Rational simplified model of finite element analysis for deck pavement of long-span steel bridge
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摘要: 为了提高大跨钢桥桥面铺装有限元分析简化模型的计算精度, 运用有限元正交数值模拟试验对模型参数进行了敏感性分析, 利用子模型技术和综合评价方法对模型几何尺寸与边界约束条件进行了优化。发现大跨钢桥桥面铺装有限元分析简化模型合理的几何尺寸与边界条件为: 纵向为3跨, 横向有8个U肋, 横隔板高度为1.2m, 纵边自由, 横边简支, 横隔板底固结。对比分析结果表明: 该简化模型具有较高的计算精度, 横向拉应变误差仅为0.7%, 纵向拉应变误差为3.7%。Abstract: In order to improve the computation precision of simplified model for finite element analysis of deck pavement of long-span steel bridge, the size and boundary conditions of the model were optimized by using sub-model technology and comprehensive evaluation method, the parameters sensitivity of the model was analyzed, the reasonable dimension and constraints of a simplified finite element model were put forward, which had 3 longitudinal spans with free borders, 8 U-shape ribs in transverseness with simple supported borders, and 1.2 m-high diaphragms with fixed bottoms.Comparison result shows that simplified finite element model has high precision, the error of transverse tensile strain is only 0.7%, and the error of longitudinal tensile strain is 3.7%.
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图 5 模型综合误差与参数水平关系
Figure 5. Relation between parameter level and model comprehensive error
表 1 几何尺寸
Table 1. Geometry dimension
mm 箱梁宽 38 700 横隔板板厚 10 箱梁高 3 000 横隔板间距 3 220 顶板板厚 14 底板板厚 12 顶板U形加劲肋 上口宽 300 底板U形加劲肋 上口宽 400 下口宽 170 下口宽 250 高 280 高 250 间距 600 间距 900 板厚 6 板厚 6 
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表 2 敏感性分析因素水平
Table 2. Factor levels of sensitivity analysis
水平 因素 N M H/m L T B 1 6 5 1.0 自由 固结 自由 2 10 3 1.6 固结 自由 固结
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表 3 敏感性分析因素排序
Table 3. Factors arrangement of sensitivity analysis
因素 N M NM L NL H T B MT LT HB 列号 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
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表 4 敏感性分析结果
Table 4. Results of sensitivity analysis
试验号 N M NM L NL H T B MT LT HB 横向拉应变/10-6 纵向拉应变/10-6 层间剪应力/MPa 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 529.4 216.6 0.540 2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 498.8 268.4 0.540 3 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2 478.8 259.7 0.540 4 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1 474.8 302.6 0.539 5 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 498.2 252.6 0.539 6 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1 499.9 291.6 0.540 7 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1 476.4 242.9 0.540 8 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2 484.6 262.5 0.539 9 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 484.1 248.7 0.540 10 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 481.3 256.2 0.539 11 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1 479.5 271.8 0.539 12 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2 479.8 259.1 0.540 13 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 485.5 285.8 0.540 14 2 2 1 1 2 2 1 2 1 1 2 2 1 1 2 477.6 251.3 0.539 15 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2 478.3 261.6 0.539 16 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1 486.1 244.4 0.539
