Reddy's Higher-order Shear Deformation Research Articles

Nonlinear analysis of pneumatic radial tyres via piece-wise Rayleigh-Ritz technique

Based on the Sanders thin shell theory and Reddy's higher-order shear deformation shell theory, a general refined shell theory is developed in this paper for the analysis of stresses and deformations of pneumatic radial tyres of composite construction. For easy and efficient simulation of the tyre, a piece-wise Rayleigh-Ritz technique is proposed and applied to get a numerical solution to the nonlinear structural problem. Bezier polynomials are used to approximate both the geometry of the free surface of reference and displacement fields of the tyres. Stress distributions and deformations of the tyres subjected to uniform inflation pressure are computed and discussed for details. From a comparison of the present results by the piece-wise Rayleigh-Ritz approach with the numerical predictions by 3D finite element method, it has been shown that the present semi-analytical solution procedure is accurate and applicable to the much complicated time-consuming nonlinear analysis for high quality tyre.

Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading

In this paper, we examine the postbuckling behavior of functionally graded material FGM rectangular plates that are integrated with surface-bonded piezoelectric actuators and are subjected to the combined action of uniform temperature change, in-plane forces, and constant applied actuator voltage. A Galerkin-differential quadrature iteration algorithm is proposed for solution of the non-linear partial differential governing equations. To account for the transverse shear strains, the Reddy higher-order shear deformation plate theory is employed. The bifurcation-type thermo-mechanical buckling of fully clamped plates, and the postbuckling behavior of plates with more general boundary conditions subject to various thermo-electro-mechanical loads, are discussed in detail. Parametric studies are also undertaken, and show the effects of applied actuator voltage, in-plane forces, volume fraction exponents, temperature change, and the character of boundary conditions on the buckling and postbuckling characteristics of the plates.

A new plate bending element based on higher-order shear deformation theory for the analysis of composite plates

A triangular element based on Reddy's higher-order shear deformation plate theory is developed. Although the plate theory is quite attractive but it could not be exploited as expected in finite-element analysis. This is due to the difficulties associated with satisfaction of inter-elemental continuity requirement of the plate theory. Keeping this aspect in view, the proposed element is developed where Reddy's plate theory is successfully implemented. It has six nodes and each node contains equal degrees of freedom. The performance of the element is tested with different numerical examples, which show its precision and range of applicability.

Postbuckling of axially loaded shear-deformable laminated cylindrical panels

A postbuckling analysis is presented for a shear-deformable laminated cylindrical panel of finite length subjected to compressive axial loads. The governing equations are based on Reddy's higher-order shear deformation shell theory with a von Karman-Donnell type of kinematic non-linearity. The non-linear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling, which includes the effects of non-linear prebuckling deformations, large deflections in the postbuckling range and initial geometric imperfections of the shell, is extended to the case of shear-deformable laminated cylindrical panels under axial compression. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick and thin cross-ply laminated cylindrical panels. The effects played by transverse shear deformation, panel geometric parameters, total number of plies, fibre orientation, the character of in-plane boundary conditions and initial geometric imperfections are studied.

Hygrothermal Effects on the Nonlinear Bending of Shear Deformable Laminated Plates

The influence of hygrothermal effects on the nonlinear bending of shear deformable laminated plates subjected to a uniform or sinusoidal load is investigated using a micro-to-micromechanical analytical model. The material properties of the composite are affected by the variation of temperature and mositure, and are based on a micromechanical model of a laminate. The governing equations of a laminated plate are based on Reddy's higher-order shear deformation plate theory with von Karman-type kinematic nonlinearity, and including hygrothermal effects. A perturbation technique is employed to determine the load-deflection and load-bending moment curves. The numerical illustrations concern nonlinear bending behavior of antisymmetric angle-ply and symmetric cross-ply laminated plates under different sets of environmental conditions. The results presented show the effects of temperature rise, the degree of moisture concentration, and fiber volume fraction on the nonlinear bending behavior of the plate.

