Showing papers on "Plate theory published in 2003"
TL;DR: In this paper, the axisymmetric large deflection bending of a functionally graded circular plate under mechanical, thermal and combined thermal-mechanical loadings, respectively, was investigated.
295 citations
TL;DR: In this article, a Galerkin-differential quadrature iteration algorithm is proposed for solution of the non-linear partial differential governing equations of FGM rectangular plates that are integrated with surface-bonded piezoelectric actuators and are subjected to the combined action of uniform temperature change, inplane forces, and constant applied actuator voltage.
273 citations
TL;DR: In this paper, a semi-analytical approach for large deflection and postbuckling responses of functionally graded rectangular plates under transverse and in-plane loads is proposed, where 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 fractions of the constituents.
Abstract: Large deflection and postbuckling responses of functionally graded rectangular plates under transverse and in-plane loads are investigated by using a semi-analytical approach. 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 fractions of the constituents. The plate is assumed to be clamped on two opposite edges and the remaining two edges may be simply supported or clamped or may have elastic rotational edge constraints. The formulations are based on the classical plate theory, accounting for the plate-foundation interaction effects by a two-parameter model (Pasternak-type), from which Winkler elastic foundation can be treated as a limiting case. A perturbation technique in conjunction with one-dimensional differential quadrature approximation and Galerkin procedure are employed in the present analysis. The numerical illustrations concern the large deflection and postbuckling behavior of functional graded plates with two pairs of constituent materials. Effects played by volume fraction, the character of boundary conditions, plate aspect ratio, foundation stiffness, initial compressive stress as well as initial transverse pressure are studied.
208 citations
TL;DR: In this paper, a nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads and under various boundary conditions is presented, where the role played by the constituent volume fraction index, temperature rise, character of out-of-plane boundary conditions and in-plane constraints, width-to-thickness ratio as well as plate aspect ratio are studied.
Abstract: Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads and under various boundary conditions is presented. Theoretical formulations are based on Reddy's higher order shear deformation plate theory and include the thermal effects due to temperature rise. Material properties are assumed to be temperature-dependent and graded in the thickness direction according to a power law distribution in terms of the volume fractions of the constituents. The temperature field considered is assumed to be uniform in the XY plane and through the plate thickness. The plate may be clamped or simply supported on two opposite edges with the remaining others being either free, simply supported or clamped. A semi-numerical approach, which makes use of multi-parameter perturbation technique, one-dimensional differential quadrature approximation and Galerkin method, is employed to calculate the nonlinear bending of the plates. Numerical results for silicon nitride/stainless steel rectangular plates are given in dimensionless graphical forms. The roles played by the constituent volume fraction index, temperature rise, character of out-of-plane boundary conditions and in-plane constraints, width-to-thickness ratio as well as plate aspect ratio are studied.
173 citations
TL;DR: In this article, a large amplitude vibration analysis of pre-stressed functionally graded material (FGM) laminated plates is presented, which are composed of a shear deformable functionally graded layer and two surface-mounted piezoelectric actuator layers.
152 citations
TL;DR: In this article, the authors considered the scattering problem of an incident plane S 0 Lamb wave in a plate with a circular partly through-thickness hole, where the wave fields in the outer part outside the hole and in the inner part beneath the hole are expanded in the possible Lamb modes and the horizontally polarized shear modes.
152 citations
TL;DR: A triangular element based on Reddy's higher-order shear deformation plate theory is developed in this article, where the plate theory could not be exploited as expected in finite-element analysis.
112 citations
TL;DR: In this article, a meshless local Petrov-Galerkin Liu (MLPG) method was used to analyze three-dimensional infinitesi- ral frequencies and forced plane strain deformations.