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表 5 极差分析结果
Table 5. Results of range analysis
因素 N M H L T B NL MT HB NM LT 横向拉应变/10-6 11.1 2.5 5.6 14.6 3.4 2.8 13.3 5.8 4.1 3.2 6.5 纵向拉应变/10-6 2.3 1.2 21.7 4.2 12.1 26.3 5.4 10.3 6.0 0.6 3.9
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表 6 方差分析结果
Table 6. Results of variance analysis
横向拉应变 方差来源 N M H L T B NL MT HB NM LT 误差 平方和 494.0 25.0 126.0 849.0 46.3 30.3 712.0 137.0 66.9 40.1 169.0 184.0 自由度 1 1 1 1 1 1 1 1 1 1 1 4 均方和 494.0 25.0 126.0 849.0 46.3 30.3 712.0 137.0 66.9 40.1 169.0 46.0 F值 10.80 0.54 2.74 18.50 1.01 0.66 15.50 2.98 1.46 0.87 3.67 显著性 显著 显著 显著 F0.05(1, 4)=7.71 F0.01(1, 4)=21.2 纵向拉应变 方差来源 N M H L T B NL MT HB NM LT 误差 平方和 20.3 5.8 1 877.0 69.9 581.0 2 763.0 118.0 426.0 143.0 1.5 61.2 310.0 自由度 1 1 1 1 1 1 1 1 1 1 1 4 均方和 20.3 5.8 1 877.0 69.9 581.0 2 763.0 118.0 426.0 143.0 1.5 61.2 77.5 F值 0.26 0.07 24.20 0.90 7.50 35.60 1.52 5.49 1.85 0.02 0.79 显著性 极显著 极显著
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表 7 模型参数优化因素水平
Table 7. Factor levels of model parameters optimization
水平 因素 H/m N L T B 1 0.8 6 自由 固结 自由 2 1.0 8 简支 简支 简支 3 1.2 10 固结 自由 固结 4 1.4 5 1.6 6 1.8
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表 8 模型参数优化结果
Table 8. Optimization results of model parameters
试验号 H N T B L 原始计算结果 修正计算结果 单项指标误差/% 模型综合误差/% 1 2 3 4 5 6 7 ex, i/10-6 ey, i/10-6 τi/MPa e′x, i/10-6 e′y, i/10-6 xi yi 一次方权系数 二次方权系数 1 1 1 3 2 2 1 2 493.1 298.1 0.539 499.0 301.7 3.2 9.5 5.4 4.6 2 1 2 1 1 1 2 1 524.3 305.1 0.540 530.6 308.8 2.9 12.1 6.1 5.0 3 1 3 2 3 3 3 3 495.8 314.3 0.540 501.8 318.1 2.7 15.5 7.1 5.5 4 2 1 2 1 2 3 1 502.7 294.0 0.539 508.8 297.5 1.3 8.0 3.6 2.8 5 2 2 3 3 1 1 3 480.1 225.1 0.540 485.9 227.8 5.7 17.3 9.8 8.3 6 2 3 1 2 3 2 2 489.5 294.3 0.540 495.4 297.8 3.9 8.1 5.4 4.8 7 3 1 1 3 1 3 2 488.1 239.7 0.540 494.0 242.6 4.2 11.9 6.9 5.9 8 3 2 2 2 3 1 1 505.9 262.2 0.539 512.0 265.4 0.7 3.7 1.7 1.3 9 3 3 3 1 2 2 3 473.8 280.7 0.540 479.5 284.1 7.0 3.1 5.6 6.1 10 4 1 1 1 3 1 3 479.1 294.4 0.539 484.9 297.9 5.9 8.1 6.7 6.4 11 4 2 2 3 2 2 2 485.9 296.7 0.539 491.8 300.3 4.6 9.0 6.1 5.6 12 4 3 3 2 1 3 1 501.0 250.8 0.540 507.0 253.8 1.7 7.9 3.8 3.0 13 5 1 3 3 3 2 1 500.4 303.3 0.540 506.4 307.0 1.8 11.4 5.1 3.9 14 5 2 1 2 2 3 3 483.9 236.9 0.540 489.7 239.8 5.0 13.0 7.8 6.8 15 5 3 2 1 1 1 2 496.5 307.0 0.540 502.5 310.7 2.5 12.8 6.1 4.8 16 6 1 2 2 1 2 3 494.9 315.9 0.540 500.9 319.7 2.8 16.0 7.4 5.8 17 6 2 3 1 3 3 2 488.3 303.0 0.539 494.2 306.6 4.1 11.3 6.6 5.7 18 6 3 1 3 2 1 1 498.2 307.6 0.539 504.2 311.3 2.2 13.0 6.0 4.6
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