Abdul Hamid Sheikh

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

A triangular element based on Reddys 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 Reddys 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.

An appropriate FE model for through-thickness variation of displacement and potential in thin/moderately thick smart laminates

A finite element model for the analysis of fibre-reinforced laminated composite plates embedded and/or surface bonded with piezoelectric layers and subjected to mechanical loading and/or electric potential has been presented in this paper. The proposed model is applicable for the analysis of thin-to-moderately thick plates. No restriction has been imposed on the pattern of variation of the potential across the plate thickness so that the potential can have any value even within the core. As the plates considered here are not too thick, the structural deformation has been modelled by single layer theory where the effect of shear deformation has been taken into account following Mindlins hypothesis. For the electric potential, layer-wise theory has been applied, as the through-thickness variation of electric potential does not follow any specific pattern. This is the first attempt wherein a combination of single layer theory and layer-wise approach has been used to solve the coupled problem of piezoelectricity in plate bending. Numerical examples have been carried out to study the performance of the proposed approach.

Large‐amplitude finite element flexural vibration of plates/stiffened plates

Large‐amplitude free flexural vibration of stiffened and unstiffened plates has been studied by using the finite element method. An isoparametric quadratic plate‐bending element has been used both for the plate and the stiffener. The dynamic version of von Karman’s field equations has been adopted and the formulation has been done in the total Lagrangian coordinate system. The in‐plane deformation and inertia have been taken into account. The resulting nonlinear equations have been solved by the direct iteration technique using a linear mode shape as the starting vector. The stiffener has been elegantly modeled so that it can be placed anywhere within the plate element and it need not follow the nodal lines. This has increased the flexibility of the mesh generation considerably. The arbitrary orientation and eccentricity of the stiffener have been incorporated in the formulation. The shear deformation has been incorporated according to Mindlin’s hypothesis. Stiffened and unstiffened plates that have vario...

Buckling of Laminated Composite Plates by a New Element Based on Higher Order Shear Deformation Theory

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 solutions and other published results, which show the precision and range of applicability of the proposed element in the present problem.

Dynamic instability of stiffened plates subjected to non-uniform harmonic in-plane edge loading

The dynamic instability characteristics of stiffened plates subjected to in-plane partial and concentrated edge loadings are studied using finite element analysis. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The method of Hills infinite determinants is applied to determine the dynamic instability regions. Numerical results are presented to study the effects of various parameters, such as static load factor, aspect ratio, boundary conditions, stiffening scheme and load parameters on the principal instability regions of stiffened plates using Bolotins method. The results show that location, size and number of stiffeners have a significant effect on the location of the boundaries of the principal instability region.

Buckling and vibration of stiffened plates subjected to partial edge loading

The buckling and vibration characteristics of stiffened plates subjected to in-plane partial and concentrated edge loadings are studied using finite element method. The initial stresses are obtained considering the pre-buckling conditions. Buckling loads and vibration frequencies are determined for different plate aspect ratios, edge conditions and different partial non-uniform edge loading cases. The non-uniform loading may also be caused due to the supports on the edges. The analysis presented determines the stresses all over the region for different kinds of loading and edge conditions. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The vibration characteristics are discussed and the results are compared with those available in the literature. Buckling results show that the stiffened plate is less susceptible to buckling for position of loading near the supported edges and near the position of stiffeners as well.

Geometric nonlinear analysis of stiffened plates by the spline finite strip method

Abstract Geometric nonlinear analysis of stiffened plates is investigated by the spline finite strip method. von Karman’s nonlinear plate theory is adopted and the formulation is made in total Lagrangian coordinate system. The resulting nonlinear equations are solved by the Newton–Raphson iteration technique. To analyse plates having any arbitrary shapes, the whole plate is mapped into a square domain. The mapped domain is discretised into a number of strips. In this method, the displacement interpolation functions used are: the spline functions in the longitudinal direction of the strip and the finite element shape functions in the other direction. The stiffener is elegantly modelled so that it can be placed anywhere within the plate strip. The arbitrary orientation of the stiffener and its eccentricity are incorporated in the formulation. All these aspects have ultimately made the proposed approach a most versatile tool of analysis. Plates and stiffened plates are analysed and the results are presented along with those of other investigators for necessary comparison and discussion.

A finite element large displacement analysis of stiffened plates

Abstract A finite element analysis of the large deflection behaviour of stiffened plates using the isoparametric quadratic stiffened plate bending element is presented. The evaluation of fundamental equations of the stiffened plates is based on Mindlins hypothesis. The large deflection equations are based on von Karmans theory. The solution algmrithm for the assembled nonlinear equilibrium equations is based on the Newton-Raphson iteration technique. Numerical solutions are presented for rectangular plates and skew stiffened plates.

A high precision shear deformable element for the analysis of laminated composite plates of different shapes

A high precision triangular element developed by the last author is upgraded for the analysis of laminated composite plates. In this element the effect of shear deformation is considered by taking transverse displacement and bending rotations as independent field variables. The interpolation function used to approximate transverse displacement is one order higher than that used for bending rotations. This has made the element free from locking in shear. For the analysis of unsymmetric laminates, in-plane displacements are also taken as the field variables. Plates having different shapes, boundary conditions, thickness ratios, number of layers, fibre orientations and something else are analysed by this element and the results obtained are compared with those obtained from other sources in most of the cases. A number of new results are presented, which are expected to be useful in future research.

Analysis of Laminated Sandwich Plates Based on an Improved Higher Order Zigzag Theory

A finite element model based on an improved higher order zigzag plate theory developed by the authors is refined in this study and applied to bending and vibration response of soft core sandwich plates. The theory satisfies interlayer transverse shear stress continuity including transverse shear stress free condition at the plate top and bottom surfaces and transverse normal compressibility of the core. The in-plane displacements vary cubically through the entire thickness, while transverse displacement is assumed to vary quadratically within the core. In order to have a better computational benefit, a C0 finite element formulation is adopted. This is refined through satisfaction of certain constrains variationally using a penalty function approach. The performance of the model is demonstrated by comparing the present results with 3D elasticity solutions and other available results.