Bending Analysis Of Plates Research Articles

An enrichment technique for bending analysis of in-plane heterogeneous thin plates with weak singularities

An enrichment technique for bending analysis of in-plane heterogeneous thin plates with weak singularities

Nonlinear bending analysis of carbon nanotube-reinforced composite plates in combined thermal and mechanical loading

Nonlinear bending analysis of carbon nanotube-reinforced composite plates in combined thermal and mechanical loading

Bending analyses of piezoelectric-piezomagnetic bi-layered composite plates based on the modified strain gradient theory

Bending analyses of piezoelectric-piezomagnetic bi-layered composite plates based on the modified strain gradient theory

New finite modelling of the nonlinear static bending analysis of piezoelectric FG sandwich plates resting on nonlinear elastic foundations

This paper presents a new finite modelling of the nonlinear static bending analysis of piezoelectric functionally graded (FG) sandwich plates resting on nonlinear elastic foundations. Finite element formulations are derived by using the first-order shear deformation theory (FSDT) of Mindlin and the finite element method. The proposed theory and mathematical model of this work are verified by comparing the results with those of other methods, and they are in good agreement. A parameter study is conducted to investigate the effects of geometrical and physical properties such as nonlinear factors, volume fraction index, nonlinear foundation parameters, applied voltages, boundary conditions, etc., on the nonlinear mechanical behaviors of piezoelectric FG sandwich plates. The novel numerical results of this work are very important, and can be used as a good reference to examine related structures as well as of use in engineering practice.

Iteration Procedure for the Analysis of Plates in Bending by Finite Strip Method. (Dept. C)

Iteration Procedure for the Analysis of Plates in Bending by Finite Strip Method. (Dept. C)

Static and dynamic NURBS-based isogeometric analysis of composite plates under hygrothermal environment

In this paper, a computationally efficient isogeometric plate model, employing nonpolynomial shear deformation theory (NPSDT), for static and dynamic analysis of laminated and sandwich composite plates under hygrothermal environment is presented. Transient and steady-state response using Rayleigh damping model and fast Fourier transformation of transient response have also been obtained for the hygrothermal environment. The non-uniform rational B-splines (NURBS) based formulation has been considered, which attribute only five-degree of freedom and satisfies the stringent continuity requirement of the NPSDT model (C1-continuity) without any additional variables. A total Lagrangian approach in conjunction with Hamilton’s principle is utilized to formulate the governing equations for thermal bending and subsequent dynamic analysis of multilayered composite plates. To model stress stiffening effect due to hygrothermal load, both von Kármán and Green–Lagrange strain displacement relations are incorporated and obtained solutions are compared. It has been shown that at higher temperature (around one fourth of the critical buckling temperature), the consideration of Green–Lagrange strain relationship for modeling stiffening effect due to hygrothermal load is important for better accuracy. Further, it has been shown that bending strip is essential in case of higher-order shear deformation theory (HSDT) to get more accurate solution. In addition, the obtained transient damped/undamped solutions may be used to get the natural frequency from their FFT solution.

A new meshless approach for bending analysis of thin plates with arbitrary shapes and boundary conditions

A new meshless approach for bending analysis of thin plates with arbitrary shapes and boundary conditions

Finite element formulation for piezoelectric semiconductor plates

Piezoelectric semiconductor plates with both semiconducting and piezoelectric properties are widely used in micro-electromechanical systems. However, it is difficult to obtain theoretical solutions due to the complexity of the mathematics required to describe these systems. In this paper, finite element formulation is present for numerical analysis of piezoelectric semiconductor plate. A plate model using a first-order Mindlin series expansion was employed. Standard Galerkin weak form was derived and discretization equations were obtained. The proposed method was verified by a custom partial-differential-equation module of COMSOL Multiphysics. Numerical analysis revealed that the deflection, electric potential, and current density of the piezoelectric semiconductor were sensitive to the initial carrier concentration within a certain range, and that the initial carrier concentration influenced the dimensionless electric displacement intensity factor of the crack tip. By allowing bending analysis of piezoelectric semiconductor plates, our numerical approach will be valuable for guiding the design of piezoelectric semiconductor structures.

Three-Dimensional Bending Analysis of Multi-Layered Orthotropic Plates by Two-Dimensional Numerical Model.

The paper presents effective numerical modelling of multi-layered plates with orthotropic properties. The method called the FEM23 is employed to construct the numerical model. The approach enables a full 3D analysis to be performed while using a 2D finite element mesh. The numerical model for a multi-layered plate is constructed by an assembling procedure, where each layer with orthotropic properties is added to the global numerical model. The paper demonstrates that the FEM23 method is very flexible in defining the multilayered plate, where the thickness of each layer as well as its mechanical orthotropic properties can be defined independently. Several examples of three-layered or nine-layered plates are analyzed in this paper. The results obtained by the FEM23 method coincide with the ones taken from the published papers or calculated with the standard 3D FEM approach. The orthotropic version of the FEM23 can be quite easily applied for other kinds of problems including thermo-mechanics, free vibrations, buckling analysis, or delamination.

