Thermal postbuckling of temperature-dependent sandwich beams with carbon nanotube-reinforced face sheets

Thermal postbuckling response of a sandwich beam made of a stiff host core and carbon nanotube (CNT)-reinforced face sheets is analyzed in this research. Distribution of CNTs across the thickness of face sheets may be uniform or functionally graded. Material properties of the constituents are considered as temperature dependent. Properties of the face sheets are obtained by means of a modified rule of mixture approach. First-order shear deformation theory and von Kármán type of geometrical nonlinearity are incorporated with the virtual displacement principle. Ritz method with polynomial basis functions is applied to the virtual displacement principle to obtain the matrix representation of the governing equations. An iterative displacement control algorithm is applied to solve the nonlinear eigenvalue problem and trace the postbuckling equilibrium path. It is shown that, graded profile of CNTs, length to thickness ratio, host thickness to face thickness ratio, volume fraction of CNTs, boundary conditions, and temperature dependency, all are important factors on critical buckling temperature and postbuckling equilibrium path of sandwich beams with CNT-reinforced face sheets. However, influence of host thickness to face thickness ratio is ignorable.     

Thermal buckling of temperature-dependent composite super elliptical plates reinforced with carbon nanotubes

In this work, the problem of thermal buckling of composite plates reinforced with carbon nanotubes (CNTs) is investigated. Distribution of CNTs as reinforcements through the thickness direction of the plate is assumed to be either uniform or functionally graded (FG). Properties of the reinforcement and matrix are both temperature dependent. Properties of the composite media are obtained according to a refined rule of mixture approach where the e?ciency parameters are introduced. The plate is in a super elliptical shape where the simple elliptical shape and rectangular shapes are obtained as especial cases. In these types of plates due to the round corners, stress concentration phenomenon is eliminated. Based on the Ritz method where the shape functions are of the polynomial type, the governing equations are obtained. These equations are solved using an iterative eigenvalue problem since the properties are temperature dependent. Numerical results are validated for the simple case of an isotropic plate. Novel numerical results are provided for plates reinforced with CNTs in different shapes, various volume fractions and different patterns of CNT distribution. It is shown that FG-X pattern of CNTs in matrix results in the maximum critical buckling temperature.     

Geometrically Non-Linear Rapid Heating of Temperature-Dependent Circular FGM Plates

Based on the uncoupled thermoelasticity assumptions, axisymmetric thermally induced vibrations of a circular plate made of functionally graded materials (FGMs) are analyzed. Each thermomechanical property of the circular plate is assumed to be functions of temperature and thickness coordinate. Solution of the transient one-dimensional heat conduction equation with the arbitrary type of time-dependent boundary conditions is carried out employing the central finite difference method combined with the Crank–Nicolson time marching scheme. Afterwards, with the establishment of the associated Hamilton's principle and the accountancy of the von Kármán type of geometrical non-linearity, the motion equations are obtained with the aid of the conventional multi-term Ritz method. The solution of highly coupled non-linear motion equations is obtained utilizing a hybrid iterative Newton–Raphson–Newmark scheme. After validating the developed computer code, some parametric studies are accomplished to show the influences of various involved parameters. It is shown that temperature dependency, geometrical non-linearity, plate thickness, power law index, and the type of thermal in-plane and out-of-plane mechanical boundary conditions, all affect the temporal evolution of plate characteristics.     

Thermal post-buckling behavior of simply supported sandwich panels with truss cores

This article presents a thermal post-buckling solution for sandwich panels with truss cores under simply supported conditions, when subjected to uniform temperature rise. The Reissner assumptions are adopted and truss cores are assumed to be continuous and homogeneous. Differential governing equations are developed based on the variational principle. The perturbation technique is employed to determine the thermal post-buckling path of sandwich panels with truss cores. Based on the present method, influences of truss core configuration, relative density, aspect ratio, and initial imperfection on the thermal post buckling behavior are discussed.     

Axisymmetric nonlinear rapid heating of FGM cylindrical shells

Large amplitude thermally induced vibrations of cylindrical shells made of a through-the-thickness functionally graded material (FGM) are investigated in the current research. All of the thermo-mechanical properties of the FGM shell are assumed to be functions of temperature and thickness coordinate. Shell is subjected to rapid surface heating on the ceramic-rich surface while the other surface of the shell is kept at reference temperature. One dimensional heat conduction equation is constructed and solved by means of a hybrid finite difference-Crank–Nicolson algorithm. The constructed heat conduction equation is nonlinear since the thermal conductivity is temperature dependent. With the aid of first-order shear deformation shell theory under the axisymmetric Donnell kinematic assumptions and von Kármán type of strain-displacement relations, the total energy of the shell is established. Implementing the conventional Ritz method, a set of nonlinear coupled algebraic equations are obtained which govern the dynamics of the shell under thermal shock. These equations are solved in time domain using the Newmark time marching scheme and the simple Picard successive method. Parametric studies are given to explore the dynamics of an FGM cylindrical shell under thermal shock.     

Thermal buckling of temperature-dependent FG-CNT-reinforced composite skew plates

Critical buckling temperatures of skew plates made from a polymeric matrix reinforced by single-walled carbon nanotubes (CNTs) are obtained in the present research. Reinforcements are distributed across the thickness of the plate uniformly or according to a prescribed nonuniform function. All of the thermomechanical properties are assumed to be temperature dependent. First-order shear deformation plate theory is used as the basic assumption to obtain the total strain and potential energies of the plate due to the thermally induced prebuckling loads. A transformation is proposed to express the components of the displacement field in an oblique coordinate system. A Ritz-based solution is implemented to obtain the matrix representation of the stability equations associated to the onset of buckling. Gram–Schmidt process is used to obtain a set of orthogonal shape functions as the basis polynomials of the Ritz method. The obtained eigenvalue problem is solved successively to extract the critical buckling temperature of the skew plate. Convergence and comparison studies are provided to assure the accuracy and correctness of the proposed formulation. Afterward, parametric studies are given to explore the influences of boundary conditions, CNT volume fraction, CNT dispersion profile, aspect ratio, skew angle, and side to thickness ratio.     

Thermal buckling analysis of moderately thick FGM plates based on the von Kármán nonlinearity and improved third order shear deformation theory

Abstract

In this study, thermal buckling of moderately thick functionally graded rectangular plates with all edges simply supported is analyzed by means of an improved third order shear deformation theory (improved TSDT). The plate is assumed to be under two types of thermal loadings, namely; uniform temperature rise and nonlinear temperature change across the thickness. The equilibrium and stability equations are derived based on the von Kármán type of geometrical nonlinearity and the improved third-order theory. By solving the stability equations, the value of buckling temperature difference is obtained. To calculate the critical buckling temperature difference, this value is minimized with respect to the half-wave parameters. The results are compared with the known data in literatures. The results indicate that, the values of critical buckling temperature difference which are obtained based on the improved TSDT, are lower in comparison with those obtained based on TSDT. Also, the results show that incorporation of the von Kármán type of geometrical nonlinearity with the improved third-order theory, gives the lower values of the critical buckling temperature difference.