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CONTENTS
Volume 3, Number 1, January 2016
 

Abstract


Key Words


Address


Abstract
The Carrera Unified Formulation (CUF) is here extended to perform free-vibrational analyses of rotating structures. CUF is a hierarchical formulation, which enables one to obtain refined structural theories by writing the unknown displacement variables using generic functions of the cross-section coordinates (x, z). In this work, Taylor-like expansions are used. The increase of the theory order leads to three-dimensional solutions while, the classical beam models can be obtained as particular cases of the linear theory. The Finite Element technique is used to solve the weak form of the three-dimensional differential equations of motion in terms of \'fundamental nuclei\', whose forms do not depend on the adopted approximation. Including both gyroscopic and stiffening contributions, structures rotating about either transversal or longitudinal axis can be considered. In particular, the dynamic characteristics of thin-walled cylinders and composite blades are investigated to predict the frequency variations with the rotational speed. The results reveal that the present one-dimensional approach combines a significant accuracy with a very low computational cost compared with 2D and 3D solutions. The advantages are especially evident when deformable and composite structures are analyzed.

Key Words
composites; carrera unified formulation; finite element method; rotordynamics

Address
Matteo Filippi and Erasmo Carrera: Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Italy


Abstract
Although the aircraft industry was the first to use fibre composites, now they are increasingly used in a range of structural applications such as flooring, decking, platforms and roofs. Interlayer delamination is a major failure mode which threatens the reliability of composite structures. Delamination can grow in size under increasing loads with time and hence leads to severe loss of structural integrity and stiffness reduction. Delamination reduces the natural frequency and as a consequence may result in resonance. Hence, the study of the effects of delamination on the free vibration behaviour of multilayer composite structures is imperative. The focus of this paper is to develop a 3D FE model and investigate the free vibration behaviour of fibre composite multilayer sandwich panels with interlayer delaminations. A series of parametric studies are conducted to assess the influence of various parameters of concern, using a commercially available finite element package. Additionally, selected points in the delaminated region are connected appropriately to simulate bolting as a remedial measure to fasten the delamination region in the aim of reducing the effects of delamination. First order shear deformation theory based plate elements have been used to model each sandwich layer. The findings suggest that the delamination size and the end fixity of the plate are the most important factors responsible for stiffness reduction due to delamination damage in composite laminates. It is also revealed that bolting the delaminated region can significantly reduce the natural frequency variation due to delamination thereby improving the dynamic performance.

Key Words
fibre composite multilayer plates; three dimensional modelling; dynamic analysis; free vibration behaviour; delamination

Address
Indunil N. Jayatilake, Warna Karunasena and Weena Lokuge: Centre of Excellence in Engineered Fibre Composites (CEEFC), School of Civil Engineering and Surveying, University of Southern Queensland Toowoomba, QLD, 4350, Australia

Abstract
Composite materials are rapidly gaining popularity as an alternative to metals for structural and load bearing applications in the aerospace, automotive, alternate energy and consumer industries. With the advent of thermoplastic composites and advances in recycling technologies, fully recyclable composites are gaining ground over traditional thermoset composites. Stamp forming as an alternative processing technique for sheet products has proven to be effective in allowing the fast manufacturing rates required for mass production of components. This study investigates the feasibility of using the stamp forming technique for the processing of thermoplastic, recyclable composite materials. The material system used in this study is a self-reinforced polypropylene composite material (Curv). The investigation includes a detailed experimental study based on strain measurements using a non-contact optical measurement system in conjunction with stamping equipment to record and measure the formability of the thermoplastic composites in real time. A Design of Experiments (DOE) methodology was adopted to elucidate the effect of process parameters that included blank holder force, pre heat temperature and feed rate on stamp forming. DOE analyses indicate that feed rate had negligible influence on the strain evolution during stamp forming and blank holder force and preheat temperature had significant effect on strain evolution during forming.

Key Words
self-reinforced polypropylene; real-time strain measurement system; design of experiments; stamp forming

Address
Shankar Kalyanasundaram and Sudharshan Venkatesan: Research School of Engineering, The Australian National University, 31 North Road, Canberra, ACT 2601, Australia

Abstract
In this paper, the condensation method which is based on the Rayleigh-Ritz method, is described for the free vibration analysis of axially loaded slightly curved beams subject to partial axial restraints. If the longitudinal inertia is neglected, some of the Rayleigh-Ritz minimization equations are independent of the frequency. These equations can be used to formulate a relationship between the weighting coefficients associated with the lateral and longitudinal displacements, which leads to \"connection coefficient matrix\". Once this matrix is formed, it is then substituted into the remaining Rayleigh-Ritz equations to obtain an eigenvalue equation with a reduced matrix size. This method has been applied to simply supported and partially clamped beams with three different shapes of imperfection. The results indicate that for small imperfections resembling the fundamental vibration mode, the sum of the square of the fundamental natural and a non-dimensional axial load ratio normalized with respect to the fundamental critical load is approximately proportional to the square of the central displacement.

