旋轉圓盤應力計算一、幾何模型及計算相關參數本題用全三維模型計算旋轉等溫等厚空心圓盤周向應力和徑向應力隨半徑變化規律。圓盤的計算參數如下：圓盤外半徑Ra=0.27m內半徑R0=0.1m圓盤厚度2mm材料密度7800kg/m3彈性模量E=2e5泊松比υ=0.3轉速ω=1000rad/s盤緣無外載，無溫度載荷二、有限元模型有限元全三維模型如下圖定義的單元類型為solid186，單元數為121，節點數為972，位移邊界條件為：兩個關鍵點施加X方向約束，兩個關鍵點施加Y方向約束，三個節點施加Z方向約束，網格信息如下圖：三、計算結果計算后的周向應力和徑向應力分布云圖如下：周向應力分布云圖徑向應力分布云圖應力隨半徑變化計算結果：設置一條路徑，均分20段，XG從0.1變化到0.27。徑向應力SX和軸向應力SY變化如下計算數據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、網格加密收斂性檢驗加密后網格模型如下定義的單元類型為solid186，單元數為2295，節點數為16650，網格信息如下圖：應力隨半徑變化計算結果如下：同樣和上次一樣，計算數據如下：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加密后的網格計算結果在圖線上看來更加精確，可以判斷出隨著網格劃分的越精細，有限元計算機誤差會更小，故收斂性檢驗成功。五、計算結果分析理論計算公式：理論計算結果（計算時同樣計算路徑上21個點的理論解）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將加密后的計算結果與理論結果進行比較，進行誤差分析。XG徑向應力相對誤差周向應力相對誤差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.