Nonlinear bending analysis of fgp plates under various boundary conditions using an analytical approach

In this paper, the nonlinear bending behavior of functionally graded porous (FGP) plates under uniformly distributed transverse loads is studied based on the neutral surface concept within the framework of first-order shear deformation theory (FSDT) including geometrical nonlinearity. The FGP materials with three porosity distribution patterns namely uniform, non-uniform symmetric and non-uniform asymmetric are considered. Using the stress function and Galerkin method, the analytical solutions are obtained to examine the load vs deflection and load vs bending moment curves for various edges boundary conditions. The present results are compared with reference solutions to show the accuracy and the effectiveness of the proposed approach. The effects of the geometric, material parameters, elastic foundations and in-plane constraints on the nonlinear bending behavior of FGP plates are studied in detail through numerical investigations.

A GFDM with supplementary nodes for thin elastic plate bending analysis under dynamic loading

This work proposes a meshless generalized finite difference method (GFDM) with supplementary nodes for the solution of thin elastic plate bending under dynamic loading. The first- and second-order time derivatives in equilibrium equation are firstly discretized with the Houbolt method. The numerical solution of the resulting spatial problem at each time step is then calculated by the GFDM. The supplementary nodes on the boundary of the problem domain are introduced in the GFDM to yield the well-determined linear system of equations. Numerical example is provided to verify the accuracy and the stability of the developed approach, and these preliminary results reveal the potential of the method.

Plate-Bending Analysis by NURBS-Based Scaled Boundary Finite-Element Method

AbstractThis paper extends the idea of using nonuniform rational B-splines (NURBS) based shape functions in the scaled boundary finite-element method (SBFEM) to plate bending formulations, which in...

A novel model and solution on the bending problem of arbitrary shaped magnetoelectroelastic plates based on the modified strain gradient theory

A size-dependent magnetoelectroelastic (MEE) plate bending model is established where the governing equations and concrete forms of three different mechanical boundary conditions under modified strain gradient theory are derived by the variational principle. Then, the meshless method of polynomial particular solutions is further developed to solve this bending problem. Finally, the influences of size effect, mechanical-electric-magnetic coupling loads, and Pasternak foundation on the bending properties of MEE plates are detailed discussed by some typical numerical examples. Of importance, by virtue of the general applicability and superior flexibility of current method, the bending analyses of MEE plates under different mechanical boundary conditions and geometrical shapes can be carried out, and some novel conclusions are concluded.

Elastic-viscoplastic analysis of plate bending with Reissner's theory by the Boundary Element Method

The development of a formulation of the Boundary Element Method (BEM) for application to elastic-viscoplastic analysis of plate bending is presented in this work. Reissner's theory is used, valid for thin and thick plates. Initially, Reissner's plate bending theory is presented, including the consideration of physical nonlinearity, and then, integral equations applied to Reissner's plates are shown. The theory for considering viscoplasticity is presented, as well as the procedures for its use with the BEM. In order to solve the equations that govern the problem, an incremental procedure is used and von Mises’ and Tresca's yield criteria are considered. This process offers an alternative method of solution for elasto-plastic problems, when steady-state condition is reached. Numerical examples are presented and results are compared with available solutions.

Analytical non-linear analysis of functionally graded sandwich solid/annular sector plates

Nonlinear behavior of functionally graded (FG) sandwich circular sector plates with simply supported radial edges under transverse loading is investigated using the first-order shear deformation theory with von Karman geometric nonlinearity. The nonlinear governing equations are reformulated and solved via single-parameter perturbation and Fourier series methods. Verification is performed by comparing numerical results with the available ones in the literature and the ones obtained via ABAQUS code. The effects of non-linearity, material constant, lay-up, and boundary conditions on bending of FG sandwich sector plates with FG core/homogenous face sheets and metallic core/FG face sheets are studied. It is shown that in sandwich plates with an FG core, the deflection and maximum tensile stress decrease by using thinner homogenous face sheets and in ones with a metallic core, increasing the thickness of FG face sheets reduces the maximum tensile and compressive stresses, while the total thickness is considered the same in all layups. Furthermore, in bending analysis of FG sandwich sector plates, linear theory is adequate for w/h<1 in plates with free circular edges, it is solely applicable for w/h<0.2 in plates with clamped circular edges and is inadequate for analysis of fully simply supported FG sandwich sector plate.

