A second-order and two-scale computation method for the quasi-periodic structures of composite materials

2010 ◽  
Vol 46 (4) ◽  
pp. 320-327 ◽  
Author(s):  
Su Fang ◽  
Cui Jun Zhi ◽  
Xu Zhan ◽  
Dong Qiao Li
Author(s):  
Chunyu Xu ◽  
Junhua Lin ◽  
Wenhao Liu ◽  
Yuanbiao Zhang

This paper predict and effectively control the temperature distribution of the steady-state and transient states of anisotropic four-layer composite materials online, knowing the density, specific heat, heat conductivity and thickness of the composite materials. Based on the transfer function, a mathematical model was established to study the dynamic characteristics of heat transfer of the composite materials. First of all, the Fourier heat transfer law was used to establish a one-dimensional Fourier heat conduction differential equation for each composite layer, and the Laplace transformation was carried out to obtain the system function. Then the approximate second-order transfer function of the system was obtained by Taylor expansion, and the Laplace inverse transformation was carried out to obtain the transfer function of the whole system in the time domain. Finally, the accuracy of the simplified analytical solutions of the first, second and third order approximate transfer functions was compared with computer simulation. The results showed that the second order approximate transfer functions can describe the dynamic process of heat transfer better than others. The research on the dynamic characteristics of heat transfer in the composite layer and the dynamic model of heat transfer in composite layer proposed in this paper have a reference value for practical engineering application. It can effectively predict the temperature distribution of composite layer material and reduce the cost of experimental measurement of heat transfer performance of materials.


2018 ◽  
Vol 40 (4) ◽  
pp. 325-348
Author(s):  
Duc Trung Le ◽  
Jean-Jacques Marigo

The paper develops a general framework to derive the effective properties of quasi-periodic elastic medium. By using the asymptotic expansion method, the solution is expanded to the second order by solving a sequence of minimization problems. The effective stiffness tensors fields entering in the expression of the macroscopic energy are obtained by solving several families of microscopic problems posed on the unit cell and which bring into play only the microstructure. As an illustrative example, we consider an anti-plane elastic case of a heterogeneous cylinder made of a bi-layer laminate and submitted to the gravity. The unit cell being one-dimensional, all the associated elementary problems can be solved in a closed form and one shows that the effective energy of the medium expanded up to the second order depends not only on the strain gradient, but also on the gradient of the volume fraction \(\theta\) characterizing the repartition of the two materials in the laminate.


2011 ◽  
Vol 19 (11) ◽  
pp. 10494 ◽  
Author(s):  
Marco Castriota ◽  
Angela Fasanella ◽  
Enzo Cazzanelli ◽  
Luciano De Sio ◽  
Roberto Caputo ◽  
...  

2011 ◽  
Vol 217 (21) ◽  
pp. 8337-8342 ◽  
Author(s):  
Fang Su ◽  
Zhan Xu ◽  
Qiao-Li Dong ◽  
Hao Jiang

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