中文摘要：

提出了一种利用光顺有限元方法计算弹性问题位移线性泛函输出的上下界方法。线性泛函输出的上下界计算基于原偏微分方程和其对偶偏微分方程的全局误差界，全局误差界的计算在泛函输出的上下界计算中起着重要的作用。光顺有限元方法的一个重要特性就是能够计算结构应变能的上界，因此结合一般有限元方法计算结构应变能的下界。给出了一种计算线性输出精确解上下界的方法，并给出了算例。

英文摘要：

An approach for computing the lower and upper bounds to the outputs that are linear functionals of displacements in elasticity with smoothed finite element method is presented. The general formulation of the lower and upper bounds to the linear functionals is based on the global error bounds in both the primal and the dual problems, the global error bounds play a major role in the output bounds solutions. The smoothed finite element method has an important characteristic property - bounding the strain energy of structure from above. Thus, with finite element method, which is bounding the strain energy from below, we can give a new solution method for computing the lower and upper bounds to the linear outputs. The algorithm is verified with examples in the end of the paper.