Static and Dynamic Thermomechanical Buckling Loads of Functionally Graded Plates.

In the paper the buckling phenomenon for static and dynamic loading (pulse of finite duration) of FGM plates subjected to simultaneous action of one directional compression and thermal field is presented. Thin, rectangular plates simply supported along all edges are considered. The investigations are conducted for different values of volume fraction exponent and uniform temperature rise in conjunction with mechanical dynamic pulse loading of finite duration

Three-dimensional free vibration analysis of thermally loaded fgm sandwich plates

Using the finite element code ABAQUS and the user-defined material utilities UMAT and UMATHT, a solid brick graded finite element is developed for three-dimensional (3D) modeling of free vibrations of thermally loaded functionally gradient material (FGM) sandwich plates. The mechanical and thermal material properties of the FGM sandwich plates are assumed to vary gradually in the thickness direction, according to a power-law fraction distribution. Benchmark problems are firstly considered to assess the performance and accuracy of the proposed 3D graded finite element. Comparisons with the reference solutions revealed high efficiency and good capabilities of the developed element for the 3D simulations of thermomechanical and vibration responses of FGM sandwich plates. Some parametric studies are carried out for the frequency analysis by varying the volume fraction profile and the temperature distribution across the plate thickness

A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates

A new sinusoidal shear deformation theory is developed for bending, buckling, and vibration of functionally graded plates. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed sinusoidal shear deformation theory contains only four unknowns and has strong similarities with classical plate theory in many aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of plate are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton’s principle. The closed-form solutions of simply supported plates are obtained and the results are compared with those of first-order shear deformation theory and higher-order shear deformation theory. It can be concluded that the proposed theory is accurate and efficient in predicting the bending, buckling, and vibration responses of functionally graded plates

Post-buckling of functionally graded microplates under mechanical and thermal loads using isogeometric analysis

The present study uses the isogeometric analysis (IGA) to investigate the post-buckling behavior of functionally graded (FG) microplates subjected to mechanical and thermal loads. The modified a strain gradient theory with three length scale parameters is used to capture the size effect. The Reddy third-order shear deformation plate theory with the von Kámán nonlinearity (i.e., small strains and moderate rotations) is employed to describe the kinematics of the microplates. Material variations in the thickness direction of the plate are described using a rule of mixtures. In addition, material properties are assumed to be either temperature-dependent or temperature-independent. The governing equations are derived using the principle of virtual work, which are then discretized using the IGA approach, whereby a C2-continuity requirement is fulfilled naturally and efficiently. To trace the post-buckling paths, Newton’s iterative technique is utilized. Various parametric studies are conducted to examine the influences of material variations, size effects, thickness ratios, and boundary conditions on the post-buckling behavior of microplates

Non-linear thermal post-buckling analysis of FGM Timoshenko beam under non-uniform temperature rise across thickness

AbstractThe present work deals with geometrically non-linear post-buckling load–deflection behavior of functionally graded material (FGM) Timoshenko beam under in-plane thermal loading. Thermal loading is applied by providing non-uniform temperature rise across the beam thickness at steady-state condition. FGM is modeled by considering continuous distribution of metal and ceramic constituents across the thickness using power law variation of volume fraction. The effect of geometric non-linearity at large post-buckled configuration is incorporated using von Kármán type non-linear strain–displacement relationship. The governing equations are obtained using the minimum potential energy principle. The system of non-linear algebraic equations is solved using Broyden’s algorithm. Four different FGMs are considered. A comparative study for post-buckling load–deflection behavior in non-dimensional form is presented for different volume fraction exponents and also for different FGMs, each for different length–thickness ratios

Temperature-dependent nonlinear analysis of shallow shells: A theoretical approach

The paper presents a theoretical formulation for the computation of temperature-dependent nonlinear response of shallow shells with single and double curvatures subjected to transverse mechanical loads while being exposed to through-depth non-uniform heating regimes such as those resulting from a fire. The material nonlinearity arises from taking into consideration the degradation of the material elastic behaviour at elevated temperatures under quasi-static conditions. Two types of boundary conditions are considered, both of which constrain the transverse deflections and allow the rotations about the edge axis to be free. One of the boundary conditions permits lateral translation (laterally unrestrained) and the other one does not (laterally restrained). A number of examples are solved for shallow shells under different types of loading conditions including: an exponential "short hot" fire leading to a high temperature over a relatively short duration; and an exponential "long cool" fire of lower temperature over a longer duration. The limits of the shallow shell equations are investigated through comparison studies. Results show that while current numerical approaches for analysis of laterally restrained shallow shells are often computationally intensive, the proposed approach offers an adequate level of accuracy with a rapid convergence rate for such structures.The Edinburgh Research Partnership in Engineering (ERPE)