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6.3 用伽辽金有限元法计算平面稳定温度场在工程实践中,经常会遇到受热结构的应力分析问题。计算结构的热应力必须已知结构的温度分布。因此,温度场的计算往往是热应力分析的前奏。在温度场问题中,它的待求函数是温度。如果内部无热源,则温度函数将不随时间变化,故称稳定温度场。对于平面稳定温度场,利用热的平衡关系,可以推导出温度T(x,y)必须满足的基本微分方程和边界条件为:
6.3 Calculation of Plane Stable Temperature Field by Galerkin Finite Element Method In engineering practice, stress analysis of heated structures is often encountered. The thermal stress of the calculated structure must know the temperature distribution of the structure. Therefore, the calculation of the temperature field is often the prelude to thermal stress analysis. In the temperature field problem, its function to be solved is temperature. If there is no heat source inside, the temperature function will not change over time, so the stable temperature field is called. For the plane-stabilized temperature field, using the heat balance relationship, it can be deduced that the basic differential equations and boundary conditions that the temperature T(x,y) must satisfy are: