Oussama Bourihane

This paper aims to propose a new approach based on meshfree method to solve the dimensionless steady nonlinear natural convection equations. The solution methodology uses the moving least squares (MLS) shape functions to discretize the weak form of the governing equations and the Newton–Raphson algorithm to compute the nonlinear solution. Parametric studies of natural convection concerning closed two‐dimensional (2D) cavity with different operating conditions filled with air is used to assess the impact of the proposed approach on the performance of computed solutions. The cavity is formed by adiabatic and isothermal walls. For that, in all considered cases, the vertical sidewalls of the enclosure are heated differentially and maintained at hot and cold temperatures. The horizontal top and bottom walls are considered thermally insulated. The thermophysical properties of the working fluid are assumed to be constant except the density variations causing a body force term in the momentum equation. No‐slip boundary condition is applied at all enclosure boundaries and all internal body boundaries. The considered cases are described and analyzed in detail to check the validity of the proposed method. A comparison is performed between the results obtained from the present computer code and those available in the literature. The influence of various controlling parameters is analyzed and discussed graphically through the obtained streamlines, isotherms, and (maximum and average) Nusselt number. The numerical results computed by the proposed method are found to be in good agreement with the reference data.

The main objective of the present work is to couple the spectral Chebyshev differential quadrature method (SCDQM) to the high order continuation method (HOCM) which was proposed in previous works with several discretization techniques. This new approach (SCDQM‐HOCM) is proposed to analyze the nonlinear bending and buckling analysis of functionally graded sandwich beams. The originality of this work consists also to use a beam model which taken into account the nonlinear term neglected in several works of the literature. This term makes it possible to have the buckling and bending problems by using the classical Timoshenko model and to handle the boundary conditions that several works could not to take into account. A strong form of nonlinear equations is established based on the first order shear deformation theory of beams with the von‐Kármán kinematic hypothesis. Regarding functionally graded materials (FGM), two typical types are investigated: sandwich beam with FGM faces and ceramic core (Type‐A), and sandwich beam with FGM core and uniform faces (Type‐B). The accuracy and efficiency of the SCDQM‐HOCM compared with finite element method coupled with high order continuation method (FEM‐HOCM) are illustrated on numerical examples of the FGM beams and then the FG sandwich beams. Furthermore, a parametric study is led to carry out the influence of different skin‐core‐skin thickness ratios, span‐to‐height ratio, and volume fraction on the bending and buckling behavior of FG sandwich beams subjected to different loadings and various boundary conditions.

In this paper, the forced nonlinear dynamic behavior of functionally graded material (FGM) plate under external dynamic loads is analyzed by means of a high‐order implicit algorithm. The model is developed using the third‐order shear deformation plate kinematics (TSDT). Unlike previous works, in this contribution, the formulation is written without resorting to any homogenization technique neither rule of mixture nor considering FGM as a laminated composite. To handle integrals in the case of inhomogeneous FGMs, the stress vector is split to four parts and it is written in dimensionless form. The resulting equations of motion are established using the Hamilton principle. Finite element discretization is adopted using a four‐node quadrilateral element with seven degrees of freedom per node. The resolution of the nonlinear equations is made by a high‐order implicit algorithm based on the asymptotic numerical method (ANM) techniques. Numerical comparisons of vibration natural frequencies and dynamic response of FGM plates under external loading with literature and laminate composite modeling results are presented to validate the accuracy and the performance of the proposed model.