Analysis of composite shellsisogeometric modelling and damage identification

Resumen

La tesis doctoral se enmarca en el campo de los materiales compuestos y enmarcado en el proyecto de investigación P08-TEP-3641 de la Junta de Andalucía. Se divide en dos grandes bloques: Uno en el campo del análisis estructural de laminas de materiales compuestos y otro en el de la detección de daños en el campo del Structural Health Monitoring (SHM). El primer bloque desarrolla e implementa una novedosa formulación de elementos finitos que unifica la definición geométrica de estructuras con el análisis numérico. El uso de Non Uniform Rational B-Splines (NURBS), permite pues definir láminas complejas desde un punto de vista geométrico y usar las mismas herramientas para su aproximación en elementos finitos. Se desarrolla particularmente una lámina de material compuesto para una teoría de tercer orden. Así mismo se estudia el conocido problema del bloqueo numérico de la solución y se plantean alternativas que mejoran su comportamiento numérico. En el segundo bloque se desarrolla un elemento finito, que presenta una delaminación interna, para estudiar la influencia de la respuesta dinámica frente a la presencia de la delaminación, y para diversos tamaños. Adicionalmente se realizan experimentos en tres placas de material compuesto, dos de ellas con una delminación interna, de tamaño diferente, para tratar de detectar la presencia de la delaminación mediante el estudio de la variación de las propiedades dinámicas de las mismas. Los resultados experimentales son comparados con los numéricos obtenidos con el modelo previamente desarrollado. Se obtiene gran similitud entre ambos. Ello verifica la técnica empleada para detectar daños como una técnica satisfactoria. La tesis se compone de 5 capítulos, que son los siguientes: 1-NURBS-based analysis of higher-order composite shells. 2-An Isogeometric locking-free higher-order shell. 3-On the Accuracy of a 4-Node Delaminated Composite Plate Element and its Application to Damage Detection. 4-Experimental analysis of orthotropic composite plates. Comparison with numerical results. 5-Modal Analysis of Delaminated Composite Plates using the Finite Element Method and Damage Detection via combined Ritz/2d-Wavelet Analysis. (collaboration for a paper). 6-Conclusions and further works BIBLIOGRAFIA (más relevante): [1] T.J.R. Hughes and J.A. Cottrell and Y. Bazilevs, ¿Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement¿, Computer Methods in Applied Mechanics and Engineering, 194(39-41): 4135¿4195, 2005, ISSN 0045-7825. [2] T.J.R. Hughes and J.A. Cottrell and Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement , Volume 194, Elsevier Science SA, PO BOX 564, 1001 Lausanne, Switzerland, 2005, ISSN 0045-7825, pages 4135¿4195. [3] L.A. Piegl and W. Tiller, The NURBS Book (Monographs in Visual Communication), Springer, New York, 2th edition, 1997. [4] J. Kiendl, K.U. Bletzinger, J. Linhard, R. Wuechner, ¿Isogeometric shell analysis with Kirchhoff-Love elements¿, Computer Methods in Applied Mechanics and Engineering, 198(49-52): 3902¿3914, 2009, ISSN 0045-7825. [5] R. Echter, B. Oesterle, M. Bischo, A hierarchic family of isogeometric shell finite elements, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 254 (2013) 170-180. doi:10.1016/j.cma.2012.10.018. [6] Y. Zou, L. Tong, G.P. Steven, ¿Vibration-based model-dependent damage (delamination) identification and health monitoring for composite structures - A review¿, Journal of Sound and Vibration, 230(2): 357¿378, 2000, ISSN 0022-460X. [7] S.W. Doebling, C.R. Farrar, M.B. Prime and D.W. Shevitz, ¿Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review¿, Technical Report LA¿13070-MS, Los Alamos National Laboratory, Los Alamos, NM. 87545, 1996. [8] C.R. Farrar, S.W. Doebling, D.A. Nix, ¿Vibration-based structural damage identification¿, Philosophical Transactions of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 359(1778): 131¿149, JAN 15 2001, ISSN 1364-503X. [9] D. Balageas, C. Fritzen, A. Gu¿emes, Structural Health Monitoring, ISTE, United Kingdom, 2007. [10] B.R. Zwink, ¿Nondestructive Evaluation of Composite Material Damage Using Vibration Reciprocity Measurements¿, Journal of Vibration and Acoustics-Transactions of the ASME, 134(4), AUG 2012, ISSN 1048-9002. [10] A. Alvandi, C. Cremona, ¿Assessment of vibration-based damage identification techniques¿, Journal of Sound and Vibration, 292(1-2): 179¿202, 2006, ISSN 0022-460X. [11] L. Yu, T. Yin, ¿Damage Identification in Frame Structures Based on FE Model Updating¿, Journal of Vibration and Acoustics-Transactions of the ASME, 132(5), 2010, ISSN 1048-9002. [12] W. Liu, W.C. Gao, Y. Sun, ¿Application of Modal Identification Methods to Spatial Structure Using Field Measurement Data¿, Journal of Vibration and Acoustics-Transactions of the ASME, 131(3), 2009, ISSN 1048-9002. --------------------------------------------------------------------------------------------------------------------------------------------------- (English version) --------------------------------------------------------------------------------------------------------------------------------------------------- INTRODUCTION: Composite materials have become more popular in recent decades. From their origins until the present day, their use has grown in sectors such as aerospace, automotive, energy and other civil engineering applications. In fact, they constitute an interdisciplinary area, where the work of many professionals (engineers, chemists, physicists, etc.) converges into a final product that must be inspected for maintenance in view of its applications. This study focuses on two particular areas, one pertaining to the field of structural analysis, the other within the field of Structural Health Monitoring (SHM). Finite Element Analysis (FEA) contributes very substantially to the development of composite materials, making possible the computation of plate and shell theories. Recently, Isogeometric Analysis (IGA) has emerged as a new finite element theory that solves some of the limitations of the standard FEA. Unifying geometry definition and analysis, this recent theory serves to define and compute complex geometries while improving computation accuracy. It stands as a very promising way to generalize the definition and analysis of structures. This