论文部分内容阅读
讨论了三维弹性连续体应力集中极小化的形状优化问题。边界元法作为应力分析工具，解析法或差分法计算应力敏度，用约束变尺度优化算法进行优化。根据形状优化的特点，给出了提高求解形状优化问题数值方法效率的措施：用子结构技术，节省了应力重分析时的计算机时；用选主元三角分解法方程组，使解析敏度分析时不解方程组。所编程序实用于分布载荷作用下的一般三维弹性连续体构件的应力集中最小的形状优化问题。该算例为轴类零件，用三次样条函数描述待优化边界的母线，并将其插值样点的坐标作为设计变量。待优化边界光滑，设计变量少。算例结果表明：优化结果正确，应力集中显著降低，程序运行稳定、高效和可靠。
The shape optimization problem of stress minimization in three-dimensional elastic continuum is discussed. Boundary element method as a stress analysis tool, analytical method or differential method to calculate the stress sensitivity, using constrained variable scale optimization algorithm to optimize. According to the characteristics of shape optimization, the measures to improve the efficiency of the numerical method for solving shape optimization problems are given: the substructure technique is adopted to save the computer time of stress reanalysis; the principal component triangular trigonometry method is used to make the analytical sensitivity analysis Do not understand equations. The program is applied to shape optimization problems with minimum stress concentration in general three-dimensional elastic continuum members under distributed loading. The example is a shaft part. The cubic spline function is used to describe the generatrix of the boundary to be optimized and the coordinates of the interpolated sample points are taken as design variables. The boundary to be optimized is smooth with few design variables. The results show that the optimization results are correct, the stress concentration is significantly reduced, and the program runs stably, efficiently and reliably.