Equivalent Continuum Modeling of Lattice Beams Based on Spectral Element Formulation

초록

A new continuum modeling approach based on the concept of spectral element analysis is developed to represent a large periodic lattice beam as an equivalent continuum extended Timoshenko beam(ETB). The procedure for developing an equivalent continuum ETB involves the derivation of the transfer matrices for both the representative lattice cell of a periodic lattice beam and the equivalent continuum ETB element. The transfer matrix for an equivalent continuum ETB element is derived analytically so that the equivalent structural properties to be determined are contained in the transfer matrix. The transfer matrix for the lattice cell is numerically derived form the assembled spectral finite element formulation via dynamic condensation by use of the continuum degrees of freedom defined in this paper. The two transfer matrices are then forced to be equal to each other to determine the equivalent structural properties of the equivalent continuum ETB. The equivalent structural properties and corresponding vibration characteristics from the present continuum model are compared with those from other existing methods to find that the present continuum method can give a very reliable continuum model compared with other methods.