旋转圆盘应力计算

旋转圆盘应力计算一、几何模型及计算相关参数本题用全三维模型计算旋转等温等厚空心圆盘周向应力和径向应力随半径变化规律。圆盘的计算参数如下：圆盘外半径Ra=0.27m内半径R0=0.1m圆盘厚度2mm材料密度7800kg/m3弹性模量E=2e5泊松比υ=0.3转速ω=1000rad/s盘缘无外载，无温度载荷二、有限元模型有限元全三维模型如下图定义的单元类型为solid186，单元数为121，节点数为972，位移边界条件为：两个关键点施加X方向约束，两个关键点施加Y方向约束，三个节点施加Z方向约束，网格信息如下图：三、计算结果计算后的周向应力和径向应力分布云图如下：周向应力分布云图径向应力分布云图应力随半径变化计算结果：设置一条路径，均分20段，XG从0.1变化到0.27。径向应力SX和轴向应力SY变化如下计算数据XG0.10.10850.1170.12550.1340.14250.151SX0.00E+001.43E+073.63E+075.82E+077.63E+078.01E+078.39E+07SY4.85E+084.56E+084.25E+083.93E+083.65E+083.48E+083.31E+080.15950.1680.17650.1850.19350.2020.21058.77E+079.14E+079.24E+078.68E+078.12E+077.57E+077.02E+073.15E+082.98E+082.84E+082.73E+082.61E+082.50E+082.39E+080.2190.22750.2360.24450.2530.26150.276.47E+075.57E+074.49E+073.40E+072.30E+071.21E+071.04E+062.27E+082.17E+082.06E+081.96E+081.86E+081.75E+081.65E+08四、网格加密收敛性检验加密后网格模型如下定义的单元类型为solid186，单元数为2295，节点数为16650，网格信息如下图：应力随半径变化计算结果如下：同样和上次一样，计算数据如下：XG9.95E-020.108030.116550.125060.133580.142090.150610.15912SX838992.92E+075.07E+076.67E+077.79E+078.54E+079.02E+079.26E+07SY4.83E+084.45E+084.13E+083.87E+083.65E+083.45E+083.28E+083.12E+080.167640.176150.184670.193180.20170.210210.218730.227249.28E+079.12E+078.80E+078.36E+077.79E+077.12E+076.35E+075.49E+072.98E+082.84E+082.72E+082.60E+082.49E+082.38E+082.27E+082.16E+080.235760.244270.252790.26130.269824.54E+073.52E+072.41E+071.24E+07359072.06E+081.95E+081.85E+081.74E+081.64E+08加密后的网格计算结果在图线上看来更加精确，可以判断出随着网格划分的越精细，有限元计算机误差会更小，故收敛性检验成功。五、计算结果分析理论计算公式：理论计算结果（计算时同样计算路径上21个点的理论解）XG0.10.108030.116550.125060.133580.142090.15061SX2.23E-08281989005035269966437366778681238559411090342732SY4.83E+084460932624.14E+083.88E+083.65E+083.46E+083.28E+080.159120.167640.176150.184670.193180.20170.21021926267349284641991302652882257108380605278178908714740453.12E+082.98E+082.85E+082.72E+082.6E+082.49E+082.38E+080.218730.227240.235760.244270.252790.26130.26982637701705516235445693806354392462441845112694077269693.82.27E+082.16E+082.06E+081.96E+081.85E+081.75E+081.64E+08将加密后的计算结果与理论结果进行比较，进行误差分析。XG径向应力相对误差周向应力相对误差0.1100.00%0.03%0.108033.35%0.32%0.116550.75%0.22%0.125060.39%0.22%0.133580.01%0.16%0.142090.17%0.12%0.150610.16%0.10%0.159120.04%0.14%0.167640.02%0.15%0.176150.12%0.13%0.184670.20%0.10%0.193180.30%0.11%0.20170.35%0.11%0.210210.41%0.11%0.218730.46%0.10%0.227240.54%0.10%0.235760.64%0.10%0.244270.82%0.10%0.252791.15%0.