Layer-wise dynamic stiffness formulation for free vibration analysis of multilayered composite structures

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Fibre reinforced advanced composite materials are rapidly replacing conventional isotropic materials, particularly in aircraft industry. In the past, the use of composite materials was mostly confined to secondary structures of civil airliner, but given their high specific strength and more importantly, their directional properties and hence ability to be tailored, they are now making headway to primary structures. However, there are potential problems associated with the dynamic behaviour of composites that are unheard of in isotropic materials. Thus, the need to overcome these problems requires the development of a new method. This project proposes a novel Layer-Wise Dynamic Stiffness Method (LW DSM) for free vibration analysis of thick composite structures. Current modelling tools for composites are primarily based on classical lamination theory (CLT) which considers an inhomogeneous laminate as an equivalent orthotropic homogeneous layer with equivalent properties. The stiffness properties of each layer are summed to obtain the global stiffness. Clearly, such a simple approach is flawed because it violates congruency and equilibrium conditions at the interfaces between layers and it may lead to large errors. The level of accuracy obtained by CLT is probably acceptable when macro behaviour of a structure with width over thickness ratio >100 is sought, but for primary structures that are intended to carry large loads and are thus thicker, the error will be much higher. Recent research has shown that for some structures the error can be over 30% on the fundamental natural frequency. In aerospace industry where safety factors are generally low to achieve a lighter mass, an error of 30 % is unacceptable and it may lead to structural failures during laboratory or flight tests. For this reason, improved modelling techniques are to be developed. Novel modelling techniques could indeed, be computationally demanding but, on the other hand, they deliver the much needed accuracy. One important recent development in this area is the so-called Layer-Wise technique in which each single layer is modelled as an individual plate by using appropriate displacement assumptions and assembly procedure. The main drawback of the LW model using FEM is that it leads to a large number of unknowns which depends on the number of layers. For example, a 20-layer 4-noded finite plate element has 252 DOF. Clearly, lots of finite elements are required to model a structure, and thus the number of DOF for a LW FE model becomes excessive, making the use of conventional LW theory practically impossible.A major break-through would be to use LW theory in conjunction with the dynamic stiffness method (DSM) to make this application realistically possible. For free vibration of plate assemblies, Dynamic stiffness (DS) elements based on classical plate theory and first order shear deformation theory have already been developed by the applicants showing huge superiority over conventional finite elements. One of the potential benefits of the DSM in sharp contrast to FEM, is that one single element is enough to model any part of the structure with uniform geometry in an exact sense without losing any accuracy, and thus reducing the number of unknowns of the problem drastically. This is possible only in DSM because instead of discretising the structure, the differential equation of motion is solved in closed-form and the solution is generalised to develop element properties which can then be rotated, offset, assembled to model a complex structure such as wing boxes.As the DSM can make the application of a LW theory feasible when investigating real composite structures, the aim of the project is to develop an accurate high precision DS element using LW theory. The proposal epitomises a break-through to overcome probably the biggest stumbling block in accurately predicting the dynamic behaviour of composite aircraft structures made of thick laminates.