Stress and Inverse Analyses of Linear Orthotropic Elastic Materials

Abstract

A hybrid stress and inverse method based on the complex representation of the Airy stress function is proposed to determine the elastic constants and the full-field stresses of a loaded orthotropic material from processing only the kinematic data in proximity to an internal cut-out with a traction-free boundary. The elastic constants of the material are inversely characterized by minimizing the difference between the processed kinematic data and its predicted counterpart obtained from the complex-variable method. Once the elastic constants are determined via the inverse approach, the hybrid stress field is evaluated based on fundamental mechanics principles—i.e., equilibrium and compatibility—instead of physically differentiating the kinematic field. The main advantage of the proposed stress analysis method is its feasibility in processing only one of the in-plane displacement component to determine the stresses. To demonstrate the effectiveness and robustness of the complex-variable method in direct and inverse analyses, several parameters are investigated, such as the number of processed data points, the level of random noise superimposed on the simulated kinematic data, the number of retained terms in the series expansion of the displacement equations, and the form and magnitude of the externally applied load.