频域有限元计算的扩展面向目标误差估计

Goal-Oriented Error Estimation Applied to Direct Solution of Steady-State Analysis With Frequency Domain Finite Element Method

研究了针对频域有限元直接动态分析的面向目标误差估计以及误差范围估计计算方法.面向目标的误差估计方法就是专门针对如何准确和经济地估算特定值误差的一种方法,利用原问题的共轭偶问题进行计算.频域有限元的直接动态分析是模拟频域扫描实验的一种计算方法,专门针对谐振激励的线性动态响应问题,利用将原自由度分解为实部和虚部描述频率的变化,从而计算变形体的动态响应.利用扩展针对有限元的面向目标误差估计的自由度,将该方法应用到直接动态分析中进行误差估计.通过建立同时包含实部和虚部自由度的能量弱形式及偶问题,并将其数值实现,估算频域直接动态分析有限元解的误差及误差范围,并通过悬臂梁的激振算例进行了验证.

Based on the concept of constitutive relation error along with residual of both origin and dual problems,a goal-oriented error estimation method with extended degrees of freedom was developed.It leads to the high quality local error bounds in the problem of direct-solution steady-state dynamic analysis with frequency domain finite element,which involves enrichments with plural variable basis functions.The solution of steady-state dynamic procedure calculated the harmonic response directly in terms of the physical degrees of freedom in the model,which used mass,damping,and stiffness matrices of the system.An enriched form of goal-oriented error estimation aiming at this frequency calculation was formed and implemented.A three dimensional finite element example was carried out to illustrate the computational procedures.