Hencky Bar-Grid Model for Plane Stress Elasticity Problems

Abstract

A novel Hencky bar-grid model (eHBM) was developed to address plane stress elasticity problems. This model comprises rigid bars arranged in a grid which are joined by frictionless hinges, frictionless pulleys, elastic primary and secondary axial springs, and torsional springs. Based on the energy approach, the in-plane displacements at the joints were determined and the in-plane stress resultants were obtained from the stress resultant–displacement relations. This paper calibrated the elastic spring stiffnesses for the eHBM for the first time by matching them with the finite-difference governing equation for elasticity problems. Some rectangular plane elasticity problems were solved by using the newly developed eHBM. The solutions obtained from the eHBM converged to the exact solutions for the continuum plane body with respect to decreasing the eHBM segment size. It was shown that the eHBM readily can handle any boundary conditions, and furnishes accurate solutions for plane elasticity problems with any complex geometry, such as a rectangular plane body with cutouts.