摘要
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α_(c)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a_(qx)、a_(qy)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 essential boundary condition can be directly put without special treatment,which can improve the computational efficiency while maintaining high accuracy.In this paper,LRPIM linear programming method is applied 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 complementarity 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 distribution and contact deformation of the contact surface are obtained.The influence of shape parameter of interpolation function and integral domain size on the calculation results is analyzed.The results show that the influence of the shape parameterαc 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 a_(qx) and a_(qy) is greater than 1.5,the calculation results begin to converge,and divergence occurs when a_(qx) and a_(qy) 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 paper has high computed accuracy.
作者
任晓通
师俊平
REN Xiaotong;SHI Junping(Department of Engineering Mechanics,Xi'an University of Technology,710048 Xi'an,China)
出处
《应用力学学报》
CAS
CSCD
北大核心
2024年第4期888-895,共8页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金资助项目(No.11872300)
陕西省自然基金重点项目(No.2021JZ-47)。
关键词
无网格
线性互补
结合面
接触特性
法向接触力
meshless method
linear complementarity
mechanical joint surface
contact characteristic
normal contact force
