接触与大变形问题的光滑有限元分析

Smoothed Finite Element Analysis of Contact and Large Deformation Problems

橡胶材料因具有良好的抗震、吸能作用,在实际工程中应用广泛.然而橡胶超弹性材料的碰撞属于强非线性问题,分析橡胶材料的接触碰撞和大变形问题对于提高装置的缓冲性能具有重要意义.光滑有限元法(smoothed finite element method,S-FEM)是一种弱形式的数值计算方法,相比于传统的有限元方法,光滑有限元法对网格的质量要求不高,允许单元在计算过程中发生较大的变形,且光滑域的构造比较灵活,在不增加自由度的前提下,可以达到较高的精度.在光滑有限元法的基础上,采用双势方法进行接触计算,以充分利用光滑有限元法计算大变形问题的优点和双势方法求解接触力的优势.通过与有限元软件MSC.Marc的数值结果对比,验证了该算法的准确性和能量守恒性,并且分析了摩擦因数对碰撞体的影响.

Rubber material is widely used in practical engineering due to its good seismic and energy absorption effect.However,the collision of hyperelastic materials is a strong nonlinear problem.It is of great significance to analyze the contact collision and large deformation of hyperelastic materials to improve the buffering performance of the device.The smoothed finite element method(S-FEM)is a weak form of numerical calculation method.Compared with the traditional finite element method,the smoothed finite element method has low requirements on the mesh quality,allows the element to undergo large deformation during the calculation process,where the construction of the smooth domain is more flexible.The S-FEM has high accuracy without additional degrees of freedom.Based on the S-FEM,the double potential method was applied to contact calculation,with both advantages of the S-FEM in calculating large deformation problems and advantages of the double potential method in solving contact force fully used.In comparison with the numerical results of finite element software MSC.Marc,the results of the proposed algorithm were verified with high accuracy and good energy conservation,and the effects of the friction coefficient on the collision body were analyzed.