Effect of Geometric Imperfections and Boundary Conditions on the Nonlinear Response of a Curved Beam

Abstract

This paper reports some observations on the use of 3-D digital image correlation system for measurement of geometric imperfections and boundary conditions of a curved beam structure. The goal of this estimation is two fold: first, to experimentally identify the influence of these parameters on the curved beam structure in developing an accurate model for simulation and second, to develop a reliable approach for experimental validation of the simulated results via carefully placing the due emphasis on the geometric imperfections and boundary conditions. This paper is a first step in developing a general framework in these directions. I. Introduction he design and development of next generation of hypersonic aircraft structure would require an ability to predict the nonlinear response of the structure under the given operating conditions with a reliable estimate of accuracy of the predicted results. The development of a reliable and accurate model for simulating the nonlinear response is an adaptive and multi-step process which requires an estimation of the inherent uncertainties in the modeling process. It has been observed that boundary conditions and the geometric imperfections are the two prominent sources of uncertainty in the response. In this research, a clamped-clamped curved beam is used to illustrate the effect of geometric imperfections and the boundary conditions on the model development and hence the response. This is achieved by a combined computational and experimental approach where the goal is to estimate and include the effect of geometric imperfections and boundary conditions in a detailed finite element model. This model is developed by a novel use of image based, 3-D digital image correlation (DIC) to capture the geometry of the curved beam system in the fixture. The resulting finite element model can then be utilized to estimate the nonlinear response of the curved beam system. The overarching goal of this research is to illustrate an approach for developing well characterized and validated models for hypersonic aircraft applications. Significant progress has been made in development of reduced–order models of aerospace structures for predicting the nonlinear response. These models are usually validated by comparing response predictions obtained from them and from the full finite element models or sometimes from experimental observations. The use of these reduced order modeling approaches to assembled structures (e.g., bonded, multi bay panels) is not well developed as this introduces uncertainty in the dynamic behavior of the resulting structure due to the boundary conditions and joining operations. This uncertainty can be incorporated in the model, by the use of a non-parametric, maximum entropy approach as demonstrated in [2, 3]. The current research presents first observations on the use of experimentally obtained geometric and boundary condition information in the development of a finite element model to simulate the nonlinear response of curved beam structures. A comparison of the response is made with the idealized geometry and clamped-clamped boundary conditions to illustrate the role they play in the uncertainty in the model.