Dynamic buckling of a thin thermoviscoplastic rectangular plate (original) (raw)
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Equilibrium and stability equations of a thin rectangular plate with length a, width b, and thickness h(x)=C1x+C2, made of functionally graded materials under thermal loads are derived based on the first order shear deformation theory. It is assumed that the material properties vary as a power form of thickness coordinate variable z. The derived equilibrium and buckling equations are then solved analytically for a plate with simply supported boundary conditions. One type of thermal loading, uniform temperature rise and gradient through the thickness are considered, and the buckling temperatures are derived. The influences of the plate aspect ratio, the relative thickness, the gradient index and the transverse shear on buckling temperature difference are all discussed.
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International Journal of Mechanical Sciences, 2014
Bifurcation behaviour of moderately thick heated annular plates made of FGMs is discussed in this study. Properties of the graded plate are distributed across the thickness based on the simple power law form. Temperature-dependency of the material properties is also taken into account. Two types of frequently used thermal loading, i.e. uniform temperature rise and heat conduction across the thickness loadings are considered. General nonlinear equilibrium equations based on the first order shear deformation plate theory (FSDT) and the associated boundary conditions are obtained employing the static version of the virtual displacements method. The pre-buckling solution is accomplished and the proper boundary conditions are chosen to assure the occurrence of bifurcation phenomenon. Stability equations are obtained based on the adjacent equilibrium criterion. Five resulted stability equations are decoupled and reduced to new equations in terms of lateral deflection and the edge zone functions. An exact asymmetrical solution is developed to calculate the critical buckling temperature difference of the plate for the above-mentioned cases of thermal loading. It is shown that the fundamental buckled configuration of annular plates may be asymmetric as previously assumed.
Computers & mathematics with applications, 2018
In this investigation, the asymmetrical buckling behaviour of FGM annular plates resting on partial Winkler-type elastic foundation under uniform temperature elevation is investigated. Material properties of the plate are assumed to be temperature dependent. Each property of the plate is graded across the thickness direction using a power law function. First order shear deformation plate theory and von Kármán type of geometrical nonlinearity are used to obtain the equilibrium equations and the associated boundary conditions. Prebuckling deformations and stresses of the plate are obtained considering the deflection-less conditions. Only plates which are clamped on both inner and outer edges are considered. Applying the adjacent equilibrium criterion, the linearised stability equations are obtained. The governing equations are divided into two sets. The first set, which is associated with the in-contact region and the second set which is related to contact-less region. The resulting equations are solved using a hybrid method, including the analytical trigonometric functions through the circumferential direction and generalised differential quadratures method through the radial direction. The resulting system of eigenvalue problem is solved iteratively to obtain the critical conditions of the plate, the associated circumferential mode number and buckled shape of the plate. Benchmark results are given in tabular and graphical presentations dealing with critical buckling temperature and buckled shape of the plate. Numerical results are given to explore the effects of elastic foundation, foundation radius, plate thickness, plate hole size, and power law index of the graded plate. It is shown that, stiffness foundation, and radius of foundation may change the buckled shape of the plate in both circumferential and radial directions. Furthermore, as the stiffness of the foundation or radius of foundation increases, critical buckling temperature of the plate enhances.
Static and Dynamic Thermomechanical Buckling Loads of Functionally Graded Plates
Mechanics and Mechanical Engineering, 2013
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.