旋轉(zhuǎn)圓盤應(yīng)力計算

旋轉(zhuǎn)圓盤應(yīng)力計算一、幾何模型及計算相關(guān)參數(shù)本題用全三維模型計算旋轉(zhuǎn)等溫等厚空心圓盤周向應(yīng)力和徑向應(yīng)力隨半徑變化規(guī)律。圓盤的計算參數(shù)如下：圓盤外半徑Ra=0.27m內(nèi)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(zhuǎn)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(shù)為121，節(jié)點數(shù)為972，位移邊界條件為：兩個關(guān)鍵點施加X方向約束，兩個關(guān)鍵點施加Y方向約束，三個節(jié)點施加Z方向約束，網(wǎng)格信息如下圖：三、計算結(jié)果計算后的周向應(yīng)力和徑向應(yīng)力分布云圖如下：周向應(yīng)力分布云圖徑向應(yīng)力分布云圖應(yīng)力隨半徑變化計算結(jié)果：設(shè)置一條路徑，均分20段，XG從0.1變化到0.27。徑向應(yīng)力SX和軸向應(yīng)力SY變化如下計算數(shù)據(jù)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(wǎng)格加密收斂性檢驗加密后網(wǎng)格模型如下定義的單元類型為solid186，單元數(shù)為2295，節(jié)點數(shù)為16650，網(wǎng)格信息如下圖：應(yīng)力隨半徑變化計算結(jié)果如下：同樣和上次一樣，計算數(shù)據(jù)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(wǎng)格計算結(jié)果在圖線上看來更加精確，可以判斷出隨著網(wǎng)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(jié)果分析理論計算公式：理論計算結(jié)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(jié)果與理論結(jié)果進行比較，進行誤差分析。XG徑向應(yīng)力相對誤差周向應(yīng)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.