Continuum Models for Beam- and Platelike Lattice Structures

Abstract

A simple, rational approach is presented for developing continuum models for large repetitive beam- and platelike lattices with arbitrary configurations subjected to static, thermal, and dynamic loadings. The continuum models for these structures are shear flexible beams and plates. They account for local effects in the repeating element of the actual structure and are characterized by their thermoelastic strain and kinetic energies, from which the equations of motion and constitutive relations can be derived. The procedure for developing the expressions for thermoelastic strain and kinetic energies of the continuum involves introducing basic assumptions regarding the variation of the temperature, displacement, and strain components in one or two directions (for plate- and beamlike lattices) and obtaining effective thermoelastic and dynamic coefficients of the continuum in terms of material properties and geometry of the original lattice structure. The high accuracy of the continuum models developed is demonstrated by means of numerical examples. AltA2,Ab,Ad