Lazreg Hadji^1,2,*, Fabrice Bernard³, Nafissa Zouatnia⁴

FDMP-Fluid Dynamics & Materials Processing, Vol.19, No.4, pp. 1043-1054, 2023, DOI:10.32604/fdmp.2022.022327

Abstract The bending and free vibration of porous functionally graded (PFG) beams resting on elastic foundations are analyzed. The material features of the PFG beam are assumed to vary continuously through the thickness according to the volume fraction of components. The foundation medium is also considered to be linear, homogeneous, and isotropic, and modeled using the Winkler-Pasternak law. The hyperbolic shear deformation theory is applied for the kinematic relations, and the equations of motion are obtained using the Hamilton’s principle. An analytical solution is presented accordingly, assuming that the PFG beam is simply supported. Comparisons with the open literature are implemented… More > Graphic Abstract

Wei Xia^1,2,*, Weilin Kong¹, Yupeng Feng¹, Shengping Shen^1,2,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.24, No.1, pp. 1-2, 2022, DOI:10.32604/icces.2022.08765

Abstract Post-buckling and panel flutter behaviors of ceramic-metal FGM plates are studied for the skins of supersonic aircrafts. The effects of asymmetric material and temperature distributions, as well as the aerodynamic loads, on the thermo-mechanical response of FGM plates are discussed using finite element simulations. The aero-thermo-elastic model is established by using the simple power law material distribution, the rule of mixture for material effective properties, the nonlinear Fourier equations of heat conduction, von-Karman strain-displacement nonlinear relations, and the piston theory for supersonic aerodynamics. The finite element equations are established using the first-order shear deformable plate elements. The thermal post-buckling equilibrium… More >

Xiaojun Huang^1,2, Liaojun Zhang^1,*, Renyu Ge², Hanbo Cui², Zhedong Xu²

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.1, pp. 23-41, 2022, DOI:10.32604/cmes.2022.019765

Abstract In the current research, an effective differential quadrature method (DQM) has been developed to solve natural frequency and vibration modal functions of circular section beams along radial functional gradient. Based on the high-order theory of transverse vibration of circular cross-section beams, lateral displacement equation was reconstructed neglecting circumferential shear stress. Two equations coupled with deflection and rotation angles were derived based on elastic mechanics theory and further simplified into a constant coefficient differential equation with natural frequency as eigenvalue. Then, differential quadrature method was applied to transform the eigenvalue problem of the derived differential equation into a set of algebraic… More >

Behrouz Karami¹, Maziar Janghorban¹, Timon Rabczuk^{2, *}

CMC-Computers, Materials & Continua, Vol.62, No.2, pp. 607-629, 2020, DOI:10.32604/cmc.2020.08032

Abstract This study investigates the forced vibration of functionally graded hexagonal nano-size plates for the first time. A quasi-three-dimensional (3D) plate theory including stretching effect is used to model the anisotropic plate as a continuum one where smallscale effects are considered based on nonlocal strain gradient theory. Also, the plate is assumed on a Pasternak foundation in which normal and transverse shear loads are taken into account. The governing equations of motion are obtained via the Hamiltonian principles which are solved using analytical based methods by means of Navier’s approximation. The influences of the exponential factor, nonlocal parameter, strain gradient parameter,… More >

Zhanqi Cheng¹, Dongdong Jin¹, Chengfang Yuan¹, Le Li^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.121, No.2, pp. 445-464, 2019, DOI:10.32604/cmes.2019.06374

Abstract In the research, the dynamic fracture failure problem of functionally graded materials (FGMs) containing two pre-cracks was analyzed using a bond-based Peridynamic (PD) method numerical model. The two convergence of decreasing the area of PD horizon (δ-convergence) and uniform mesh refinement (m-convergence) were studied. The effects of both crack position and distance between two cracks on crack propagation pattern in FGMs plate under tensile loads are studied. Furthermore, the effects of different gradient patterns on the dynamic propagation of cracks in FGMs are also investigated. The simulate results suggest that the cracks positions and the distance between them can significantly… More >

