ratio and the piezoelectricity with different filling fractions are analyzed. The results show that the largest gap width is not always obtained for a square lattice. In some situations, a rectangular lattice may generate larger gaps. The band gap characteristics are influenced obviously by the piezoelectricity with the larger lattice constant ratios and the filling fractions.     

第四届全国环境力学研讨会简介

由于社会与经济可持续发展的重要需求,近年来环境力学研究得到迅速发展,成为力学学科一个新的重要生长点.     

序

2009年4月3日,中国科学院力学研究所、中国工程物理研究院、中国科学技术大学、中国空气动力学研究与发展中心、中国航天空气动力技术研究院、总参工程兵三所和中国力学学会联合举办纪念郭永怀先生百年诞辰暨学术报告会.郭永怀先生是中国近代力学事业的奠基人之一.他不仅参与了中国20世纪五六十年代的力学学科规划,支持和规划近代力学大型实验装置的战略布局,并身体力行地倡导了高速空气动力学、磁流体力学和爆炸力学等新兴学科,培养青年力学人才.