Anupam Chakrabarti

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.

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.

An efficient C0 FE model for the analysis of composites and sandwich laminates with general layup

A C0 continuous finite element model is developed to model the refined higher order shear deformation theory. The proposed element is an upgraded version of an element based on higher order shear deformation theory. The C0 continuity of the present element is compensated in the stiffness matrix calculations. The computational efficiency is achieved by the C0 continuous finite element model by satisfying the inter-laminar shear stress continuity at the interfaces and zero transverse shear stress conditions at plate top and bottom. The performance of the upgraded element is illustrated with many numerical examples.

Dynamic Response of Composite Beams with Partial Shear Interaction Using a Higher-Order Beam Theory

Dynamic response of composite beams with partial interaction is presented using a one-dimensional finite-element model based on a higher-order beam theory. The proposed model takes into account the effect of partial shear interaction between the adjacent layers, as well as the transverse shear deformation of the beam. A third order variation of the axial displacement of the fibers over the beam depth is taken to have a parabolic variation of shear stress, which vanishes at both the top and bottom fibers of the transverse composite surface, as clearly derived on the free and tangentially unloaded surface of the continua. In the proposed finite-element model, there is no need to incorporate any shear correction factor, and the model is free from the shear locking problem. The proposed numerical model is validated by comparing the results with those available in the literature. Many new results are presented, because there are no published results on vibration and buckling of composite beams based on higher-order beam theory.

VIBRATION AND BUCKLING ANALYSIS OF LAMINATED SANDWICH PLATE HAVING SOFT CORE

Free vibration and buckling of laminated sandwich plate having soft core is studied by using an efficient C0 continuous finite element (FE) model based on higher-order zigzag theory (HOZT). In this theory, the in-plane displacement field for both the face sheets and the core is obtained by superposing a global cubically varying displacement field on a zigzag linearly varying displacement field with a different slope in each layer. The transverse displacement is assumed to be quadratic within the core while it remains constant in the faces beyond the core. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the plate. The nodal field variables are chosen in an efficient manner to overcome the problem of C1 continuity requirement of the transverse displacement. Numerical examples on free vibration and buckling covering different geometric and material features of laminated composite and sandwich plates are presented. Many new results are also presented which should be useful for future research.

Structural damage identification:A random sampling-high dimensional model representation approach

Structural damage identification and quantification of damage using non-destructive methods are important aspects for any civil, mechanical and aerospace engineering structures. In this study, a novel damage identification algorithm has been developed using random sampling-high dimensional model representation approach. A global sensitivity analysis based on random sampling-high dimensional model representation is adopted for important parameter screening purpose. Three different structures (spring mass damper system, simply supported beam and fibre-reinforced polymer composite bridge deck) have been used for various single and multiple damage conditions to validate the proposed algorithm. The performance of this method is found to be quite satisfactory in the realm of damage detection in structures. The random sampling-high dimensional model representation-based approach for meta-model formation is particularly useful in damage identification as it works well when large numbers of input parameters are involved. In this study, two different optimization methods have been used and their relative capability to identify damage has been discussed. Performance of this damage identification algorithm under the influence of noise has also been addressed in this article.

Static and Dynamic Analysis of Functionally Graded Skew Plates

The static and dynamic analysis of functionally graded material (FGM) skew plates under mechanical load is studied. The FEM formulation based on a third-order shear deformation (TOSD) theory that does not require any shear correction factor is used in the analysis. The C 1 continuity requirement of the higher-order theory has been overcome in this study by adopting a C 0 continuous isoparametric Lagrangian element with seven degrees of freedom at each node. The Mori-Tanaka homogenization scheme is used to estimate the effective propertiesoftheconstituents,and it isassumedthatmechanical propertiesvaryaccordingtoapower-lawdistributionofthevolumefraction of the constituents. The efficiency of the present model has been validated by comparing the results obtained with those available in the literature. The effects of skew angle, boundary conditions, volume-fraction exponent, loading conditions, aspect ratio, thickness ratio, and other parameters on deflection, natural frequency,and critical buckling load of functionally graded skew plates are reported forthe first time based on TOSD that can serve as the benchmark for future research. DOI: 10.1061/(ASCE)EM.1943-7889.0000523.

BUCKLING ANALYSIS OF FUNCTIONALLY GRADED SKEW PLATES: AN EFFICIENT FINITE ELEMENT APPROACH

In the present study, an attempt has been made to present the Co finite element formulation based on third order shear deformation theory for buckling analysis of functionally graded material skew plate under thermo-mechanical environment. Here, prime emphasis has been given to study the influence of skew angle on the buckling behavior of functionally graded plate. Two dissimilar homogenization schemes, namely Mori–Tanaka scheme and Voigt rule of mixture are employed to sketch their influence for the interpretation of data. Temperature-dependent material properties of the constituents of the plate are considered to perform thermal analysis. Numerical examples are solved using different mixture of ceramic and metal plates to generate the new results and relative imperative conclusions are highlighted. The roles played by the different factors like loading condition, volume fraction index, skew angle, boundary condition, aspect ratio, thickness ratio and homogenization schemes on buckling behavior of the FGM skew plates are presented in the form of tables and figures.

Vibration of laminated sandwich beams having soft core

Free vibration response of laminated sandwich beams having a soft core is studied by using a recently developed C0 finite element beam model. The model has been developed based on higher order zigzag theory where the in-plane displacement variation is considered to be cubic for both the face sheets and the core. The transverse displacement is assumed to be quadratic within the core while it remains constant in the faces beyond the core. The model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the beam. The nodal field variables are chosen in an efficient manner to overcome the problem of continuity requirement of the derivatives of transverse displacements. Numerical examples on free vibration covering different features of laminated composite and sandwich beams are presented. Many new results are also presented which should be useful for future research.

Dynamic response of functionally graded skew shell panel

The dynamic response of functionally graded skew shell is investigated using a C0 finite element formulation. Reddys higher order theory has been employed to perform the analysis and the volume fractions of the ceramic and metallic components are assumed to follow simple linear distribution law. The present study attempts to focus mainly on the influence of skew angle on frequency parameter and displacement of shell panel with various geometries. Comprehensive numerical results are demonstrated for cylindrical, spherical and hypar shells for different boundary conditions and skew angles.The findings obtained for functionally graded skew shell panels are new and can be used as bench mark for researchers in this field.