求解平面和轴对称热冲击问题的热权函数有限元法

FINITE ELEMENT IMPLEMENTATION OF THERMAL WEIGHT FUNCTION METHOD FOR DETERMINATION OF TRANSIENT SIF IN THERMAL SHOCK PROBLEMS

根据三维通用权函数法的普遍表达式 ,给出了轴对称问题和平面问题热权函数法的基本公式 .并利用刚度阵导数法 ,将热权函数法与有限元法直接耦合 ,给出了二维问题的热权函数有限元法计算格式 .实例计算表明 ,该文给出的计算方法具有极高的计算效率和满意的工程应用精度 .

Thermal weight function (TWF) method is introduced to calculate the transient stress intensity factors(SIF) at crack tips in thermal shock problems through direct integration of products of TWF and temperatures. TWF is independent of time. Since repeated stress analyses (by FEM or BEM) needed for every instant in other methods are avoided by using the TWF method, the procedure of calculation is greatly simplified. Different from the mechanical weight function (MWF) method, a characteristic feature for the TWF method is that the integration should be carried out along the boundary as well as over the whole area. So, it seems difficult to derive a lot of approximate equations for the TWF method. The stiffness derivative method is used to couple the TWF method with finite element method. Formulations of finite element implementation of TWF method are given for 2-D problems. Examples show that good accuracy and high efficiency can be reached for the present formulations.