Abstract: We use a meshless local Petrov-Galerkin Liu (2001) have used the MLPG method to find natu- (MLPG) method to analyze three-dimensional infinitesi- ral frequencies and forced plane ,strain deformations.of mal elastodynamic deformations of a homogeneous rect- a cantilever beam. Batra and Chmg .(2002~ have de!m- angular plate subjected to different edge conditions. We eated the time evolution of the stress-mtenslty factor m a employ a higher-order plate theory in which both trans- double edge-cracked plate. verse shear and transverse normal deformations are con- Atluri and Shen (2002a,b) have compared the perfor- sidered. Natural frequencies and the transient response manceof six' variants of the MLPG method for solving to external loads have been computed for isotropic Poisson's equation. Qian et al. (2002) used two of these and orthotropic plates. Computed results are found to formulations to study elastostatic deformations of a thick agree with those obtained from the analysis of the 3- rectangular plate with a compatible higher-order shear dimensional problem either analytically or by the finite and normal deformable plate theory (HOSNDPT) pro- element method.
100 citations
TL;DR: In this article, a state-space approach is developed to analyze the bending and free vibration of a simply supported, cross-ply laminated rectangular plate featuring interlaminar bonding imperfections, for which a general linear spring layer model is adopted.
Abstract: State-space approach is developed to analyze the bending and free vibration of a simply supported, cross-ply laminated rectangular plate featuring interlaminar bonding imperfections, for which a general linear spring layer model is adopted The analysis is directly based on the three-dimensional theory of orthotropic elasticity and is completely exact Numerical comparison is made, showing that although the plate theory developed in the literature behaves well for moderately thick perfect laminates it can become inaccurate when bonding imperfections are present The special problem of the laminate in cylindrical bending is also considered, and the validity of the assumption of cylindrical bending is investigated through numerical examples
79 citations
TL;DR: In this article, a variational asymptotic analysis of composite plates is presented, which is based on a three-dimensional, anisotropic elasticity problem that takes all possible deformation into account.
79 citations
TL;DR: In this article, a higher order zig-zag plate theory is developed to refine the predictions of the mechanical, thermal, and electric behaviors partially coupled by superimposing linear zigzag field to the smooth globally cubic varying field through the thickness.
Abstract: A higher order zig-zag plate theory is developed to refine the predictions of the mechanical, thermal, and electric behaviors partially coupled. The in-plane displacement fields are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field through the thickness. Smooth parabolic distribution through the thickness is assumed in the out-of-plane displacement in order to consider transverse normal deformation and stress. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface conditions of transverse shear stresses. Artificial shear correction factors are not needed in the present formulation. Thus the proposed theory has only seven primary unknowns and they do not depend upon the number of layers. Through the numerical examples of partially coupled analysis, the accuracy and efficiency of the present theory are demonstrated. The present theory is suitable in the predictions of deformation and stresses of thick smart composite plate under mechanical, thermal, and electric loads combined.
TL;DR: In this article, a combined analytical and experimental study of flexural-torsional buckling of pultruded fiber-reinforced plastic (FRP) composite cantilever I-beams is presented.
TL;DR: In this article, two meshless local Petrov-Galerkin (MLPG) formulations were used to analyze infinitesimal deformations of a homogeneous and isotropic thick elastic plate with a higher-order shear and normal deformable plate theory.
Abstract: We use two meshless local Petrov-Galerkin formulations, namely, the MLPG1 and the MLPG5, to analyze infinitesimal deformations of a homogeneous and isotropic thick elastic plate with a higher-order shear and normal deformable plate theory. It is found that the two MLPG formulations give results very close to those obtained by other researchers and also by the three- dimensional analysis of the problem by the finite element method.
TL;DR: In this paper, the dynamic response of shear deformable laminated plates exposed to thermomechanical loading and resting on a two-parameter (Pasternak-type) elastic foundation is investigated.
TL;DR: In this paper, a dynamic stability analysis of symmetrically laminated FGM rectangular plates with general out-of-plane supporting conditions, subjected to a uniaxial periodic in-plane load and undergoing uniform temperature change is conducted.
Abstract: This paper conducts a dynamic stability analysis of symmetrically laminated FGM rectangular plates with general out-of-plane supporting conditions, subjected to a uniaxial periodic in-plane load and undergoing uniform temperature change. Theoretical formulations are based on Reddy’s third-order shear deformation plate theory, and account for the temperature dependence of material properties. A semi-analytical Galerkin-differential quadrature approach is employed to convert the governing equations into a linear system of Mathieu–Hill equations from which the boundary points on the unstable regions are determined by Bolotin’s method. Free vibration and bifurcation buckling are also discussed as subset problems. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with FGM layers made of silicon nitride and stainless steel. The influences of various parameters such as material composition, layer thickness ratio, temperature change, static load level, boundary constraints on the dynamic stability, buckling and vibration frequencies are examined in detail through parametric studies.
