A critical review of recent research on functionally graded plates

THE appearance of a treatise in English upon the mathematical theory of elasticity is an event the potential importance of which may be judged by the that the author, in his frequent suggestions for collateral reading, refers to only three such, those of Southwell, Timoshenko, and Love. In spirit and content Sokolnikoff}s book differs greatly from each and all of these. It may be described by a possible sub-title: “A pure mathematician surveys topics related to certain problems in the mathematical theory of elasticity”. It is symptomatic of the change in outlook of American mathematics over the past few decades. Mathematical Theory Of Elasticity Prof. I. S. Sokolnikoff with the collaboration of Asst. Prof. R. D. Speche. Pp. xi + 373. (New York and London: McGraw-Hill Book Co., Inc., 1946.) 22s. 6d.

Mathematical Theory Of Elasticity

A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates

In this paper the authors derive a higher-order shear deformation theory for modeling functionally graded plates accounting for extensibility in the thickness direction. The explicit governing equations and boundary conditions are obtained using the principle of virtual displacements under Carrera’s Unified Formulation. The static and eigenproblems are solved by collocation with radial basis functions. The efficiency of the present approach is assessed with numerical results including deflection, stresses, free vibration, and buckling of functionally graded isotropic plates and functionally graded sandwich plates.

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Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique

A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates

The present work evaluates the effect of thickness stretching in plate/shell structures made by materials which are functionally graded (FGM) in the thickness directions. That is done by removing or retaining the transverse normal strain in the kinematics assumptions of various refined plate/shell theories. Variable plate/shell models are implemented according to Carrera’s Unified Formulation. Plate/shell theories with constant transverse displacement are compared with the corresponding linear to fourth order of expansion in the thickness direction ones. Single-layered and multilayered FGM structures have been analyzed. A large numerical investigation, encompassing various plate/shell geometries as well as various grading rates for FGMs, has been conducted. It is mainly concluded that a refinements of classical theories that include additional in-plane variables could results meaningless unless transverse normal strain effects are taken into account.

Effects of thickness stretching in functionally graded plates and shells

This book deals with the Finite Element Method for the analysis of elastic structures such as beams, plates, shells and solids. The modern approach of Unified Formulation (UF), as proposed by the lead author, deals with the consideration of one-dimensional (beams), two-dimensional (plates and shells) and three-dimensional (solids) elements. Applications are given for structures which are typically employed in civil, mechanical, and aerospace engineering fields. Additional topics include mixed order elements, extension to layered composite structures, and the analysis of multifield problems involving mechanical, electrical and thermal loadings.

Finite Element Analysis of Structures through Unified Formulation

Finite Element Analysis of Structures Through Unified Formulation: Carrera/Finite

In this paper, the static and free vibration analysis of laminated shells is performed by radial basis functions collocation, according to a sinusoidal shear deformation theory (SSDT). The SSDT theory accounts for through-the-thickness deformation, by considering a sinusoidal evolution of all displacements with the thickness coordinate. The equations of motion and the boundary conditions are obtained by the Carrera’s Unified Formulation, and further interpolated by collocation with radial basis functions.

Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations

Maria Cinefra

Papers

A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates

Effects of thickness stretching in functionally graded plates and shells

Finite Element Analysis of Structures through Unified Formulation

Finite Element Analysis of Structures Through Unified Formulation: Carrera/Finite

Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations