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Liu and et al. [3] used the genetic algorithm (GA) to directly determine lay-ups with rough increment angles.
The EL and ET are moduli of longitudinal elasticity in the L and T directions, respectively, GLT is a shear modulus and νLT, νTL are the Poisson ratios.
Gurdal, et al.: Design and Optimization of Laminated Composite Materials (John Wiley & Sons 1999) [2] H.
Fukunaga and et al.: J.
Liu, et al.: Comput.

Hoffmann et al. revealed that the composition required for the formation of the Al16Ti5O34 phase would be derived from mol% 8 Al2O3 × 5 TiO2 = 61.5% Al2O3 : 38.5% TiO2.
Phase diagram of Al2O3/TiO2 system by Hoffmann et. al. [11] One of the methods for determining the phase composition of single crystal structures is the Raman technique.
Vol. 32-3 (2013), p. 309-315 [5] E.L.

El-Sayed et al. [26], Khalid et al. [65], and Vignesh et al. [63] .
El Hdiy, H.
El-Sayed, W.M.
El-Bassyouni, S.M.
Al-Shehri, S.

In this work, two time integration algorithms for the anisotropic damage model proposed by Lemaitre et al. [1] are compared.
For a comparison of different explicit (or strongly) nonlocal approaches see, e.g., de Vree et al. [11].
Most more recent works focus on gradient-extended damage models (e.g., Miehe et al. [12] or [13]), some of which can be shown to be equivalent to explicitly nonlocal approaches.
Some care must be taken when these implicit gradient models are implemented (e.g., Simone et al. [15]).
The product H s�H is defined by H s�H = 1 2 (HikHjl ei ⊗ ej ⊗ ek ⊗ el + HilHjk ei ⊗ ej ⊗ ek ⊗ el) . (10) For the plastic deformations the following von Mises yield function is applied Φ =
 
 
eσD
 
 
− √2 3 (σy + Q) , (11) where σy denotes the initial yield stress and Q describes isotropic hardening.

The state-of-the-art of DDBA method was provided in the book by Priestley et al. [2], while some considerations on the method can be seen in Sullivan and Calvi [5] and in Welch et al. [6], which we recommend.
The spectral intensity that causes Sd,el to develop can be then derived, once known the shape of elastic displacement response spectrum (Fig. 1d).
In this work, the simplified Judd and Fonseca’s model [14], modified as discussed in Loss et al. [15], is used.
On the other hand, the equivalent viscous damping is assumed of 18 %, as recommended by Filiatrault et al. [16], for an inter-storey drift of shear walls higher than 0.35 %, and it complies with the model proposed by Loss et al. [15].
From an estimated damping correction factor of 0.7, we have evaluated a final equivalent elastic spectral displacement capacity of Scap,el=158 mm.

Among them, Chandrasekhara and Namboodiri [15] carried out a study on mixed convection about inclined surfaces in a saturated porous media by taking only variable permeability, whereas, Mohammadein and El-Shaer [16] and Shivakumara et al [17] were discussed the combined effects of mixed convective flow over a semi-infinite vertical plate by taking into account of variable permeability, thermal conductivity, Soret, and Dufour.
Suresh Babu et al [21] have been discussed the effects of variable fluid properties for the vertical plate embedded in a sparsely packed porous medium.
Also, our results are compared with Nalinakshi et al. [21] in the absence of external magnetic field in Table-2 and found in good agreement up to six decimal places of accuracy for VP case.
Chamkha and Al-Humoud, Mixed convection heat and mass transfer of non-Newtonian fluids from a permeable surface embedded in a porous medium, Int.
El-Shaer, Influence of variable permeability on combined free and forced convection flow past a semi-infinite vertical plate in a saturated porous medium, Heat Mass Transfer, 40 (2004) 341-346

A preferred alternative is the Lagrange multiplier method that was first introduced by Hughes et al. [1] for contact-impact problems.
The first extension of the mortar FEM to the unilateral contact problem was made by Belgacem et al. [8] presenting a theoretical basis that was implemented by Hild [9].
These two blocks share the same elastic constants Eb and νb = 0.3, and the constitutive parameters for the layer are El = 1 and νl = 0.3 together with a friction coefficient µ = 0.25 between both materials.
Our interest is to investigate the effect of the stiffness ratio Eb/El on the contact forces and the solution algorithm efficiency.
Fig. 10: Effect of regularization in the convergence for Eb/El = 1000.

TRIP steels containing Mn, Si, Al, Mo, and Nb have been examined using a laboratory simulation of a continuous hot dipped galvanizing line.
This effect, however, would be expected to be minor compared to the effects of the Mn and Al in, for example, TRIP steels.
It is interesting to note that, based on the CCT diagrams, little if any athermal bainite was formed in any of the TRIP steels (Si-Al or the Al only) cooled at 15 °C/sec.
CCT curve for TRIP steel with 0.15C-1.5Mn-0.3Si-1.0 Al-0.15Mo-0.03Nb (CT=550°C), 770°C, 60 sec (35%γ) [12].
Aaronson et al., (AIME, Warrendale, PA, 1982), p. 855

Kim et al. [9] performed the dynamic approach for the tube bulging process, the predicted deformation shapes were verified with experimental results.
For the stability of the solution, t∆ must be limited within the size: ρννν )21)(1()1( −+− ==∆ EL c L t e e )5( eL , in Eq.(5), represents the characteristic length of element, and c , E ,νandρare the sound speed in the material, modulus of elasticity, Poisson's ratio, and the mass density, respectively.
Gouveia et al., Int.
Lu et al., J.
Harpell et al., J.

Lim, et al, Shape-Controlled Synthesis of Metal Nanocrysals: Simple Chemistry Meets Complex Physics?
El-Sayed, Gold Nanorods: From Synthesis and Properties to Biological and Biomedical Applications, Adv.
Wei, et al, Sensitive measurement of optical nonlinearities using a single beam, IEEE J.
El-Sayed, Preparation and Growth Mechanism of Gold Nanorods (NRs) Using Seed-Mediated Growth Method, Chem.
Cao, et al, Shape dependence of nonlinear optical behaviors of gold nanoparticles, Mater.