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

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.

The project will generate new knowledge and stimulate further research, but more importantly, it will have a significant impact on composite design industries, particularly in the aerospace sector. This is because the proposed development of dynamic stiffness composite elements using layer wise theory will make accurate and efficient design of large composite structures, such as a wing box, possible by overcoming the inadequacy of existing methods. A wide range of companies will benefit from the proposed research. Initially, leading developers of structural modelling software and suppliers to aerospace industry will be able to implement the proposed layer wise dynamic stiffness plate elements in their software, which will significantly enhance the state of the art in aircraft design. These companies have been identified as MSC (Nastran), SAMTECH (Samcef), Simulia (Abaqus) and Ansys Inc. Subsequently, aerospace companies such as Airbus, BAE System, EADS, ESA, Thales Alenia, Agusta, and Rolls- Royce, who are engaged in designing large composite structures, will use the newly-developed dynamic stiffness elements through the software developed by the above companies, resulting in more accurate and efficient design without compromising the safety. Furthermore, research establishments, like MERL Ltd., dealing with both fundamental and applied aspects of material engineering research will benefit from the proposed work by taking full advantage of the superior modelling capability of the new dynamic stiffness composite elements. The impact of the proposed research amongst the academic community will be very considerable because it will promulgate new ideas for research and development of postgraduate courses in composite science. The current courses in composites are generally restricted to the use of classical lamination theory, which has many serious limitations. With the growing trend for the requirement of future design engineers equipped with an in-depth knowledge and understanding of advanced composite materials, the proposed research is ideally suited to act as a catalyst to fulfill this requirement and is thus a step in the right direction. Project partners SAMTECH and MERL who are well known contributors to aerospace structural design have expressed their keen interest in this research. Their active participation will fuel the project and be enormously helpful to promote the new dynamic stiffness theory and the resulting software to aerospace, automobile, shipbuilding and other industries. Both companies will take part in regular quarterly project development meetings, provide their input and share their experience in the design of composite structures. In order to ensure an effective dissemination of the research, the following actions will be undertaken: i) An inaugural meeting involving all project partners and other organisation identified by City Research Enterprise Unit (CREU) will be arranged; ii) A web-site will be set up to publish content and progress of the project; iii) Writing up of research papers for publication in high impact factor journals and established conferences; iv) Possible commercial exploitation of the software resulting from the project will be explored though CREU; v) A final meeting will be held in the end to consolidate the principal findings of the research, distribute materials summarising main outcomes to all project partners and discuss possible follow-up projects. The new knowledge that will accrue from this project will impact upon national economy by creating future investments in research, new business opportunities as well as increasing skills of new generation of composite structural designers. In the long run, the impact on society will be felt in the form of lower fuel consumption and reduced carbon footprint as result of using efficiently designed light weight composite structures