采用有限差分方法求解固体弹性应力场(英文)

Calculation of the Solid-elastic Stress Field with the Finite Difference Method

为了采用全有限差分方法进行涡轮气热弹耦合计算,研究了固体弹性应力场计算的物理模型,给出了任意曲线坐标系下的控制方程。同时研究了定常问题的有限差分求解方法和边界条件的给定,编制了定常问题的应力场求解程序;并通过对具有解析解的受集中载荷的悬臂梁和一端受径向集中力的曲梁进行数值计算来验证该固体弹性应力场的求解方法。结果表明,边界条件的二阶精度处理的格式所得结果与解析解数据吻合得较好,而一阶精度格式结果与解析解有较大的误差。

In order to investigate the conjugated calculation of fluid-thermal-elasticity in turbine engine with the full finite difference method. The physics model of solid-elasticity for numerical simulation is studied. The governing equation in curvilinear coordinate system is derived. The finite difference method and the boundary condition under steady-state conditions are investigated. And the code to solve stress field under steady-state conditions is programmed. The cantilever girder with a uniformity load and curvature girder with a concentrated load are calculated to validate the capability of the code to solve the stress field of solid elasticity. The numerical results which has the second order precision boundary conditions are well match the analytic result, although the result of which has the once order precision boundary conditions showed big difference from the analytic result.