含热阻多层材料壳体的温度场计算

A Shell Temperature Element for Multi-Layer Composite Materials with Thermal Resistance

构造了适用于含热阻多层复合材料壳体温度场计算的壳体温度单元,由于热阻的出现,假设壳体沿厚度方向的温度分布为分段多项式函数,使其满足壳体在内、外表面的边界条件,并在壳体温度单元上每个节点引入额外自由度,从而确定了分段多项式函数的系数。在此基础上,以双层材料为例,假设分布函数为二次分段多项式,给出了有限元列式。算例表明,该单元用于稳态问题时,使用二次分段多项式,温度计算结果就能达到较高的精度;用于瞬态问题时,使用三阶分段多项式,可使温度计算结果具有较高的精度。另外,通过将蜂窝夹芯板的夹芯层等效为热阻,利用构造的壳体温度单元计算了蜂窝夹芯板的热传导问题,计算结果与实验结果符合较好。

A shell temperature element has been developed for the calculation of shell tem- perature field of multi-layer composite materials with thermal resistance.A multi-piece poly- nomial function,which satisfies boundary conditions on the shells inner and outer surfaces, is used to describe shell temperature along its radius direction as thermal resistance exists. Coefficients of the multi-piece quadratic function can be calculated by introducing extra free- doms on each shell element node.Finite element expression has been obtained based on the shell temperature element developed in this paper in the case of a two-layer material and quadratic function.Numerical examples show that satisfying precision can be achieved by quadratic function when this element is used for steady problem;while enough precision can be guaranteed by cubic function when it is used for unsteady problem.Besides,by consider- ing the core of honeycomb composite as thermal resistance,the thermal conduction problem of the honeycomb composite has been simulated by the shell temperature element,and the simulation results agree well with the experimental results.