Quasistaticity
A problem for the evolution in time of some system is said to have a quasistatic approximation if the velocity and acceleration are neglected. These derivatives can usually be neglected if they have coefficients mat are small parameters. For example, in the buckling of an elastic structure under the action of a load, the equilibrium states can be characterized by a bifurcation diagram showing solution pairs (λ,u) consisting of a load parameter λ and some magnitude u of the solution. The stability of the structure is often interpreted by assuming that the solution pairs move along a branch of solutions as the load parameter increases slowly with time, In this case, the system is reckoned to undergo a quasistatic motion in which it moves through a family of equilibrium states parametrized by time or by the load treated as increasing with time.For such problems, formal asymptotic methods might accurately exhibit the detailed effects of the small parameters. Rigorous asymptotic justifications, which provide error estimates and are typically far harder to carry out, are used by those compulsive about mathematical hygiene, but often do not say more that the formal methods.The purpose of mis lecture is to give rigorous justifications of the quasistatic behavior of solutions of the differential equations governing a couple of conceptually simple problems from particle and continuum mechanics. The justification for making these justifications is that the solutions of these simple problems exhibit strange and surprising behavior.
Stuart S. Amman
Department of Mathematics, Institute for Physical Science and Technology, and Institute for Systems Research,University of Maryland, College Park, Maryland 20742-4015, USA
国际会议
The 5th International Conference on Nonlinear Mechanics(第五届国际非线性力学会议)
上海
英文
1-3
2007-06-11（万方平台首次上网日期，不代表论文的发表时间）