Buckling, Post-buckling and Vibrations of Composite Plates under Combined Thermomechanical Loads

A big technological leap in Carbon Fibre Reinforced Plastics (CFRP's) has brought to the market materials that are able to operate under severe thermomechanical loading conditions and yet remain lightweight. This is of high interest for new developments in aerostructures, such as supersonic airliners or the hydrogen aircraft. A continuous need for improvement in weight efficiency motivates this research, which delves into the possibility of using thermomechanical buckling to increase structural performance in future CFRP aerostructures. In this regard, it is well understood that plates that buckle under mechanical loads can operate safely, and they can even carry a significant amount of load before they experience material failure. Since future high-speed composite aircraft will have to endure thermomechanical loads, it is fair to consider that some parts of these new vehicles could, to some degree, be capable to operate under thermomechanical post-buckling.

The goal of this PhD dissertation is to advance the knowledge on thermomechanical buckling of composite plates, by investigating diverse aspects of the behaviour of this phenomenon. In particular, special attention is given to study the occurrence of mode jumps in post-buckling. Mode jumping phenomena alter the shape of a plate and can impact certain aspects of its functionality, e.g. aerodynamics, yet they could have potentially interesting future applications if they were to be appropriately controlled. Three kinds of methodologies, analytical, numerical and experimental, have been followed during this research. However, a clear emphasis has been put in the latter, since this thesis is mostly focused in the design and execution of experiments in thermomechanical buckling of composite plates.

This dissertation is composed of four independent investigations, being the first of them an analytical study on linear thermomechanical buckling, and the other three experimental studies on deep thermomechanical post-buckling behaviour. Four independent studies are presented in Chapters 2 to 5 of this thesis. In Chapter 2, an analytical, closed-form solution for the study of linear buckling of thin, symmetric and balanced composite laminated plates subjected to thermomechanical loads was derived. The formulation is based on a Duhamel-Neumann constitutive approach, and laminate theory to derive the plate governing equations. The mechanical load was introduced in the formulation as plate size variation, and heating load was implemented as uniform temperature increment. The formulation was limited to simply supported boundary conditions. The obtained formula relates critical buckling temperatures to initially applied plate size variation. In Chapter 3, a numerical-experimental study of thermal buckling under heating is presented. A set of parametric analysis was performed to identify composite plates that present a mode jump when heated. Two composite plates were identified and were subsequently tested in a newly developed test setup for thermal buckling of composite plates. The aforementioned setup was devised around a frame with a low coefficient of thermal expansion, so that the plate could experience buckling and mode jumping when heated, and could successfully reproduce thermal buckling and mode jumping in the tested plates. Chapter 4 reports a combined numerical-experimental study of composite plates, analysing the interaction between mechanical and thermal loads in relation to buckling and mode jumping. A novel test setup for thermomechanical testing was designed. This setup made use of the frame used in previous chapter to restrain thermal expansion, and by applying compression to the frame, mechanical shortening could be indirectly applied to the plate. In this way, it was possible to study interactions between thermal and mechanical loading states. Experimental results revealed that a linear decrease of the mode jumping temperature could be observed for increasing levels of compression, and the same was also true when the order of applications of the loads was inverted. Chapter 5 presents an experimental investigation on vibrations of heated composite plates leading to thermal buckling. The experiments were performed considering two main goals: the application of the Vibration Correlation Technique for the detection of thermal buckling in composite plates; and the exploration of the frequency variations before and after the occurrence of a mode jump in post-buckling regime. Two variations of the test setups used in previous chapters were used. The setups shared thermal expansion frame, while they differentiate on the type of heating source and mechanical boundary conditions. The plates were excited acoustically using a loudspeaker, and the vibration frequencies were monitored and acquired using a laser vibrometer. Buckling temperatures were successfully predicted using the Vibration Correlation Technique. Changes in frequency, potentially related to the occurrence of the mode jump, were also detected.