CAJ | 학술논문

基于瞬时变分原理，应用乘积型二元三次B样条函数，建立了弹性地基板的样条动力方程.引入样条参数及其对时间的导数作为状态变量，导出了状态方程.对空间域，采用样条元法；对时间域，采用现代控制论中的状态空间法.此外，建立了一种状态变量的递推计算格式，可以直接计算出动力响应量.文末给出若干数值算例，计算结果表明本文方法的计算精度与效率是令人满意的.
기우순시변분원리，응용승적형이원삼차B양조함수，건립료탄성지기판적양조동력방정.인입양조삼수급기대시간적도수작위상태변량，도출료상태방정.대공간역，채용양조원법；대시간역，채용현대공제론중적상태공간법.차외，건립료일충상태변량적체추계산격식，가이직접계산출동력향응량.문말급출약간수치산례，계산결과표명본문방법적계산정도여효솔시령인만의적.
Based on the instantaneous variational principle and the cubic B spline functions, the spline dynamicequation for plates on elastic foundation was established. The spline parameters and their derivatives with re-spect to time were taken as state variables, and the state space equation was derived. The spline finite elementprocedure was used in space domain and the state space technique was used in time domain. In addition, astate space recursive scheme was developed,so that the dynamic responses can be calculated directly. The nu-merical results were presented to show the accuracy and efficiency of this method.