Regular truss structure model equivalent to continuum structure

Abstract

It is difficult to solve the structural problems related to agricultural engineering, due to the wide ranges of the means of related variables and complex structural shapes. For these reasons, discrete models are required that are able to replace or simplify solid structure components used in traditional analysis methods. Therefore, the objective of this study was to develop a regular truss structure model that behaves the same way as a solid structure. It was assumed that if a unit element consists of truss elements with each hinge at the end of the element and the size of the element is infinitesimal, the stress distribution and displacement field will be constant throughout the domain of the unit element. Additionally, the behavior of the truss element was assumed to be in a linear state in a two-dimensional plane. The law of energy conservation, based on the theory of elasticity, was applied to determine the equilibrium conditions between discretized and solid elements. The restrictive condition that we obtained revealed that applications are limited to only ideal elastic materials with a Poisson’s ratio of 1 to 3. The volumetric ratio of the equivalent truss to the continuum structures was 3:1, regardless of the size or number of the mesh. To calculate the internal stress and strain of the unit element, the geometric relationships of each truss member, which has its own role against different stress directions, were used. The calculated von Misses stresses were used to verify this model. Stress concentrations, as explained based on Saint Venant’s principle, were also observed in the equivalent truss structure model. The main stress paths, indicating the areas where reinforcement bars should be placed, were successfully shown without the requirement that each element be transformed in the direction of principal stress; this was done by eliminating elements with only compressive and near-zero stresses. Keywords: structural analysis, regular mesh, equivalent truss structure model, discretized element, energy method DOI: 10.3965/j.ijabe.20150805.1742 Citation: Choi W, Lee J, Yoon S. Regular truss structure model equivalent to continuum structure. Int J Agric & Biol Eng, 2015; 8(5): 151－161.