TL;DR: In this paper, a vibration analysis of cross-ply laminated square plates subjected to different sets of boundary conditions is presented. The analysis is based on a five-degree-of-freedom shear deformable plate theory and the requirement of the continuity conditions among the layers for the symmetric crossplated plates are fulfilled by the use of shape functions incorporated into this theory.
TL;DR: An analytical model based on classical laminate plate theory (CLPT) was developed to predict the longitudinal elastic modulus of a 2-D braided fiber composite as discussed by the authors, which represents a generalization of the plain weave case as the angle between the strands is not restricted to 90°.
Abstract: An analytical model based on classical laminate plate theory (CLPT) was developed to predict the longitudinal elastic modulus of a 2-D braided fiber composite. A sinusoidal function was used to model the path of undulating strands. This work represents a generalization of the plain weave case as the angle between the strands is not restricted to 90°. The results predicted by the model are in good agreement with other models and are in excellent agreement with experimental results for braided Kevlar 49/epoxy resin tubes. The predicted and experimental results confirmed that the longitudinal elastic modulus of a braided tube is less than that of one composed of laminated layers.
TL;DR: In this article, an analytical description of thermal-stress states in a ceramic-metal functionally graded material (FGM) plate subjected to through-thickness heat flow by combining micromechanical with macromachanical approaches is presented.
Abstract: The purpose of this paper is to present an analytical description of thermal-stress states in a ceramic–metal functionally graded material (FGM) plate subjected to through-thickness heat flow by combining micromechanical with macromechanical approaches. The micromechanical approach stems from Eshelby's equivalent inclusion method and Mori–Tanaka's mean-field approximation, and the macromechanical approach is based on the classical laminated plate theory. This analytical method takes account of the microscale-level stress relaxation due to interfacial diffusion between ceramic and metal phases as well as creep of both phases. Some numerical examples for the Al2O3–Ni system are also shown, and the necessity of considering inelastic deformation in a thermal-stress analysis in an FGM is discussed.
TL;DR: In this article, a simply supported, shear deformable laminated plate subjected to a transverse dynamic load combined with initial in-plan static loads and resting on a two-parameter (Pasternak-type) elastic foundation is considered.
TL;DR: In this article, a triangular element was applied to the buckling of composite plates to study its performance and the results showed that the transverse shear stress has parabolic through thickness variation and it is zero at top and bottom surfaces of the plate.
Abstract: The simple higher-order shear deformation theory proposed by Reddy has been successfully implemented in a triangular element recently developed by the authors. In this paper the element is applied to buckling of composite plates to study its performance. In this plate theory the transverse shear stress has parabolic through thickness variation and it is zero at top and bottom surfaces of the plate. Moreover, it does not introduce any additional unknown in the formulation. Thus, the plate theory is quite simple and elegant but it cannot be implemented in most of the elements, as the plate theory demands C 1 continuity of transverse displacement along the element edges. This has inspired the authors to develop this new element, which has shown an excellent performance in static analysis of composite plates. To demonstrate the performance of the element in the problem of buckling, examples of isotropic and composite plates under different situations are solved. The results are compared with the analytical so...
TL;DR: In this paper, a third-order Hermitian zig-zag plate theory is presented as development of the classical cubic zigzag displacement field, which offers some interesting improvements, such as through-the-thickness linear varying transverse displacement, evaluation of the normal transverse deformability in general and of the corresponding normal stress in particular, traction equilibrium condition on the external surfaces and use of the displacements and transverse shear stresses of external surfaces as degrees of freedom of the plate model.
TL;DR: In this paper, a hierarchical plate element is formulated based on Mindlin's plate theory including rotatory inertia effects and based on a skew co-ordinate system, and a non-dimensional frequency parameter and mode shapes are presented for a range of skew angle ( β ), aspect ratio ( a/b ), thicknesswidth ratio ( h / b ), cutout dimensions and different boundary conditions.
