焊接残余应力求解的边界元数学模型

Boundary element math model of welding residual stresses determination

焊接残余应力和变形之间存在着确定关系,二者可通过焊接过程中产生的非协调应变联系起来,文中以焊接初应变为基础,利用边界元的直接法,推导出了通过焊接变形求解二维焊接残余应力的数学模型。给定焊缝中初应变的初值,根据焊接构件边界上已知的位移信息,可由边界积分方程求出边界上所有未知的位移分量和表面力分量。在边界位移已知的条件下,应用该模型可对焊接构件内部残余应力进行求解。构件边界上的应力可由弹性体的边界应力和边界面力的关系,通过物理方程和几何方程求出。通过计算实例,验证了模型的可行性。

There is a definite correlation between the welding residual stresses and deformations,which can be connected by the incompatible strains formed in the welding process.Based on the initial welding strain,a math model of 2D welding residual stresses determination was deduced through direct boundary clement method.If the value of the initial welding strain was given,and in light of the measured boundary displaces,all the unknown displacemcnts and traction at the boundary could be calculated by using the boundary integral equation.Thereby,by using the model,the residual stresses of the weld structure could be solved.The stresses at the boundary can be calculated by the physical equation and the geometric equation according to the correlation between the stresses and the traction at the boundary.The feasibility of the model was verified through a concrete computing instance.