Contact analysis of mechanical joint surface based on meshless method
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典型的无网格方法采用移动最小二乘函数(moving least squares,MLS)作为近似函数,但由于MLS不具备Kronecker delta函数性质,本质边界施加困难.LRPIM是采用径向基点插值形函数的无网格方法,本质边界条件无需特殊处理,可以直接施加,在保持高精度的前提下提高计算效率.将LRPIM应用于机械结合面接触问题的计算.根据位移连续条件推导了含接触特性的线性互补方程,建立了基于LRPIM的计算模型,采用线性互补算法利用数值积分计算了几种典型的接触问题,得到了接触面压力分布和接触变形,分析了插值函数形状参数和积分域尺寸对计算结果的影响.研究结果表明,插值函数形状参数αc对接触力的影响较小,而形状参数q取-0.5~1.2时有较好的收敛效果;积分域无量纲尺寸aqx、aqy大于1.5时计算结果开始收敛,大于2.5时出现发散现象,取值2.1时收敛效果最佳.将计算结果与已有结果进行比较,表明本研究方法有较高的求解精度.
The conventional meshless method uses the moving least squares(MLS)as an approximate function,but since MLS does not have the property of Kronecker delta,it is difficult to exert the essential boundary condition.LRPIM is a meshless method using radial interpolation approximate function.The es-sential boundary condition can be directly put without special treatment,which can improve the computa-tional efficiency while maintaining high accuracy.In this paper,LRPIM linear programming method is ap-plied to the contact problem of mechanical joint surface.LRPIM meshless method was used to calculate the global stiffness and global force;according to the displacement condition,the contact linear complementari-ty equation is derived;a calculation model based on LRPIM is established.Several typical contact problems are calculated by using linear complementary algorithm and numerical integration.The pressure distribu-tion and contact deformation of the contact surface are obtained.The influence of shape parameter of inter-polation function and integral domain size on the calculation results is analyzed.The results show that the influence of the shape parameter αc of the interpolation function on the contact force is small,and the shape parameter q takes-0.5~1.2,which has a good convergence effect.When the dimensionless size of the integral domain axq and aqy is greater than 1.5,the calculation results begin to converge,and diver-gence occurs when aqx and aqy is greater than 2.5.The convergence effect is the best when they are equal to 2.1.The calculation results are compared with the existing results,indicating that the method in this pa-per has high computed accuracy.
meshless methodlinear complementaritymechanical joint surfacecontact characteristicnor-mal contact force