TL;DR: In this article, two-dimensional theories and finite elements are assessed to analyze displacement and stress factors in sandwich, composites plates, and two benchmarks are used to conduct the assessment; the first benchmark is a rectangular sandwich plate loaded by a transverse pressure located at the center.
Abstract: Two-dimensional theories and e nite elements are assessed to analyze displacement and stress e elds in sandwich, composites plates. Two benchmarks are used to conduct the assessment. The e rst benchmark is a sandwich plate loaded by harmonic distribution of transverse pressure for which a three-dimensional closed-form solution exists in the literature. The second benchmark is a rectangular sandwich plate loaded by a transverse pressure located at the center. More than 20 plate theories and e nite elements were implemented in a unie ed formulation recently proposed by the authors. Classical theories based on displacement assumptions are compared to advanced mixed modelsformulatedonthebasisofReissner’ smixedvariationaltheorem.Bothequivalentsingle-layermodelsaswell as layerwise models are considered. Analytical closed-form solutions and e nite elements are given. The considered benchmarks highlight both the performance and limitations of the considered two-dimensional theories. The convenience of layerwisedescription and advanced mixed theorieshas been demonstrated. Thesecond benchmark especially proved the need for layerwise models to capture the local effects.
TL;DR: In this paper, the first known Williams-type singularities caused by homogeneous boundary conditions in the first-order shear deformation plate theory (FSDPT) are thoroughly examined.
TL;DR: In this article, the dynamic behavior of an orthotropic plate simply supported on a pair of parallel edges and under a system of moving loads is analyzed based on Lagrange equation and modal superposition.
Abstract: The dynamic behavior of an orthotropic plate simply supported on a pair of parallel edges and under a system of moving loads is analyzed based on Lagrange equation and modal superposition. Thin plate theory is assumed for the plate model and no restriction is placed on the type of loading. Parameters of the plate affecting its dynamic behavior are discussed, and a new classification of the plates for computing the mode shapes and natural frequencies is proposed. The impact factors and the dynamic responses of a typical bridge deck are studied using the proposed method. Preliminary results indicate that the effect of eccentric loads on the impact factor depends on the proportion ratio between the flexural and torsional rigidities of the bridge deck, and the multilane loading case is less critical than a single-lane loading case.
TL;DR: In this article, the relationship between the findings of the two models allowing shear deformation results to be obtained from the results of classical thin theories are displayed without using any shear correction factors.
TL;DR: In this paper, a 3D dynamic equation of elasticity is proposed for determining the free vibration frequencies and mode shapes of annular and circular plates with nonlinear thickness variation along the radial direction.
TL;DR: This paper considers two lowest-order methods of this family of elements called MITC (mixed interpolation of tensorial components) of Reissner--Mindlin equations based on quadrilateral meshes and obtains optimal H1 and L2 error estimates for both methods.
Abstract: This paper deals with the numerical approximation of the bending of a plate modeled by Reissner--Mindlin equations. It is well known that, in order to avoid locking, some kind of reduced integration or mixed interpolation has to be used when solving these equations by finite element methods. In particular, one of the most widely used procedures is based on the family of elements called MITC (mixed interpolation of tensorial components). We consider two lowest-order methods of this family on quadrilateral meshes.
Under mild assumptions we obtain optimal H1 and L2 error estimates for both methods. These estimates are valid with constants independent of the plate thickness. We also obtain error estimates for the approximation of the plate vibration problem. Finally, we report some numerical experiments showing the very good behavior of the methods, even in some cases not covered by our theory.
TL;DR: In this article, an extended Kantorovich method (EKM) was applied to the system of partial differential equations to reduce the governing equations to a double set of three second-order ordinary differential equations in the variables x and y, which were then solved in an iterative manner until convergence was achieved.
TL;DR: In this paper, the optimization of laminated and sandwich plates with respect to buckling load and thickness has been performed, using different sets of constraints such as the fundamental frequency, the maximum deflection under transverse uniform distributed load, the mass and the buckling loads.