焊接残余应力对非线性矩形薄板奇点影响的讨论

Welding residual stress influence on the singular point of nonlinear quadrate thin plate

根据板壳理论建立了具有焊接残余应力矩形簿板的非线性动力学方程;利用Galerkin原理,首次获得了具有焊接残余应力矩形簿板的非线性运动方程。在该非线性运动方程的基础上,研究了焊接残余应力对矩形簿板稳定中心点具有稳定解的邻域范围的影响;讨论了焊接残余应力对矩形簿板稳定中心点具有稳定解的邻域范围所对应的积分常数临界值的影响。研究结果表明:随焊接残余应力的增加,非线性矩形薄板相平面图中稳定中心点具有稳定解的邻域范围增大,非线性矩形薄板运动范围增大。

According to the theory of plates and shells, the nonlinear dynamics equation of quadrate thin plate with welding residual stress is established; the nonlinear motion equation of quadrate thin plate with welding residual stress is obtained using Galerkin method. On the basis of the nonlinear motion equation, welding residual stress influence on the scope of neighborhood of stable solution abut, centrality singular point of quadrate thin plate is discussed; welding residual stress influence on critical value of constant of integration abut the scope of neighborhood of stable solution is debated. It concluded that the welding residual stress increases with an increase in the scope of neighborhood of stable solution abut centrality singular point of quadrate thin plate in phase-plane diagram and that it increases with an increase in range of movement of nonlinear quadrate thin plate.