针对传统确定性拓扑优化方法在处理载荷不确定性时可能导致结构应力敏感的问题,提出一种基于速度场水平集框架的结构应力最小化鲁棒性拓扑优化方法.首先,采用P范数函数对结构最大应力进行全局度量.进而通过多项式混沌展开法(polynomialc...针对传统确定性拓扑优化方法在处理载荷不确定性时可能导致结构应力敏感的问题,提出一种基于速度场水平集框架的结构应力最小化鲁棒性拓扑优化方法.首先,采用P范数函数对结构最大应力进行全局度量.进而通过多项式混沌展开法(polynomialchaosexpansion,PCE)建立载荷不确定性下结构最大应力随机响应的代理模型,并直接从PCE展开系数解析提取最大应力的均值与标准差,建立以二者线性组合最小化为目标的鲁棒性拓扑优化模型,从而兼顾应力性能的平均表现与波动程度.在优化过程中,采用速度场水平集方法描述结构边界的演化,结合直接微分法与伴随变量法,推导了全局最大应力统计矩对速度设计变量的解析灵敏度,为拓扑演化提供精确梯度信息,并引入全局收敛移动渐近线法(globally convergent method of moving asymptotes,GCMMA)实现设计变量的高效更新.为验证所提方法的有效性与稳定性,通过两个典型数值算例开展系统仿真,并结合蒙特卡罗模拟(Monte Carlo simulation,MCS)对优化结果进行对比分析.此外,还讨论了权重系数、载荷变异系数及体积约束限值对最终构型与应力性能的影响规律.展开更多
ABSTRACT Numerical simulations with the Advanced Regional Prediction System （ARPS） model were performed to investigate the impact of microphysical drop size distribution （DSD） on tornadogenesis in a subtropical s...ABSTRACT Numerical simulations with the Advanced Regional Prediction System （ARPS） model were performed to investigate the impact of microphysical drop size distribution （DSD） on tornadogenesis in a subtropical supercell thunderstorm over Anhui Province, eastern China. Sensitivity experiments with different intercept parameters of rain, hail and snow DSDs in a Lin-type microphysics scheme were conducted. Results showed that rain and hail DSDs have a significant impact on the simulated storm both microphysically and dynamically. DSDs characterized by larger （smaller） intercepts have a smaller （larger） particle size and a lower （higher） mass-weighted mean fall velocity, and produce relatively stronger （weaker） and wider （narrower） cold pools through enhanced （reduced） rain evaporation and hail melting processes, which are then less favorable （favorable） for tornadogenesis. However, tornadogenesis will also be suppressed by the weakened mid-level mesocyclone when the cold pool is too weak. When compared to a U.S. Great Plain case, the two microphysical processes are more sensitive to DSD variations in the present case with a higher melting level and deeper warm layer. This suggests that DSD-related cloud microphysics has a stronger influence on tornadogenesis in supercells over the subtropics than the U.S. Great Plains.展开更多
文摘针对传统确定性拓扑优化方法在处理载荷不确定性时可能导致结构应力敏感的问题,提出一种基于速度场水平集框架的结构应力最小化鲁棒性拓扑优化方法.首先,采用P范数函数对结构最大应力进行全局度量.进而通过多项式混沌展开法(polynomialchaosexpansion,PCE)建立载荷不确定性下结构最大应力随机响应的代理模型,并直接从PCE展开系数解析提取最大应力的均值与标准差,建立以二者线性组合最小化为目标的鲁棒性拓扑优化模型,从而兼顾应力性能的平均表现与波动程度.在优化过程中,采用速度场水平集方法描述结构边界的演化,结合直接微分法与伴随变量法,推导了全局最大应力统计矩对速度设计变量的解析灵敏度,为拓扑演化提供精确梯度信息,并引入全局收敛移动渐近线法(globally convergent method of moving asymptotes,GCMMA)实现设计变量的高效更新.为验证所提方法的有效性与稳定性,通过两个典型数值算例开展系统仿真,并结合蒙特卡罗模拟(Monte Carlo simulation,MCS)对优化结果进行对比分析.此外,还讨论了权重系数、载荷变异系数及体积约束限值对最终构型与应力性能的影响规律.
基金jointly supported by the National Natural Science Foundation of China (Grant Nos.41175118, 40775005 and 41175043)the National Basic Research Program of China (Grant No.2013CB430105)partially supported by the China Special Fund for Meteorological Research in the Public Interest (Grant Nos.GYHY200906003 and GYHY201306040)
文摘ABSTRACT Numerical simulations with the Advanced Regional Prediction System （ARPS） model were performed to investigate the impact of microphysical drop size distribution （DSD） on tornadogenesis in a subtropical supercell thunderstorm over Anhui Province, eastern China. Sensitivity experiments with different intercept parameters of rain, hail and snow DSDs in a Lin-type microphysics scheme were conducted. Results showed that rain and hail DSDs have a significant impact on the simulated storm both microphysically and dynamically. DSDs characterized by larger （smaller） intercepts have a smaller （larger） particle size and a lower （higher） mass-weighted mean fall velocity, and produce relatively stronger （weaker） and wider （narrower） cold pools through enhanced （reduced） rain evaporation and hail melting processes, which are then less favorable （favorable） for tornadogenesis. However, tornadogenesis will also be suppressed by the weakened mid-level mesocyclone when the cold pool is too weak. When compared to a U.S. Great Plain case, the two microphysical processes are more sensitive to DSD variations in the present case with a higher melting level and deeper warm layer. This suggests that DSD-related cloud microphysics has a stronger influence on tornadogenesis in supercells over the subtropics than the U.S. Great Plains.
