THE ANALYTICAL SOLUTIONS BASED ON THE CONCEPT OF FINITE ELEMENT METHODS

On the basis of the concept of finite element methods, the rigorous analytical solutions of structural response in terms of the design variables are researched in this paper. The spatial trusses are taken as an example for the solution of the analytical expressions of the explicit displacements which are proved mathematically; then some conclusions are reached that are useful to structural sensitivity analysis and optimization. In the third part of the paper, a generalized geometric programming method is sugguested for the optimal model with the explicit displacement. Finally, the analytical solutions of the displacements of three trusses are given as examples.

A three-dimensional Eulerian method for the numerical simulation of high-velocity impact problems

In the present paper, a three-dimensional （3D） Eulerian technique for the 3D numerical simulation of high-velocity impact problems is proposed. In the Eulerian framework, a complete 3D conservation element and solution element scheme for conservative hyperbolic governing equations with source terms is given. A modified ghost fluid method is proposed for the treatment of the boundary conditions. Numerical simulations of the Taylor bar problem and the ricochet phenomenon of a sphere impacting a plate target at an angle of 60~ are carried out. The numerical results are in good agreement with the corresponding experimental observations. It is proved that our computational technique is feasible for analyzing 3D high-velocity impact problems.

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.

Modeling the Earth's magnetosphere under the influence of solar wind with due northward IMF by the AMR-CESE-MHD model

We present a newly developed global magnetohydrodynamic(MHD) model to study the responses of the Earth's magnetosphere to the solar wind. The model is established by using the space-time conservation element and solution element(CESE) method in general curvilinear coordinates on a six-component grid system. As a preliminary study, this paper is to present the model's numerical results of the quasi-steady state and the dynamics of the Earth's magnetosphere under steady solar wind flow with due northward interplanetary magnetic field(IMF). The model results are found to be in good agreement with those published by other numerical magnetospheric models.