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Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 16
CIVIL ENGINEERING COMPUTATIONS: TOOLS AND TECHNIQUES Edited by: B.H.V. Topping
Chapter 16
Analysis and Optimal Design of Multilayer Structure Subjected to Impulse Loading A.J. Aref^{1}, X. Luo^{1} and G.F. Dargush^{2}
^{1}Department of Civil, Structural and Environmental Engineering, A.J. Aref, X. Luo, G.F. Dargush, "Analysis and Optimal Design of Multilayer Structure Subjected to Impulse Loading", in B.H.V. Topping, (Editor), "Civil Engineering Computations: Tools and Techniques", SaxeCoburg Publications, Stirlingshire, UK, Chapter 16, pp 369389, 2007. doi:10.4203/csets.16.16
Keywords: wave propagation, layered structure, optimization, impulse loading.
Summary
In this ongoing research, we are developing new material architectures
for mitigating the effects of impulsive loadings using functionally
graded materials (FGM). Stress attenuation is obtained by tuning material
properties and length of each layer, along with the total length of
a multilayer structure utilizing the geometric dispersion [1]
found in layered structures.
A number of researchers have looked at wave propagation in layered structures. For example, Robnik [2] proposed an analytic approximation method using the WentzelKramersBrillouin (WKB) approximation, which may be applied to discrete and continuous media. Tenenbaum and Zindeluk [3] proposed an approach to the direct scattering problem in onedimensional inhomogeneous bodies. Nygren et al. [4] presented an optimization analysis of elastic junctions with regard to transmission of wave energy of an incident extensional wave at a nonuniform elastic junction between two uniform and collinear elastic bars. Gusev [5,6] studied the optimal synthesis of multilayer structures by implementing the ultimate performance under the action of elastic waves. In contrast to the body of literature on time harmonic wave propagation, there is much less published work on the optimization of layered structures subjected to transient loading. Anfinsen [7] studied the problem of maximizing or minimizing the amplitude of stress waves propagating through a onedimensional elastic layered structure using difference equations, which were solved using ztransform methods. Some other works on transient optimal design of multilayer structures can been found in References [810]. Perhaps the closest work that has been done by other researchers is that by Velo and Gazonas [11]. They investigated the optimal design of a twolayered elastic strip subjected to transient loading by assuming a Goupillaudtype layered medium. The chosen design parameter was the impedance ratio between the two layers. However, there are additional control parameters (i.e., length of each layer) that need to be determined to obtain the final optimal design even after the optimal impedance ratio is found. In this paper, an optimal design procedure is proposed to obtain the optimal length of each layer. First, the stress transfer function is obtained for a multilayer structure with one fixed end boundary condition based on a transfer matrix method. Given this stress transfer function, stress output at the fixed end could be computed under any arbitrary transient load. Then, analytical solutions of stress at the fixed surface is obtained for both twolayered Goupillaudtype media and a large second layer structure using an inverse Laplace transform method. Optimal criteria is then proposed and the optimal structure is determined for this twolayered structure, based upon an analysis of the stress at the fixed end. The analysis shows that the optimal solution depends on the applied load, however, the optimal procedure works for any arbitrary transient load. By applying the load and following the optimal procedure proposed in this paper, the optimal structure can be achieved. Finite element simulations are also carried out using the commercial code ABAQUS [12] for comparison with the analytical results. References
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