Three-dimensional finite-element analysis of laminated composites

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.

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

In the present study, a new computational model which incorporates the effect of transverse shear and normal deformation is presented for the thermal analysis of laminated composite and sandwich plates. The present theory involves nine unknowns and uses a polynomial function in terms of thickness coordinates which is expanded up to fifth-order. In the present fifth-order shear and normal deformation theory (FOSNDT), the governing equations are variationally consistent and obtained by using the principle of virtual work. Plates are analyzed for simply supported boundary conditions using Navier’s solution technique. Numerical results obtained by using the present theory are compared with three-dimensional elasticity solution and other higher-order theories available in the literature. It is found that the present theory is accurately predicting the thermal response of laminated composite and sandwich plates compared to any other theory available in the literature.

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

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.

Transverse shear effects in discrete optimization of laminated compressed cylindrical shells

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.

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.

In this paper a finite element method is presented to study the effects of delamination on free vibration characteristics of graphite-epoxy composite pretwisted rotating shells. Lagrange’s equation of motion is used to derive the dynamic equilibrium equation and moderate rotational speeds are considered wherein the Coriolis effect is negligible. An eight noded isoparametric plate bending element is employed in the formulation incorporating rotary inertia and effects of transverse shear deformation based on Mindlin’s theory. To satisfy the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front, a multipoint constraint algorithm is incorporated which leads to unsymmetric stiffness matrices. Parametric studies are performed in respect of location of delamination, fibre orientation, rotational speed and twist angle on natural frequencies of cylindrical shallow shells. Numerical results obtained for symmetric and unsymmetric laminates are the first known non-dimensional frequencies for the analyses carried out here.

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

To investigate the clinical application effect of the along-axis extraction method in the extraction of impacted mandibular third molars (IMTM) and to compare the biomechanical characteristics of different root extraction techniques through three-dimensional finite element analysis. A total of 68 patients requiring IMTM extraction were enrolled and randomly divided into two groups: the experimental group underwent the along-axis extraction method, while the control group underwent the traditional buccal bone removal and root extraction method. The duration of the procedure, intraoperative and postoperative complications were recorded. Three-dimensional finite element analysis further revealed the stress distribution in the tooth root, jawbone, periodontal ligament, and mandibular canal during different root extraction methods. The duration of root extraction, pain score and swelling on the first postoperative day in the control group were (7.87±3.90) min, 4.62±1.90 and (11.37±5.12) mm, respectively, which were significantly higher than those in the experimental group [(5.74±2.37) min, 3.87±1.19 and (7.22±3.39) mm, respectively]. The root fracture rate and lingual bone plate fracture rate in the control group were significantly higher than those in the experimental group (P < 0.05). The results of finite element analysis showed that the control group ' s lingual al-veolar bone had the higher peak equivalent stress, and lingual bone plate fracture was prone to occur. The periodontal ligament of the experimental group had the higher equivalent stress value, making it more likely to rip and more likely to cause root displacement. When subjected to force, the experimental group' s instantaneous root displacement was higher, but the control group ' s root displacement was more pronounced in the lingual direction. This study suggests that the along-axis extraction me-thod can not only effectively shorten the operative time but also reduce postoperative complications after extraction of impacted mandibular third molars, and enhance the safety of the operation and the patient' s comfort. Three-dimensional finite element analysis shows the biomechanical characteristics of various root extraction techniques visually, serves as a valuable guide for choosing and refining clinical surgical techniques, and confirms that extracting a tooth' s root along its long axis yields better clinical results.