键基近场动力学框架下的应变计算方法

Strain calculation method under framework of bond-based peridynamics

为了将键基近场动力学与连续介质力学联系起来,借助键伸长率和沿键方向线应变在空间上的对应关系,发展了一种键基近场动力学框架下的应变计算方法.利用薄板受拉、圆孔应力集中和悬臂梁空间变形问题的近场动力学模拟,验证了新方法在应变计算上的可靠性和准确性,并分析了计算范围和键取向数对精度的影响.模拟结果表明,新方法的计算结果与有限元结果或解析解吻合良好,计算范围对应变精度的影响可以忽略,键取向数则对应变精度影响较大.当取用所有方向的键时,应变的相对误差能控制在2%以内.因此,减小计算范围能在几乎不降低应变精度的情况下有效减少计算成本,增加键取向数则可以提升应变精度.

To connect the bond-based peridynamics with the continuum mechanics,a strain calculation method under the framework of bond-based peridynamics was developed based on the spatial correspondence between the bond stretch and the linear strain along the bond direction.The reliability and accuracy of the new method in strain calculation were verified by peridynamic simulations of thin plate tension,stress concentration in a circular hole and spatial deformation of a cantilever beam.The effects of the calculation range and the number of the bond orientations on the accuracy were studied.The simulation results show that the calculation results of the new method are in good agreement with the finite element results or analytical solutions.The influence of the calculation range on the strain accuracy can be ignored.However,the number of the bond orientations have great influence on the strain accuracy.The relative error can be controlled within 2%when the bonds in all directions are taken.Therefore,narrowing the calculation range can effectively reduce the calculation cost without decreasing the strain accuracy.Meanwhile,more bond orientations lead to higher strain accuracy.