A.V. Ekhlakov², O.M. Khay², Ch. Zhang², J. Sladek³, V. Sladek³

Structural Durability & Health Monitoring, Vol.6, No.3&4, pp. 329-350, 2010, DOI:10.3970/sdhm.2010.006.329

Abstract In this paper, transient crack analysis in two-dimensional, isotropic, continuously non-homo -ge -neous and linear elastic functionally graded materials is presented. A boundary-domain element method based on boundary-domain integral representations is developed. The Laplace-transform technique is utilized to eliminate the dependence on time. Laplace-transformed fundamental solutions of linear coupled thermoelasticity for isotropic, homogeneous and linear elastic solids are applied to derive boundary-domain integral equations. The numerical implementation is performed by using a collocation method for the spatial discretization. The time-dependent numerical solutions are obtained by the Stehfest's inversion algorithm. For an edge crack in a finite domain under thermal shock,… More >

P.H. Wen¹, M.H. Aliabadi²

Structural Durability & Health Monitoring, Vol.8, No.3, pp. 223-248, 2012, DOI:10.32604/sdhm.2012.008.223

Abstract A mesh-free method for modelling crack growth in functionally graded materials is presented. Based on the variational principle of the potential energy, mesh-free method has been implemented with enriched radial bases interpolation functions to evaluate mixed-mode stress intensity factors, which are introduced to capture the singularity of stress at the crack tip. Paris law and the maximum principle stress criterion are adopted for defining the growth rate and direction of the fatigue crack growth respectively. The accuracy of the proposed method is assessed by comparison to other available solutions. More >

J. Sladek¹, V. Sladek, Ch.Zhang²

Structural Durability & Health Monitoring, Vol.1, No.2, pp. 131-144, 2005, DOI:10.3970/sdhm.2005.001.131

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-d), anisotropic and linear elastic solids with continuously varying material properties. Both quasi-static and transient elastodynamic problems are considered. For time-dependent problems, the Laplace-transform technique is utilized. A unit step function is used as the test function in the local weak-form. It is leading to local boundary integral equations (LBIEs) involving only a domain-integral in the case of transient dynamic problems. The analyzed domain is divided into small subdomains with a circular shape. The moving least-squares (MLS) method is adopted for approximating the physical… More >

K. Y. Liu^1,2, S. Y. Long^1,2,3, G. Y. Li¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.5, No.2, pp. 99-120, 2008, DOI:10.3970/icces.2008.005.099

Abstract A meshless local Petrov-Galerkin method (MLPG)^[1] for the analysis of cracks in isotropic functionally graded materials is presented. The meshless method uses the moving least squares (MLS) to approximate the field unknowns. The shape function has not the Kronecker Delta properties for the trial-function-interpolation, and a direct interpolation method is adopted to impose essential boundary conditions. The MLPG method does not involve any domain and singular integrals to generate the global effective stiffness matrix if body force is ignored; it only involves a regular boundary integral. The material properties are smooth functions of spatial coordinates and two interaction integrals^[2,3] are… More >

Wei Xia^1,2,*, Kun Wang¹, Haitao Yang¹, Shengping Shen¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.21, No.2, pp. 27-27, 2019, DOI:10.32604/icces.2019.05197

Abstract Panel flutter arises from the aeroelastic instability of the skin structures on the high-speed vehicles, usually in supersonic regime and combined with thermal environment. Unlike the catastrophic flutter of the wings, panel flutter tends to be treated as non-catastrophic one. The nonlinear panel flutter response is of great interest to find the fatigue loading spectra. Present work introduces an aeroelastic model for a thermal isolating panel made from functionally graded materials (FGMs). The Mindlin plate theory is employed to establish the structural equations, the first-order piston theory is adopted for the supersonic aerodynamic loads, and the von-Karman strain-displacement relation is… More >