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自适应是降低有限元计算结果对网格依赖性的有效途径,基于p型有限元法建立了三维非稳定温度场的自适应分析方法,自适应的策略采用单元升阶法,误差估计方法取温度的高阶计算值作为精确解的“最佳估计”。通过三维混凝土板算例,研究了绝热温升和放热系数、模型尺寸、计算时步长度、边界温差对计算误差和单元阶次的影响。结果表明:在边界温差不大时,绝热温升比表面放热系数对计算误差影响更大;在高阶计算中小尺寸模型比大尺寸模型误差明显减小;计算时步长的变化反映了温度场的时间梯度,越大的时步长需越高的计算阶数;模型边界的温差变化表现了温度场的空间梯度,越大的边界温差需越高的计算阶数。
Adaptive method is an effective way to reduce the dependence of the finite element calculation on the grid. Based on the p-type finite element method, the adaptive analysis method of the three-dimensional unstable temperature field is established. The adaptive method adopts the unit ascending method and the error estimation method The higher-order value of temperature is the “best estimate” of the exact solution. Through the example of three-dimensional concrete slab, the effects of adiabatic temperature rise and exothermic coefficient, model size, calculated time length and boundary temperature difference on calculation error and element order are studied. The results show that the adiabatic temperature rise has more influence on the calculation error than the large size model when the temperature difference is not large. The variation of the step size in the calculation shows that the temperature The time gradient of the field and the larger time step require the higher calculation order. The temperature variation of the model boundary shows the spatial gradient of the temperature field and the higher the calculation range of the boundary temperature difference.