Extended continuum model for dynamic analysis of beam-like truss structures with geometrical nonlinearity

Abstract

An approach to extend the application of the continuum model to beam-like lattice truss structures with geometrical nonlinearity is presented in this paper. The geometrical nonlinearity within the truss structures is accounted for by dividing it into substructures and introducing a co-rotational coordinate system to decompose the substructure motion into rigid body motion and pure deformations. The linear continuum model of each substructure is derived using the continuum model based on the small deformation hypothesis in the local coordinate system, in which the deformation of the truss structure is still small. Then, the linear mass and stiffness matrices of the continuum elements are converted into the nonlinear equivalent mass and stiffness matrices for the global coordinate system. The equations of motion for the truss structure are established using Lagrange's equations. Three numerical simulation examples are considered and the results show that the proposed model requires fewer degrees of freedom and has better efficiency than the finite element model based on the truss elements while also obtaining the desired accuracy.