• Steel and Composite Structures
• /
• v.25 no.4
• /
• pp.389-401
• /
• 2017

In this work, a new higher shear deformation theory (HSDT) is developed for the free vibration and buckling of functionally graded (FG) sandwich plates. The proposed theory presents a new displacement field by using undetermined integral terms. Only four unknowns are employed in this theory, which is less than the classical first shear deformation theory (FSDT) and others HSDTs. Equations of motion are obtained via Hamilton's principle. The analytical solutions of FG sandwich plates are determined by employing the Navier method. A good agreement between the computed results and the available solutions of existing HSDTs is found to prove the accuracy of the developed theory.

• Structural Engineering and Mechanics
• /
• v.57 no.1
• /
• pp.127-140
• /
• 2016

In this paper, a new first shear deformation plate theory based on neutral surface position is developed for the static and the free vibration analysis of functionally graded plates (FGPs). Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher order shear deformation theories. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Based on the present shear deformation plate theory and the neutral surface concept, the governing equations are derived from the principle of Hamilton. There is no stretching-bending coupling effect in the neutral surface based formulation. Numerical illustrations concern flexural and dynamic behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, length to thickness ratios. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Structural Engineering and Mechanics
• /
• v.49 no.6
• /
• pp.793-810
• /
• 2014

This research work deals with the development of a new Triangular finite element for the linear analysis of plate bending with transverse shear effect. It is developed in perspective to building shell elements. The displacements field of the element has been developed by the use of the strain-based approach and it is based on the assumed independent functions for the various components of strain insofar as it is allowed by the compatibility equations. Its formulation uses also concepts related to the fourth fictitious node, the static condensation and analytic integration. It is based on the assumptions of tick plate.s theory (Reissner-Mindlin theory). The element possesses three essential external degrees of freedom at each of the four nodes and satisfies the exact representation of the rigid body modes of displacements. As a result of this approach, a new bending plate finite element (Pep43) which is competitive, robust and efficient.

• Steel and Composite Structures
• /
• v.18 no.4
• /
• pp.1063-1081
• /
• 2015

In this paper, a new nonlocal hyperbolic refined plate model is presented for free vibration properties of functionally graded (FG) plates. This nonlocal nano-plate model incorporates the length scale parameter which can capture the small scale effect. The displacement field of the present theory is chosen based on a hyperbolic variation in the in-plane displacements through the thickness of the nano-plate. By dividing the transverse displacement into the bending and shear parts, the number of unknowns and equations of motion of the present theory is reduced, significantly facilitating structural analysis. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG nano-plate are computed using Mori-Tanaka homogenization scheme. The governing equations of motion are derived based on the nonlocal differential constitutive relations of Eringen in conjunction with the refined four variable plate theory via Hamilton's principle. Analytical solution for the simply supported FG nano-plates is obtained to verify the theory by comparing its results with other available solutions in the open literature. The effects of nonlocal parameter, the plate thickness, the plate aspect ratio, and various material compositions on the dynamic response of the FG nano-plate are discussed.

• Structural Engineering and Mechanics
• /
• v.26 no.1
• /
• pp.43-68
• /
• 2007

Using the Mindlin-Reissner plate theory, many quadrilateral plate bending elements have been developed so far to analyze thin and moderately thick plate problems via displacement based finite element method. Here new formulation has been made to analyze thin and moderately thick plate problems using force based finite element method called Integrated Force Method (IFM). The IFM is a novel matrix formulation developed in recent years for analyzing civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper the force based new bilinear quadrilateral plate bending element (MQP4) is proposed to analyze the thin and moderately thick plate bending problems using Integrated Force Method. The Mindlin-Reissner plate theory has been used in the formulation of this element which accounts the effect of shear deformation. Standard plate bending benchmark problems are analyzed using the proposed element MQP4 via Integrated Force Method to study its performance with respect to accuracy and convergence, and results are compared with those of displacement based 4-node quadrilateral plate bending finite elements available in the literature. The results are also compared with the exact solutions. The proposed element MQP4 is free from shear locking and works satisfactorily in both thin and moderately thick plate bending situations.

• Coupled systems mechanics
• /
• v.9 no.6
• /
• pp.575-597
• /
• 2020

Equilibrium equations of a porous FG plate resting on Winkler-Pasternak foundations with various boundary conditions are derived using a new refined shear deformation theory. Different types of porosity distribution rate are considered. Governing equations are obtained including the plate-foundation interaction. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The novel rule of mixture is proposed to describe and approximate material properties of the FG plates with different distribution case of porosity. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature. Effects of variation of porosity distribution rate, boundary conditions, foundation parameter, power law index, plate aspect ratio, side-to-thickness ratio on the deflections and stresses are all discussed.

• Steel and Composite Structures
• /
• v.13 no.1
• /
• pp.91-107
• /
• 2012

In this research, mechanical buckling of hybrid functionally graded plates is considered using a new four variable refined plate theory. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. Governing equations are derived from the principle of minimum total potential energy. The closed-form solution of a simply supported rectangular plate subjected to in-plane loading has been obtained by using the Navier method. The effectiveness of the theories is brought out through illustrative examples.

• Steel and Composite Structures
• /
• v.21 no.1
• /
• pp.123-136
• /
• 2016

This work focuses on the behavior of the static analysis of functionally graded plates materials (FGMs) with porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose a new refined plate theory is used in this work, it contains only four unknowns, unlike five unknowns for other theories. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The parabolic distribution of transverse shear stresses along the thickness of the plate is taken into account in this analysis; the material properties of the FGM plate vary a power law distribution in terms of volume fraction of the constituents. The rule of mixture is modified to describe and approximate material properties of the FG plates with porosity phases. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature, the influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.

• Structural Engineering and Mechanics
• /
• v.5 no.1
• /
• pp.69-83
• /
• 1997

A new efficient hybrid/mixed thin~moderately thick plate bending element with 6-node (HM6-14) is formulated based on the Reissner-Mindlin plate bending theory. The convergence of this element is proved by error estimate theories and verified by patch test respectively. Numerical studies on such an element as HM6-14 demonstrate that it has remarkable convergence, invariability to geometric distorted mesh situations, to axial rotations, and to node positions, and no "locking" phenomenon in thin plate limit. The present element is suitable to many kinds of shape and thin~moderately thick plate bending problems. Further, in comparison with original hybrid/mixed plate bending element HP4, the present element yields an improvement of solutions. Therefore, it is an efficient element and suitable for the development of adaptive multi-field finite element method (FEM).

• Structural Engineering and Mechanics
• /
• v.75 no.2
• /
• pp.193-209
• /
• 2020

This paper presents a new hyperbolic shear deformation plate theory including the stretching effect for free vibration of the simply supported functionally graded plates in thermal environments. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. This theory has only five unknowns, which is even less than the other shear and normal deformation theories. The present one has a new displacement field which introduces undetermined integral variables. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume power laws of the constituents. The equation of motion of the vibrated plate obtained via the classical Hamilton's principle and solved using Navier's steps. The accuracy of the proposed solution is checked by comparing the present results with those available in existing literature. The effects of the temperature field, volume fraction index of functionally graded material, side-to-thickness ratio on free vibration responses of the functionally graded plates are investigated. It can be concluded that the present theory is not only accurate but also simple in predicting the natural frequencies of functionally graded plates with stretching effect in thermal environments.