Postbuckling of Shear Deformable Laminated Cylindrical Shells

A postbuckling analysis is presented for a shear deformable laminated cylindrical shell of finite length subjected to compres- sive axial loads. The governing equations are based on Reddy's higher-order shear deformation shell theory with a von Karman-Donnell type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of shear deformable laminated cylindrical shells under axial compression. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilib- rium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, unstiffened or stiffened, moderately thick, cross-ply laminated cylindrical shells. The effects of transverse shear deformation, shell geometric parameters, total number of plies, fiber orientation, and initial geometric imperfections are studied.

Nonlinear bending response of functionally graded plates subjected to transverse loads and in thermal environments

Nonlinear bending analysis is presented for a simply supported, functionally graded rectangular plate subjected to a transverse uniform or sinusoidal load and in thermal environments. 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 governing equations of a functionally graded plate are based on Reddy's higher-order shear deformation plate theory that includes thermal effects. Two cases of the in-plane boundary conditions are considered. A mixed Galerkin-perturbation technique is employed to determine the load-deflection and load-bending moment curves. The numerical illustrations concern nonlinear bending response of functional graded rectangular plates with two constituent materials. The influences played by temperature rise, the character of in-plane boundary conditions, transverse shear deformation, plate aspect ratio and volume fraction distributions are studied.

Thermal postbuckling of shear-deformable laminated plates with piezoelectric actuators

A thermal postbuckling analysis is presented for a simply supported, shear-deformable laminated plate with piezoelectric actuators subjected to the combined action of thermal and electric loads. The temperature field considered is associated with a parabolic distribution over the plate surface and a uniform distribution in the thickness direction. The electric field is assumed to be the transverse component, E Z, only. The material properties are assumed to be independent of the temperature and the electric field. The governing equations of a laminated plate are based on Reddy's higher-order shear-deformation plate theory that includes thermo-piezoelectric effects. The initial geometric imperfection of the plate is taken into account. The analysis uses a mixed Galerkin-perturbation technique to determine thermal buckling temperature and postbuckling equilibrium paths. The numerical illustrations concern the thermal postbuckling behavior of perfect and imperfect, symmetric cross-ply laminated plates with fully covered or embedded piezoelectric layers under different sets of thermal and electric loading conditions. The effects played by transverse shear deformation, the plate aspect ratio, stacking sequence, thermal load ratio, applied voltage as well as initial geometric imperfections are studied.

Hygrothermal effects on the postbuckling of shear deformable laminated plates

The influence of hygrothermal effects on the postbuckling of shear deformable laminated plates subjected to a uniaxial compression is investigated using a micro-to-macro-mechanical analytical model. The material properties of the composite are affected by the variation of temperature and moisture, and are based on a micro-mechanical model of a laminate. The governing equations of a laminated plate are based on Reddy's higher-order shear deformation plate theory that includes hygrothermal effects. The initial geometric imperfection of the plate is taken into account. Two cases of the in-plane boundary conditions are considered. A perturbation technique is employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, antisymmetric angle-ply and symmetric cross-ply laminated plates under different sets of environmental conditions. The influences played by temperature rise, the degree of moisture concentration, the character of in-plane boundary conditions, transverse shear deformation, plate aspect ratio, total number of plies, fiber orientation, fiber volume fraction and initial geometric imperfections are studied.

Thermal Postbuckling of Preloaded Shear Deformable Laminated Plates

Postbuckling analysis is presented for a simply supported, shear deformable laminated plate subjected to a uniform lateral pressure and thermal loading, and resting on an elastic foundation. The temperature fields considered are associated with a nonuniform tentlike and parabolic distribution over the plate surface. The material properties are assumed to be independent of temperature. The lateral pressure is first converted into an initial deflection, and the initial geometric imperfection of the plate also is taken into account. The formulations are based on Reddy's higher-order shear deformation plate theory and include the plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine the thermal postbuckling equilibrium paths. The numerical illustrations concern the thermal postbuckling behavior of preloaded antisymmetric angle-ply laminated plates under a tentlike temperature field and symmetric cross-ply laminated plates under a parabolic tem...

