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从热传导的偏微分方程和有限元法入手,分析了结合面上节点初始温度取值不同时,造成温度场计算结果偏差的数学原因.根据能量守恒原理,推导出确定混凝土浇筑结合面上节点初始温度的计算公式,揭示了结合面上节点温度初值与新老混凝土的密度、比热容、单元划分大小、温度之间的数量关系.为取平均值的经验做法提供了理论上的依据,并能准确的计算出因初始温度取值不同导致的误差值.最后结合一个数值算例,与理论解相比较,采用该取值方法所得计算结果的最大误差不超过理论解的6%.
Starting from the partial differential equations of heat conduction and the finite element method, the mathematical reason for the deviation of calculation results of temperature field is analyzed when the initial temperature of joint on the joint surface is different. According to the energy conservation principle, The calculation formula of temperature reveals the relationship between the initial temperature of joints and the density of new and old concrete, the specific heat capacity, the size of unit division and the temperature, and provides the theoretical basis for the empirical method of averaging Accurate calculation of the error caused by the different initial temperature values.According to a numerical example, compared with the theoretical solution, the maximum error of the calculated results does not exceed 6% of the theoretical solution.