Elastic Parameter Identification of Plate Structures Using Modal Response: An ECE Based Approach

Abstract

This article describes an inverse method for the identification of heterogeneous anisotropic elastic parameters of plate structure from an incomplete modal response. Many efforts in this area have shown that derivatives of the displacement mode shapes or curvature mode shapes are much more sensitive to the heterogeneous parameter distribution of the structure when compared with the mode shapes themselves. Thus, the curvature mode shapes are used widely to quantify the material profile. Following this observation, a strategy based on the error in constitutive equation (ECE) function, which naturally incorporates this fact seamlessly into the identification procedure, is proposed. The identification problem is posed as an optimization problem in that the cost function measures the discrepancy in the constitutive equation, which connects kinematically admissible curvature/strains and dynamically admissible couples/stresses. The resulting system becomes an extended system with primary and Lagrangian variables as the unknown with penalized measurement as the forcing function. The material update then follows by way of constitutive discrepancy, and an explicit update formula is derived. Although the regularization resulting from ill-posedness is achieved through the penalization parameter associated with the modified ECE function, this also helped to incorporate the partial and corrupted data map in the reconstruction strategy. Finally, a few numerical examples are considered to show the applicability of the proposed scheme.