Postbuckling of shear deformable laminated plates under biaxial compression and lateral pressure and resting on elastic foundations

Postbuckling analysis is presented for a simply supported, shear deformable laminated plate subjected to biaxial compression combined with uniform lateral pressure and resting on an elastic foundation. The lateral pressure is first converted into an initial deflection and the initial geometrical imperfection of the plate is also taken into account. The formulations are based on the Reddy's higher-order shear deformation plate theory, and including the plate-foundation interaction. The analysis uses a perturbation technique to determine the buckling loads and the postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, antisymmetrically angle-ply and symmetrically cross-ply laminated plates under combined loading and resting on Pasternak-type or softening nonlinear elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The effects played by foundation stiffness, transverse shear deformation, plate aspect ratio, total number of plies, fiber orientation, the biaxial load ratio and initial lateral pressure are studied.

Non-linear bending of shear deformable laminated plates under lateral pressure and thermal loading and resting on elastic foundations

A non-linear bending analysis is presented for a simply supported shear deformable composite laminated plate subjected to a combined uniform lateral pressure and thermal loading and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on Reddy's higher-order shear deformation plate theory, including the plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine the load-deflection curves and load-bending moment curves. Numerical examples are presented that relate to the performances of antisymmetric angleply and symmetric cross-ply laminated plates subjected to thermomechanical loading and resting on two-parameter elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influences due to a number of effects e.g. foundation stiffness, plate aspect ratio, total number of plies, fibre orientation and initial thermal bending stress, are studied. Typical results are presented in a dimensionless graphical form.

K�rm�n-type equations for a higher-order shear deformation plate theory and its use in the thermal postbuckling analysis

Karman-type nonlinear large deflection equations are derived according to the Reddy's higher-order shear deformation plate theory and used in the thermal postbuckling analysis. The effects of initial geometric imperfections of the plate are included in the present study which also includes the thermal effects. Simply supported, symmetric cross-ply laminated plates subjected to uniform or nonuniform parabolic temperature distribution are considered. The analysis uses a mixed Galerkinperturbation technique to determine thermal buckling loads and postbuckling equilibrium paths. The effects played by transverse shear deformation, plate aspect ratio, total number of plies, thermal load ratio and initial geometric imperfections are also studied.

Thermal post-buckling analysis of imperfect laminated plates using a higher-order shear deformation theory

Thermal post-buckling analysis is presented for a simply supported, composite laminated plate subjected to uniform or non-uniform tent-like temperature loading. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the Reddy's higher-order shear deformation plate theory, and include thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine thermal buckling loads and post-buckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, antisymmetrically angle-ply and symmetrically cross-ply laminated plates. The effects played by transverse shear deformation, thermal load ratio, plate aspect ratio, total number of plies, fiber orientation and initial geometrical imperfections are studied. Typical results are presented in dimensionless graphical form.

Thermal buckling analysis of antisymmetric angle-ply laminates based on a higher-order displacement field

A higher-order deformation theory, which accounts for transverse shear and transverse normal strains, is derived for the thermal buckling analysis of antisymmetric angle-ply laminates that are simply supported and subject to a uniform temperature rise. The theory includes six dependent variables but can account for cubic distribution of in-plane displacements and parabolic distribution of transverse normal displacement. By using the present higher-order displacement field and the three-dimensional Hooke's law, exact-closed form solutions of the thermal buckling temperature are obtained. For purposes of comparison, numerical values of buckling temperature based on the first-order shear deformation theory and Reddy's higher-order shear deformation theory are also calculated, by reducing the present higher-order deformation theory. The results show that surprising discrepancies exist among the present theory and the other two theories, which indicates the importance of incorporating the effect of transverse normal strain in the thermal buckling analysis of antisymmetric angle-ply laminates.