| The rotation-free(RF)element method represents an unconventional finite element method,in which rotation is not an explicit representation of the degree of freedom,and the interpolation domain of the element is overlapping.Its obvious advantage is that the non-convergence problem caused by rotation in finite element method can be avoided.In this paper,theoretical derivation and finite element simulation method are used to study the RF plane beam element in linear and non-linear analysis,taking the plane cantilever beam with concentrated load at the end as an example.In the part of theoretical derivation,firstly,the linear expression of RF plane beam element is deduced,and then a numerical example is given.By using the co-rotation method and the hypothesis of small strain,the linear element is extended to geometrically nonlinear analysis,and the nonlinear expression of the beam element is obtained.At the same time,according to the convergence criterion,the completeness and compatibility of the RF plane beam element are theoretically proved,and the numerical example is given.In the finite element simulation part,the traditional two-node beam element is used to analyze the planar cantilever beam with concentrated load at the end,and the calculation results of the two-node beam element are obtained,and the theoretical calculation results are compared with the results of the finite element simulation.Finally,the element is applied to the static analysis of conductor structure.Finally,the element is applied to cable deformation analysis,and the RF plane beam element is used to calculate a cable line.The results show that:(1)The stiffness matrix of RF plane beam element can be approximated to a constant matrix,and it does not need to be updated in geometric non-linearity analysis.(2)Compared with the traditional two-node beam element,it is found that the RF plane beam element can avoid the convergence problem caused by rotation,and the results are the same. |
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