An analysis of 2D piezoelectric half-plane with a fixed conductor surface

Solutions to a piezoelectric half-plane with a fixed conductor surface electrode subjected to two generalized singularities (line dislocation and/or line force and free charge) are presented. Coulomb forces acting on the singularities due to the boundary polarization charges of medium and the induction charges of conductor electrode are analyzed in detail. The interaction between the two singularities is also analyzed numerically. Results show that Coulomb forces will become important as the free charge approaches the boundary or two singularities move closely. Project supported by the National Science Foundation of China (No. 10172036).     

Switched processes generalized mandelbrot sets for complex index number

IntroductionTheMsetgeneratedfromthecomplexmapzz2 +cinthecomplexC_planehasbeenwidelystudiedintherecenttwentyyearsandtheintricateregularstructurehiddeninithasbeenfound ,whichenrichesgreatlythefractaltheory[1].In 1 987and 1 991 ,LakhtakiaandGujar,etal.,respectively ,discussedthegeneralizedMsetsfromthecomplexmappingzza +c(α∈R1)andpresentedseveralconjecturesaboutthevisualstructurecharacteristicsofthegeneralizedMsets[2 ,3].Onthebasisoftheabovefindings,theauthorhastheoreticallyanalyzedthestr…     

Effect of microstructure on the hardening and softening behaviors of polycrystalline shape memory alloys Part II: Numerical simulation under axisymmetrical loading

Based on the microstructure-based constitutive model established in Part I, a detailed numerical investigation on the role of each microstructure parameter in the kinematical and kinetic evolution of polycrystalline SMA under axisymmetrical tension loading is performed. Some macroscopic constitutive features of stress-induced martensite transformation are discussed. The subject supported by the Research Grant Committee (RGC) of Hong Kong SAR, the National Natural Science Foundation of China and the Provincial Natural Science Foundation of Jiangxi Province of China     

Perturbation of symmetries of Birkhoff system and adiabatic invariants

The perturbation of symmetries of the free Birkhoff system under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of adiabatic invariants and the conditions for their existence are given. Then these results are generalized to the constrained Birkhoff system. One example is presented to illustrate these results. The project supported by the National Natural Science Foundation (19972010) and the Doctoral Program Foundation of Institution of Higher Education of China and the Natural Science Foundation of Henan Province     

Nonstationary effects on safe basins of a forced softening Duffing oscillator

The safe basin of a forced softening Duffing oscillator is studied numerically. The changes of safe basins are observed under both stationary and nonstationary variations of the external excitation frequency. The kind of nonstationary variations of the excitation frequency can greatly change the erosion rate and the shape of the safe basin. The other effects of nonstationary variations on the safe basin are also discussed. Supported by the National Natural Science Foundation, the Aviation Science Foundation and the Doctoral Training Foundation of China.     

MAXIMAL ELEMENTS FOR GB-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

A new family of set-valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set-valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature. Contributed by DING Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province of China ([2000]25) Biography: DING Xie-ping (1938∼)     

On the generalized PLK method and its applications

In this paper, we propose a generalized form of the PLK method. To solve weakly nonlinear problems, in straining the related coordinates, we choose a kind of transformations including nonlinear functionals of dependent variables to linearize asymptotically the original problems, and give more perfect asymptotic solutions with the first-term approximation and the derived transformations. The analysis for some practical examples shows that the generalized method is straightforward and effective and might be applied to more complicated nonlinear problems. To the memory of the late Professor Kuo Yung-huai for the 80th anniversary of his birth. The project is supported by the National Natural Science Foundation of China.     

Conservation laws and symmetries of systems with unilateral constraints in phase space

By introducing the generalized quasi-symmetry of the infinitestinal transformation for transformation groupG _r , this paper studies the conservation laws and symmetries of dynamical systems with unilateral constraints in phase space. Noether's theorem and Noether's inverse theorem for mechanical systems with unilateral constraints in phase space are obtained and two kinds of equivalent forms of generalized Killing equations which are used to determine the generators of the infinitestinmal group transformation are given. The project sponsored by the National Natural Science Foundation and the Doctoral Programme Foundation of Institution of Higher Education of China.     

Application of the quadrilateral area coordinate method： a new element for laminated composite plate bending problems

Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate (QAC) method. Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion. In this paper, a new displacement-based, 4-node 20-DOF (5-DOF per node) quadrilateral bending element based on the first-order shear deformation theory for analysis of arbitrary laminated composite plates is presented. Its bending part is based on the element AC-MQ4, a recent-developed high-performance Mindlin-Reissner plate element formulated by QAC method and the generalized conforming condition method; and its in-plane displacement fields are interpolated by bilinear shape functions in isoparametric coordinates. Furthermore, the hybrid post-processing procedure, which was firstly proposed by the authors, is employed again to improve the stress solutions, especially for the transverse shear stresses. The resulting element, denoted as AC-MQ4-LC, exhibits excellent performance in all linear static and dynamic numerical examples. It demonstrates again that the QAC method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models. The project is supported by the National Natural Science Foundation of China (10502028), the Special Foundation for the Authors of the Nationwide (China) Excellent Doctoral Dissertation (200242), and the Science Research Foundation of China Agricultural University (2004016).