Base force element method of complementary energy principle for large rotation problems

Using the concept of the base forces, a new finite element method （base force element method, BFEM） based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM.

PLASTIC LIMIT ANALYSIS OF DUCTILE COMPOSITE STRUCTURES FROM MICRO-TO MACRO-MECHANICAL ANALYSIS

The load-bearing capacity of ductile composite structures comprised of periodic composites is studied by a combined micro/macromechanicai approach. Firstly, on the microscopic level, a representative volume element （RVE） is selected to reflect the microstructures of the composite materials and the constituents are assumed to be elastic perfectly-plastic. Based on the homogenization theory and the static limit theorem, an optimization formulation to directly calculate the macroscopic strength domain of the RVE is obtained. The finite element modeling of the static limit analysis is formulated as a nonlinear mathematical programming and solved by the sequential quadratic programming method, where the temperature parameter method is used to construct the self-stress field. Secondly, Hill＇s yield criterion is adopted to connect the micromechanicai and macromechanical analyses. And the limit loads of composite structures are worked out on the macroscopic scale. Finally, some examples and comparisons are shown.

Boundary element analysis for elastic and elastoplastic problems of 2D orthotropic media with stress concentration

Both the orthotropy and the stress concentration are common issues in modem structural engineering. This paper introduces the boundary element method （BEM） into the elastic and elastoplastic analyses for 2D orthotropic media with stress concentration. The discretized boundary element formulations are established, and the stress formulae as well as the fundamental solutions are derived in matrix notations. The numerical procedures are proposed to analyze both elastic and elastoplastic problems of 2D orthotropic me- dia with stress concentration. To obtain more precise stress values with fewer elements, the quadratic isoparametric element formulation is adopted in the boundary discretization and numerical procedures. Numerical examples show that there are significant stress concentrations and different elastoplastic behaviors in some orthotropic media, and some of the computational results are compared with other solutions. Good agreements are also observed, which demonstrates the efficiency and reliability of the present BEM in the stress concentration analysis for orthotropic media.

敦煌吐蕃医书所载毕吉伤药方考——从敦煌藏文医书所载毕吉疗伤方看拜占庭医药的东传

据藏史记载,拜占庭医学于公元7世纪传入藏区。拜占庭医师噶雷诺(Galenos)担任松赞干布的御医,其长子定居后藏,是西藏地方最早以"毕吉"为号的医师。8世纪,又有一位名为赞巴希拉哈(■,tsan-pa-shi-la-ha),号称毕吉(■,bi-ji)的拜占庭医师入藏。他编著了《毕吉黄函》(■,bi-jivi-po-ti-khaser,又名《御览光芒》■,rgyal-povi-bla-yig-vod-vbar),是藏医毕吉学派的开山文献。吐蕃时期,拜占庭医师的地位居于外来医师之首,对吐蕃医学发展贡献卓著。拜占庭医学和毕吉学派是吐蕃时期医学史研究的重要内容。在英藏敦煌藏文医书中,多处出现了毕吉[■(be-c?)或■(be-ci)]和毕吉疗伤药[■(be-ci’i-rma-rts?)或■(be-ci-rma-rtsi)],并记述了白色、红色和紫色三种疗伤方。这些记载虽不系统,但为藏医史的记载提供了佐证,对研究拜占庭医药东传的历史有重要意义。本文从ITJ756I和ITJ757号文书中引录相关的记载,做汉译和注释。联系藏医史和《毕吉黄函》进行论证,推定其为毕吉和毕吉疗伤方,并对拜占庭医药的东传及其影响做初步探讨。

Structural dynamic responses of a stripped solar sail subjected to solar radiation pressure

The stripped solar sail whose membrane is divided into separate narrow membrane strips is believed to have the best structural efficiency.In this paper,the stripped solar sail structure is regarded as an assembly made by connecting a number of boom-strip components in sequence.Considering the coupling effects between booms and membrane strips,an exact and semianalytical method to calculate structural dynamic responses of the stripped solar sail subjected to solar radiation pressure is established.The case study of a 100 m stripped solar sail shows that the stripped architecture helps to reduce the static deflections and amplitudes of the steady-state dynamic response.Larger prestress of the membrane strips will decrease stiffness of the sail and increase amplitudes of the steady-state dynamic response.Increasing thickness of the boom will benefit to stability of the sail and reduce the resonant amplitudes.This proposed semi-analytical method provides an efficient analysis tool for structure design and attitude control of the stripped solar sail.

STRENGTH PROPERTIES OF JOINTED ROCK MASSES BASED ON THE HOMOGENIZATION METHOD

This paper aims to determine the strength properties of jointed rock masses by means of the homogenization method. To reflect the microstructure of jointed rock masses, a representative element volume （REV） is selected. Assuming being rigid and perfectly plastic and utilizing the Mohr-Coulomb yield criterion for rock and joints, an upper bound limit analysis method is proposed based on the homogenization theory. By using the finite element method and Goodman joint element, a nonlinear mathematical programming with equality constraints is formulated, which can be solved by a direct iterative algorithm. Numerical results show the strength of jointed rock masses behaves anisotropy with different joint directions. This method presents an effective tool for the strength analysis of jointed rock masses.

Upper Bound Shakedown Analysis of Plates Utilizing the C^(1) Natural Element Method

This paper proposes a numerical solution method for upper bound shakedown analysis of perfectly elasto-plastic thin plates by employing the C^(1) natural element method.Based on the Koiter’s theorem and von Mises yield criterion,the nonlinear mathematical programming formulation for upper bound shakedown analysis of thin plates is established.In this formulation,the trail function of residual displacement increment is approximated by using the C^(1) shape functions,the plastic incompressibility condition is satisfied by introducing a constant matrix in the objective function,and the time integration is resolved by using the Konig’s technique.Meanwhile,the objective function is linearized by distinguishing the non-plastic integral points from the plastic integral points and revising the objective function and associated equality constraints at each iteration.Finally,the upper bound shakedown load multipliers of thin plates are obtained by direct iterative and monotone convergence processes.Several benchmark examples verify the good precision and fast convergence of this proposed method.

MODE III 2-D FRACTURE ANALYSIS BY THE SCALED BOUNDARY FINITE ELEMENT METHOD

The scaled boundary finite element method （SBFEM） is a novel semi-analytical technique that combines the advantages of the finite element method and the boundary element method with unique properties of its own. This method has proven very efficient and accurate for determining the stress intensity factors （SIFs） for mode I and mode II two-dimensional crack problems. One main reason is that the SBFEM has a unique capacity of analytically representing the stress singularities at the crack tip. In this paper the SBFEM is developed for mode III （out of plane deformation） two-dimensional fracture anMysis. In addition, cubic B-spline functions are employed in this paper for constructing the shape functions in the circumferential direction so that higher continuity between elements is obtained. Numerical examples are presented at the end to demonstrate the simplicity and accuracy of the present approach for mode Ⅲ two-dimensional fracture analysis.