Transverse shear effects in discrete optimization of laminated compressed cylindrical shells

The effect of transverse shear deformation on the buckling of two-layer composite columns with interlayer slip

A geometrically nonlinear formulation for the behavior of composite delaminated beams of arbitrary stacking sequence, and with the effects of transverse shear deformation included, is presented. The formulation is based on a first-order shear deformation kinematic model, which incorporates the bending-stretching coupling effect and also assumes an arbitrary initial imperfection. The nonlinear differential equations are solved by Newton’s method using a finite-difference scheme. The growth of the delamination is also studied by applying the J-integral in order to derive a formula for the energy release rate, which includes transverse shear. Results are presented which illustrate the shear effect, especially with respect to the ratio of the in-plane extensional over shear modulus and with respect to the ratio of plate length over thickness. It is seen that transverse shear can affect largely the displacement profiles, rendering the structure more compliant, and can promote growth by increasing the energy release rate, but this latter effect is moderate and mainly noticable only at the later stages in the postbuckling regime.

Vibrations of Moderately Thick Shallow Spherical Shells at Large Amplitudes

Analytical formulations and solutions for natural frequency analysis of functionally graded material (FGM) plates based on two higher-order refined shear deformation theories with 9 and 12 degrees-of-freedom are presented. The displacement model with 12 degrees-of-freedom considers the effect of both transverse shear and normal strain/stress while the other considers only the effect of transverse shear deformation. In addition another higher-order model and the first-order model developed by other investigators and available in the literature are also presented for the evaluation purpose. For mathematical modeling purposes, the Poissons ratio of the material is considered as constant whereas Youngs modulus is assumed to vary through the thickness according to the power law function. The equations of motion are derived using Hamiltons principle. Solutions are obtained in closed-form using Naviers technique and solving the eigenvalue equation. The accuracy of the theoretical formulations and the solution method using the present two higher-order refined models is first established by comparing the results generated in the present investigation with the 3D elasticity solutions already reported in the literature. After establishing the accuracy of predictions, benchmark results for the natural frequencies using all the four models are presented for single layer FGM plate and multi layered FGM sandwich plate with varying edge ratios and side-to-thickness ratios.

The effects of transverse shear deformations and structural damping on the flutter phenomena of a composite rotor blade in hover have been investigated using the finite element method. First-order shear deformation theory with rotary inertia effects and a damped element model of composite laminates are employed for the structural formulation. A quasisteady aerodynamic theory with a dynamic inflow model is used. Torsion-related out-of-plane warping and noncirculatory aerodynamic components are also incorporated in the formulation. Using these structural and aerodynamic tools, several numerical studies are carried out, first to validate the current approach and second to show the effects of transverse shear deformations and structural damping on the aeroelastic stability of a composite rotor as a function of fiber orientation. The predictions derived by the frequency analysis of this model are found to be more accurate than those given by an alternative approach compared with experimental data. It is shown that the transverse shear flexibility tends to lower the frequency of the rotor, and generally has a destabilizing effect on the lag mode and a stabilizing effect on the flap mode. It is also presented that the magnitude of structural damping can be controlled by changing ply orientation angle. CT cd c, EA

An analysis is presented for the study of the effect of transverse shear deformation on the natural frequencies of layered composite paraboloidal shells. The applicability of linear shell theory due to Reissner is assumed and governing equations are solved for the natural frequencies using the transfer matrix approach. The results of the present analysis are compared with the results for paraboloidal shells reported in the literature and good agreement is found. Transverse shear deformation effects are carried out separately for axisymmetric torsional vibration modes, axisymmetric bending-extensional vibration modes and nonsymmetric vibration modes. The variation of the effect of transverse shear deformation with respect to different rim boundary conditions, geometry of the paraboloid, material type (isotropic-orthotropic), lamination arrangement and particular meridional and circumferential vibration modes is investigated.

Non-linear vibration and postbuckling of generally laminated circular cylindrical thick shells with non-uniform boundary conditions

Vibration Of A Delaminated Beam-plate Relative To Post-buckling States With Shear Deformation Theory

The present study is to assess the accuracy of the few computational models based on various shear deformation theories in predicting the static and dynamic behaviour of antisymmetric angle-ply laminated composite plates. In the present investigation two higher order refined computational models incorporate the laminate deformations which account for the effects of both transverse shear and normal deformation and a non-linear variation of in-plane displacements are used. In addition to above, few higher order models and the first order model developed by other investigators and available in the literature are also considered for the evaluation. The equations of equilibrium are obtained using Principle of Minimum Potential Energy and the equations of motion using Hamilton’s principle. Solutions are obtained in closed-form using Navier’s solution technique. The solutions of the static analysis are obtained by solving the boundary value problem and the natural frequencies are obtained by solving the eigenvalue problem. The accuracy of the solutions obtained from the different models are established by comparing the results with the solutions wherever available in the literature. Results generated independently using the various models are presented for antisymmetric angle ply composite plates which will serve as benchmark solutions for future investigations.

Three-dimensional finite-element analysis of laminated composites

Shear plugging and perforation of ductile circular plates struck by a blunt projectile

This paper presents for the first time an investigation into the static characteristics of FG sandwich beams with porous ceramic core and sandwich beams with FG porous core resting on a two-parameter Winkler-Pasternak elastic foundation using a new three-node higher-order finite element model with five degrees-of-freedom per node based on quasi-3D deformation theory, that accounts both the effects of transverse shear and normal deformations. The beams are subjected to uniformly distributed loads, and their material properties vary gradually through the thickness according to the power-law distribution. The governing equation of motion is derived from Lagrange’s equations. Uniform, symmetric, and asymmetric porosity patterns are considered. The accuracy of the proposed model is verified through comparisons with existing results. A comprehensive parametric study is carried out to explore the effects of various parameters such as boundary conditions, skin-to-core thickness ratio, power-law index, slenderness, porosity, and elastic foundation parameters on the displacements and stresses of FG sandwich beams. Benchmark results presented in this study can serve as a reference for future research endeavors on FG sandwich beams with porous cores.

In this study, a static and free vibration analysis of single layer FG and sandwich FG plates is carried out using a fifth order shear and normal deformation theory. The displacement field of the present theory includes the terms considering the effect of transverse shear and normal deformation. Also, the terms of the thickness co-ordinate are expanded upto fifth order to predict the accurate bending behavior of the plates. The equations of motion are derived based on Hamilton’s principle, and further solved using Navier’s solution scheme. The present results of displacement, stresses and natural frequencies in sandwich FG plates are obtained and compared with other higher order theories available in literature to check the validity and efficacy of the theory.

Mechanics and fracture of crack tip deformable bi-material interface

The vibration responses of a pre-stressed rotating cylindrical shell under stationary constant point load are analyzed by numerical method. The cylindrical shell is modeled by a nine-node super-parametric finite element which includes the effects of transverse shear deformation, axial deformation and rotary inertia. The geometric nonlinearity due to large deformation is also considered in the model. The numerical integer method is applied to attain the vibration responses. The effects of initial axial stress and rotating speed on the vibration of cylindrical shell are investigated in detail.