Key Words
condensation method; connection coefficient matrix; slightly curved beam; natural frequencies; axial load

Address
Yusuke Mochida and Sinniah Ilanko: The School of Engineering, The University of Waikato,
Private Bag 3105, Hamilton 3240, New Zealand

Abstract
Climate changes brought on by human interventions have proved to be more devastating than predicted during the recent decades. Recognition of seriousness of the situation has led regulatory organisations to impose strict targets on allowable carbon dioxide emissions from automotive vehicles. As a possible solution, it has been proposed that Fibre Metal Laminate (FML) system is used to reduce the weight of future vehicles. To facilitate this investigation, FML based on steel and self-reinforced polypropylene was stamp formed into dome shapes under different blank holder forces (BHFs) at room temperature and its forming behaviour analysed. An open-die configuration was used in a hydraulic press so that a 3D photogrammetric measurement system (ARAMIS) could capture real-time surface strains. This paper presents findings on strain evolutions at different points along and at 45o to fibre directions of circular FML blank, through various stages of forming. It was found initiation and rate of deformation varied with distance from the pole, that the mode of deformations range from biaxial stretching at the pole to drawing towards flange region, at decreasing magnitudes away from the pole in general. More uniform strain distribution was observed for the FML compared to that of plain steel and the most significant effects of BHF were its influence on forming depth and level of strain reached before failure.

Key Words
fibre metal laminate, real-time strain measurement system, self-reinforced polypropylene, stamp forming

Address
J. Nam: Research School of Engineering, Australian National University, 31 North Road, Canberra, ACT 2601, Australia
Wesley Cantwell: College of Engineering, University of Liverpool, Brownlow Hill, Liverpool L69 3GJ, United Kingdom
Raj Das: Department of Mechanical Engineering, University of Auckland, 20 Symonds St, Auckland, New Zealand
Adrian Lowe and Shankar Kalyanasundaram: Research School of Engineering, Australian National University, 31 North Road, Canberra, ACT 2601, Australia

Abstract
In this paper, a zero-dimensional mathematical formulation for rapid and explosive decompression analyses of pressurized aircraft is developed. Air flows between two compartments and between the damaged compartment and external ambient are modeled by assuming an adiabatic, reversible transformation. Both supercritical and subcritical decompressions are considered, and the attention focuses on intercompartment venting systems. In particular, passive and active vents are addressed, and mathematical models of both swinging and translational blowout panels are provided. A numerical procedure based on an explicit Euler integration scheme is also discussed for multi-compartment aircraft analysis. Various numerical solutions are presented, which highlight the importance of considering the opening dynamics of blowout panels. The comparisons with the results from the literature demonstrate the validity of the proposed methodology, which can be also applied, with no lack of accuracy, to the decompression analysis of spacecraft.

Key Words
rapid decompression; explosive decompression; isentropic model; active venting; blowout panels

Address
Alfonso Pagani and Erasmo Carrera: Department of Mechanical and Aerospace Engineering, Politecnico di Torino Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Abstract
This paper presents the free vibration analysis of damaged beams by means of 1D (beam) advanced finite element models. The present 1D formulation stems from the Carrera Unified Formulation (CUF), and it leads to a Component-Wise (CW) modelling. By means of the CUF, any order 2D and 1D structural models can be developed in a unified and hierarchical manner, and they provide extremely accurate results with very low computational costs. The computational cost reduction in terms of total amount of DOFs ranges from 10 to 100 times less than shell and solid models, respectively. The CW provides a detailed physical description of the real structure since each component can be modelled with its material characteristics, that is, no homogenization techniques are required. Furthermore, although 1D models are exploited, the problem unknown variables can be placed on the physical surfaces of the real 3D model. No artificial surfaces or lines have to be defined to build the structural model. Global and local damages are introduced by decreasing the stiffness properties of the material in the damaged regions. The results show that the proposed 1D models can deal with damaged structures as accurately as a shell or a solid model, but with far lower computational costs. Furthermore, it is shown how the presence of damages can lead to shell-like modal shapes and torsional/bending coupling.

Key Words
Carrera unified formulation; beam; finite element; advanced models; damage analysis

Address
Marco Petrolo and Erasmo Carrera: Department of Mechanical and Aerospace Engineering, Politecnico di Torino,
Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Ali Saeghier Ali Saeed Alawami: School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Bundoora VIC 3083, Australia


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