Comparative study on common methods for elastic force modeling and modal simulation of beam elements with absolute nodal coordinates

By theoretical derivation and numerical analysis, the modal parameters of two-dimensional absolute nodal coordinate beam elements under different elastic force modeling methods were studied. The continuum mechanics, enhanced continuum mechanics and strain splitting method were introduced, and the limitations of the application of the strain splitting method were deduced, and the characteristics of the three methods were explained from the theoretical point of view. Based on the generalized characteristic equations, the four natural modes of the absolute nodal coordinate beam element under different elastic force modeling methods were obtained. Taking the simply supported beam structure as an example, the effects of the absolute nodal coordinate beam element elastic force modeling method on the four natural modes were analyzed. Under different elastic force modeling methods, the four natural frequencies of the transverse low-order elements were higher than those of the transverse high-order elements, and the performance was more "rigid". For the continuum mechanics method, there is an error of 20%~30% between the low-order shear natural frequency of each element and the analytical solution, while the strain decomposition method and the enhanced continuum mechanics method can control the error of the shear natural frequency within 4%, and improve the element convergence accuracy.