A continuum model for the nonlinear analysis of beam-like lattice structures

Abstract

A simple equivalent continuum model has been developed for the geometrically nonlinear analysis of beam-like lattice structures. Two important features of the model are the simplicity of the calculation of the continuum properties and the ability of the continuum to accurately predict the behavior of rigid-joint as well as pin-joint lattices. The equivalence of the continuum and lattice is established by requiring the strain energy of the continuum to equal the strain energy of the lattice for a finite set of assumed deformation modes. It is shown that an additional strain energy term not found in classical Timoshenko beam theory must be included in the continuum strain energy function in order to accurately approximate the behavior of rigid-joint frames. A finite element discretization is applied to the continuum to obtain numerical solutions for the continuum model. By comparison with discrete finite element results for the lattice, the accuracy of the continuum methodology is demonstrated for both static and dynamical problems. For the nonlinear problems studied, the continuum solutions were found to require only a small fraction of the CPU time needed for the discrete finite element solutions.