通过带有三角函数的高斯积分的求解，提出了一系列描述载荷不确定性的均值函数，给出了柔顺度期望和方差的精确解析公式，并且用数值算例验证了该方法的快速准确性。利用所导出的解析公式，求解以柔顺度期望为目标的稳健性拓扑优化问题，获得了典型设计实例的构型设计。设计结果表明考虑载荷大小和方向的不确定性对于结构拓扑优化的结果有较为显著的影响，也验证了解析公式的正确性和拓扑优化模型的有效性。(By solving the Gauss integral with trigonometric functions, a series of mean functions describing the load uncertainty are proposed, and the exact analytical formulas for compliance expectation and variance are given. Numerical examples are given to illustrate the accuracy and accuracy of the method. By using the derived analytical formula, a robust topology optimization problem with the objective of flexibility expectation is solved, and the configuration design of a typical design example is obtained. The design results show that the uncertainty of the load size and direction has a significant impact on the results of structural topology optimization, and the correctness of the analytical formula and the validity of the topology optimization model are also verified.)