Plane Stress Analysis of Simply Supported Rectangular Plates by The Nodal Line Finite Difference Method.(Dept.C)

The nodal line finite difference method developed earlier by the author has been successfully applied to bending analysis of rectangular plates. In the present work, the method is extended to solve plane stress problems of rectangular plates. The analysis deals with the in-plane displacements and requires the solution of two simultaneous second-order partial differential equations. These equations are transformed into two simultaneous ordinary differential equations which in turns are cast in two simultaneous nodal line difference equations. Numerical results obtained by the finite strip method and this indicates the applicability and the power of the present technique.

Nodal Line Finite Difference Method in The Analysis of Rectangular Plates on Elastic Foundation.(Dept.C)

A nodal line finite difference bending analysis of isotropic rectangular plates with free lateral boundary conditions. Using the nodal line finite difference method, is presented. The analysis describes the linear elastic behavior of rectangular plates resting on a winkler type ipundation and loaded on its upper surface with arbitrary transverse loads. A basic function fits one of the boundary conditions of two opposite free ends is used to express the displacement unration along the nodal lines. To satisfy the other condition of the two opposite free ends, edge moments equal in magnitude but opposite in direction were applied at the ends of the nodal lines. Numerical results were obtained and compared with those obtained from another numerical solution. The comparison demonstrated a good agreement and indicated the validity of the presented technique.

Bending, axial buckling and shear buckling analyses of FG-porous plates based on a refined plate theory

ABSTRACT In this paper, numerical solutions are presented for static bending and mechanical buckling analyses of functionally graded porous (FGP) plates. The plate is modelled based on a refined plate theory and three porosity distributions with the same total mass density are considered. The set of the governing equations is derived using minimum potential energy and is solved numerically using the differential quadrature method (DQM). Convergence and accuracy of the solution are confirmed and the effects of porosity parameter, porosity distribution pattern, thickness and aspect ratio of the plate and boundary conditions on the deflection, intensity and distribution of stress and critical buckling load are investigated. It is shown by the numerical examples that an increment in the porosity parameter leads to a reduction in the critical buckling load and an increase in static deflection of the plate. Numerical results reveal that the effect of the porosity parameter on the distribution and intensity of the stress components strongly is dependent on the porosity distribution pattern.

3-D elasticity numerical solution for magneto-hygrothermal bending of FG graphene/metal circular and annular plates on an elastic medium

Three-dimensional (3-D) asymmetric and axisymmetric bending analyses of solid circular and annular plates lying on an elastic medium with different boundary conditions are presented in this article. The present nanocomposite circular and annular plates are made of aluminum (Al) matrix reinforced with graphene platelets (GPLs) that uniformly distributed or functionally graded (FG) through the thickness. This model is exposed to transverse external load, thermal load and humid conditions as well as in-plane magnetic field. Lorentz magnetic force is obtained by applying Maxwell's equations. While, the temperature and moisture, along the transverse direction, are deduced by solving the one-dimensional heat conduction and moisture diffusion equations, respectively. The governing equations are established based on the three-dimensional elasticity theory. By applying the differential quadrature method (DQM) along both radial and thickness directions, the solution of magneto-hygrothermal bending of the circular and annular plates is obtained. Convergence and comparison investigations are introduced to illustrate the precision and validity of the present solution. The present paper aims to deduce the displacements and stresses of the FG graphene/metal circular and annular plates employing the DQM. Moreover, various parametric studies are presented to investigate the effects of outer-to-inner radius ratio, thickness to radius ratio, weight fraction of GPLs, boundary conditions, elastic foundation parameters, temperature, moisture concentrations on the stresses and displacements of the present model.

Geometrically nonlinear flexural analysis of multilayered composite plate using polynomial and non-polynomial shear deformation theories

In this paper, the geometrically nonlinear bending analysis of multilayered composite plates is carried out through a rigorous comparative study employing Green-Lagrange and von Kármán nonlinearity. The responses are analyzed for various transverse loads and boundary conditions, and emphasized the impending structural condition, which requires the consideration of full geometric nonlinearity. The study is conducted using a C0 finite element plate model using third-order and non-polynomial shear deformation theories (TSDT and NPSDT). The principle of virtual work is utilized to formulate the weak-form of governing equations, and discretized using nine-noded Lagrange elements with seven degrees-of-freedom per node. The performance of the present model has been validated by comparing present results with those available in the literature and obtained ANSYS results. The results reveal that the consideration of Green-Lagrange nonlinearity is essential for plates with all sides subjected to movable simply supported boundary conditions or with one free edge. The present study also provides a clear idea about the utilization of TSDT and NPSDT for the anti-symmetric and symmetric cross-ply plate, respectively, to get more accurate solution. Further, the effect of penalty for various theories and problems is also highlighted, and its prominent impact is asserted for some cases.