Analytical solution for bending and buckling analysis of functionally graded plates using inverse trigonometric shear deformation theory

A new inverse trigonometric shear deformation theory for isotropic and functionally graded sandwich plates

Dynamic response of functionally graded plates under moving heat source

Buckling analysis of three dimensional braided composite plates under uniaxial loading using Inverse Hyperbolic Shear Deformation Theory

On the effects of coupling between in-plane and out-of-plane vibrating modes of smart functionally graded circular/annular plates

An efficient C0 finite element modeling of an inverse hyperbolic shear deformation theory for the flexural and stability analysis of laminated composite and sandwich plates

Imperfection sensitivity in the nonlinear vibration of functionally graded plates

Enhanced meshfree method with new correlation functions for functionally graded plates using a refined inverse sin shear deformation plate theory

Static analysis of orthotropic functionally graded (FG) elastic, rectangular, and simply supported (diaphragm) plates under transverse loads is presented based on a higher order shear and normal deformation theory (HOSNT). Although functionally graded materials (FGMs) are highly heterogeneous in nature, they are generally idealized as continua with mechanical properties changing smoothly with respect to the spatial coordinates. The material properties of FG plates are assumed here to be varying through the thickness of the plate in a continuous manner. The Poisson’s ratios of the FG plates are assumed to be constant, but their Young’s moduli vary continuously in the thickness direction according to the volume fraction of constituents, which are mathematically modeled as an exponential function. The governing equations of equilibrium for the FG plates are derived on the basis of a HOSNT assuming varying material properties. Numerical solutions are obtained by the use of the Navier solution method. ...

Thermal buckling of functionally graded plates according to a 2D higher-order deformation theory

Analytical and finite element modeling of laminated composite and sandwich plates: An assessment of a new shear deformation theory for free vibration response

In the present work, the inverse trigonometric shear deformation theory (ITSDT) is applied to analytically perform the free vibration and buckling analysis of functionally graded (FG) sandwich plate. The governing equations are derived using the principle of virtual work, incorporating linear structural kinematics and the generalized Hooke’s law. These equations are solved in closed form for simply supported boundary conditions to obtain the buckling and vibration response. For the analysis, two types of FG sandwich plates are considered i.e., Type – A and Type – B. For the Type – A plate, the core and face sheets of the FG sandwich plate are made up of Ceramic and FG material, respectively. Whereas in case of Type- B plate, the core is composed of FG material, while the top and bottom face sheets are made up of ceramic and metal, respectively. The power law is employed to vary the material properties in the FG material. The evaluated results for the FG sandwich Type – A plate are compared with the already reported results in the literature wherever possible and are found in good agreement. The influence of the various parameters such as span to thickness (a/h), aspect ratio (a/b), power law index (p) and core thickness (schemes) are investigated on the dimensionless fundamental frequency and dimensionless critical buckling load of the FG sandwich plate, on those basis, noteworthy conclusions are drawn.

In the present study, the static and free vibration analysis of functionally graded carbon nano-tubes reinforced (FG-CNTR) sandwich plates are studied in the framework of inverse hyperbolic shear deformation theory. The governing differential equations are derived using Hamilton’s principle and solved with the Navier’s solution technique. The analytical approach is used to obtain the deflections, stresses, natural frequencies, and corresponding mode shapes of FG-CNTR sandwich plates with different material properties, stacking sequences, span thickness ratios, core to face sheet thickness ratios, and loading conditions. Different types of reinforcement distribution such as uniformly distribution (UD) and functionally graded (FG) distribution of FG-O, FG-X, FG-/\, and FG-V are considered for the analysis. Also, the efforts are made to achieve the best possible arrangement for the stacking sequences and the appropriate reinforcement distribution that will produce improved static and free vibration responses for the FG-CNTR sandwich plates.

This comprehensive textbook compiles cutting-edge research on beams and circular plates, covering theories, analytical solutions, and numerical solutions of interest to students, researchers, and engineers working in industry. Detailing both classical and shear deformation theories, the book provides a complete study of beam and plate theories, their analytical (exact) solutions, variational solutions, and numerical solutions using the finite element method. Beams and plates are some of the most common structural elements used in many engineering structures. The book details both classical and advanced (i.e., shear deformation) theories, scaling in complexity to aid the reader in self-study, or to correspond with a taught course. It covers topics including equations of elasticity, equations of motion of the classical and first-order shear deformation theories, and analytical solutions for bending, buckling, and natural vibration. Additionally, it details static as well as transient response based on exact, the Navier, and variational solution approaches for beams and axisymmetric circular plates, and has dedicated chapters on linear and nonlinear finite element analysis of beams and circular plates. Theories and Analyses of Beams and Axisymmetric Circular Plates will be of interest to aerospace, civil, materials, and mechanical engineers, alongside students and researchers in solid and structural mechanics.

Finite element formulation of a generalized higher order shear deformation theory for advanced composite plates

An assessment of a non-polynomial based higher order shear and normal deformation theory for vibration response of gradient plates with initial geometric imperfections