Equivalent continuum representation of structures composed of repeated elements

Abstract

A procedure for determining the equivalent continuum properties of a structure composed of repeated patterns of discrete elements with both displacement and rotational coordinates is presented. These nodal coordinates are transformed to rigid-body and strain gradient variables using a polynomial approximation. The maximum number of independent variables that may be retained is determined by applying a ranking procedure to the resulting transformation matrix. The possibility of introducing errors by requiring the analyst to supply the strain gradient terms directly is reduced by identifying the appropriate variables through the use of the polynomial expansion and the ranking procedure. Additional constraints may be imposed in this analysis. The equivalent continuum parameters result when a further transformation to the appropriate kinematic variables is applied and the strain energy expression is reduced to these variables. Three-dimensional beamand plate-like structures are treated. The results correspond to findings using other approaches.