采用显式有限元方法求解开放系统动力响应的主要环节和问题

Problems in numerical solution of complex open system by using explicit finite element method

分析了采用显式有限元方法求解开放系统动力响应的主要环节中影响精度和稳定性的因素及其相互关系,指出数值解的精度和稳定性是这些因素共同作用的结果。归纳了合理输入数字荷载应满足的条件以及系统离散化准则。基于有限元方法推导了吸收边界的一般表达式,并据此提出吸收边界和透射边界之间存在确定的函数关系,并不是两类独立人工边界的新见解。认为内域的阻尼稳定性和人工边界的近场稳定性是大型复杂开放系统动力响应数值方法研究和应用中的关键科学问题,并从应用的角度提出了解决问题的思路和看法。

Both factors and their interrelation affecting accuracy and stability of numerical solution of dynamic response of complex open system were studied by explicit finite element method, and it is concluded that accuracy and stability of numerical solution are results from the combined action of all factors. Both conditions demanded to be met in inputting numerical load and criterion of the open system discretization were summarized. The common expression for the absorbing boundary was derived based on the finite element method, and following new viewpoint is suggested: there is a function relationship, rather than independence, between absorbing boundary and transmitting boundary. It is suggested that both damping stability of inner domain and near-field stability of artificial boundary are key scientific problems in studying and applying of numerical solution for the dynamic response of largescale complex open system, and some new opinions of answering the purpose of practical engineering application are suggested.