work develops a composite shell with the novel Isogeometric Analysis (IGA) formulation, allowing for a definition of complex geometries through the use of non uniform rational B-Splines (NURBS). Chapter 1 (Paper:NURBS-based analysis of higher-order composite shells ) implements a shell for the most widely used ESL theories for shell structures, and verifies its implementation for some benchmark and numerical static and dynamic problems. However, as happens with the standard finite element formulations, the same numerical issues accompany IGA. Chapter 2 develops a locking-free shell with this formulation. Both shear-locking and curvature-locking are avoided, and the obtained results present better accuracy. The second area of focus lies in the field of SHM, and more concretely in delamination detection in Carbon Fiber Reinforced Polymer (CFRP) plates. Therefore, numerical and experimental analyses are performed in order to study the possibilities of delamination detection through the use of piezoelectric (PZT) sensors and actuators. Chapter 3 (Paper: On the Accuracy of a 4-Node Delaminated Composite Plate Element and its Application to Damage Detection) develops a delaminated finite element for a composite plate. Mode shape changes, frequency shifts and Frequency Response Function (FRF) changes are computed to study the effect of delamination in the dynamic response for several delamination sizes. Chapter 4 presents an experimental study for three orthotropic composite plates [0 90]3S, two of them with an internal delamination, provided by Airbus (EADS-CASA, Puerto de Santa María). Analysis of the FRF gives rise to several conclusions, some of them illustrated by means of the element developed in Chapter 3. In Chapter 5 (Paper: Modal Analysis of Delaminated Composite Plates using the Finite Element Method and Damage Detection via combined Ritz/2d-Wavelet Analysis), the developed element from Chapter 3 is used to contribute with some numerical FEM results in order to test a new damage detection technique, from a theoretical point of view. The author limits mention of this contribution on the delaminated model and results, since no further work has been done. Therefore, appears as co-author. Finally in Chapter 6, general conclusions and lines of future work are expounded. CONCLUSIONS: This Doctoral Thesis pursues several objectives to study composite applications in the field of the aerospace industry. Two main blocks comprise this research: - Developing a composite shell with a novel IGA formulation. - Studying the effect of delamination on composite plates. Isogeometric Analysis is a very promising methodology, unifying geometric definition and Finite Element Analysis in one tool. This methodology allows us to define complex geometries using NURBS. Firstly, an isoparametric composite shell has been implemented for a higher-order ESL theory, through the use of higher-order NURBS, resulting in a good formulation for static and modal analysis. Although higher-order NURBS present better accuracy than standard finite element ones, the shell is further improved, in order to avoid locking. Particularly shear-locking is avoided through the use of a hierarchic discrete difference vector theory, while curvature-locking is avoided by the use of projection techniques. The following conclusions and observations can thus be extracted from the first part (Chapters 1 and 2): - IGA admits complex geometries, without requiring mesh refinements. - The strain and stress are continuous. - IGA presents the same numerical issues as the standard finite element method does. Isoparametric higher-order NURBS work well for most of the standard problems. - The proposed locking-free shell presents better results for very thin shells and for high-curvature ones. - The proposed locking-free shell presents better results for higher frequencies. Several benchmark and numerical problems are compared with the IGA ones in order to test the implemented shell and to proof its efficiency. In further works, other locking strategies will be performed. The theory will be generalized for a non-linear regime. For the time being, and within the field of Structural Health Monitoring (SHM), two objectives are achieved. Firstly, a delaminated composite element was implemented with the standard finite element theory, to study how dynamic properties were affected by the presence of delamination from a comprehensive point of view. Mode shape changes, frequency shifts and FRF changes are analized in order to quantify the influence of delamination. In general, changes tend to be greater as the delamination size grows, requiring the use of higher order frequencies to detect small delaminations. Secondly, the experimental validation of this idea was performed with three composite orthotropic plates [0 90]3S , two of them having internal delamination. Similar behaviour was observed in the experiments and the simulations, the frequency shifts obtained from the FRF being the variable used to compare both methods. The following conclusions can therefore be extracted from the second part (Chapters 3 and 4): -Mode shape changes are more powerful to identify delamination than frequency shifts. -The PULSE-System does not introduces relevant noise for different experiments. -A variance for frequencies in the experiment was set for the studied bandwidth, since the experiment was performed on three different plates. -Amplitude changes in the FRF were only taken into account if the changes were noticeable. -The plates were free of in-plane stresses. -FRF analysis was able to identify delamination. In order to clearly detect small delaminations, higher frequencies were required. -The behaviour resulting from theory and experiments was similar. -Model based methods should be used from a comprehensive point of view. Finally, an additional contribution from a paper involving the collaboration of this author is provided, giving the numerical results for some delaminated plates, in order to validate a new damage detection technique developed by a member of the group. In future work, the study of Lamb waves on delaminated plates will be performed from a numerical point of view. ------------------------------------------------------------------------------------------------------------------------------------------------------