Volume 2, Issue 1

This paper presents a versatile and efficientmodeling and solution framework for free vibration analysis of composite laminated cylindrical and spherical panels modeled according to two-dimensional equivalent singlelayer and layerwise theories of variable order.Aunified formulation of the equations of motion is adopted which can be used for both thin and thick structures. The discretization procedure is based on the spectral collocation method and is presented in a compact matrix form which can be directly and easily implemented. The convergence and accuracy of the proposed approach is evaluated for panels having different boundary conditions, thickness and shallowness ratios, and lamination layups.

The system studied in this paper consists of thin structure with several piezoelectric patches bonded on its surface. The patches are used as actuators and sensors. Based on Kirchhoff-Love hypothesis, linear constitutive relations, plane stress formulation and Hamilton principle, we have developed a 2D model for this system using the finite element method. It is not a standard 2D model, since the calculation is performed on a structure that does not have symmetries that allow such easy assumptions. The originality of the work consists in the use of the concept of neutral plane to model this asymmetric system in 2D. This technique, beside good precision, saves computational time. An experimental device has been also built and tested to validate the model. The structural damping is included in the model to match the damping behavior of the real system. Optimizations of the thickness of piezoelectric patches and materials used in the thin structures are also presented in the paper.

This paper investigates the in-plane free vibrations of multi-stepped and multi-damaged parabolic arches, for various boundary conditions. The axial extension, transverse shear deformation and rotatory inertia effects are taken into account. The constitutive equations relating the stress resultants to the corresponding deformation components refer to an isotropic and linear elastic material. Starting from the kinematic hypothesis for the in-plane displacement of the shear-deformable arch, the equations of motion are deduced by using Hamilton’s principle. Natural frequencies and mode shapes are computed using the Generalized Differential Quadrature (GDQ) method. The variable radius of curvature along the axis of the parabolic arch requires, compared to the circular arch, a more complex formulation and numerical implementation of the motion equations as well as the external and internal boundary conditions. Each damage is modelled as a combination of one rotational and two translational elastic springs. A parametric study is performed to illustrate the influence of the damage parameters on the natural frequencies of parabolic arches for different boundary conditions and cross-sections with localizeddamage.Results for the circular arch, derived from the proposed parabolic model with the derivatives of some parameters set to zero, agree well with those published over the past years.

Elastic two-layer curved composite beam with partial shear interaction is considered. It is assumed that each curved layer separately follows the Euler-Bernoulli hypothesis and the load slip relation for the flexible shear connection is a linear relationship. The curved composite beam at one of the end cross sections is fixed and the other end cross section is subjected by a concentrated radial load. Two cases are considered. In the first case the loaded end cross section is closed by a rigid plate and in the second case the radial load is applied immediately to it. The paper gives solutions for radial displacements, slips and stresses. The presented examples can be used as benchmark for the other types of solutions as given in this study.

Within a setting where the isogeometric analysis (IGA) has been successful at bringing two different research fields together, i.e. Computer Aided Design (CAD) and numerical analysis, T-spline IGA is applied in this work to frictionless contact and mode-I debonding problems between deformable bodies in the context of large deformations. Based on the concept of IGA, the smooth basis functions are adopted to describe surface geometries and approximate the numerical solutions, leading to higher accuracy in the contact integral evaluation. The isogeometric discretizations are here incorporated into an existing finite element framework by using Bézier extraction, i.e. a linear operator which maps the Bernstein polynomial basis on Bézier elements to the global isogeometric basis. A recently released commercial T-spline plugin for Rhino is herein used to build the analysis models adopted in this study. In such context, the continuum is discretized with cubic T-splines, as well as with Non Uniform Rational B-Splines (NURBS) and Lagrange polynomial elements for comparison purposes, and a Gauss-point-to-surface (GPTS) formulation is combined with the penalty method to treat the contact constraints. The purely geometric enforcement of the non-penetration condition in compression is generalized to encompass both contact and mode-I debonding of interfaces which is approached by means of cohesive zone (CZ) modeling, as commonly done by the scientific community to analyse the progressive damage of materials and interfaces. Based on these models, non-linear relationships between tractions and relative displacements are assumed. These relationships dictate both the work of separation per unit fracture surface and the peak stress that has to be reached for the crack formation. In the generalized GPTS formulation an automatic switching procedure is used to choose between cohesive and contact models, depending on the contact status. Some numerical results are first presented and compared in 2D for varying resolutions of the contact and/or cohesive zone, including frictionless sliding and cohesive debonding, all featuring the competitive accuracy and performance of T-spline IGA. The superior accuracy of T-spline interpolations with respect to NURBS and Lagrange interpolations for a given number of degrees of freedom (Dofs) is always verified. The isogeometric formulation is also extended to 3D bodies, where some examples in large deformations based on T-spline discretizations show an high smoothness of the reaction history curves.

The minimization of weight and maximization of payload is an ever challenging design procedure for air vehicles. The present study has been carried out with an objective to redesign control surface of an advanced all-metallic fighter aircraft. In this study, the structure made up of high strength aluminum, titanium and ferrous alloys has been attempted to replace by carbon fiber composite (CFC) skin, ribs and stiffeners. This study presents an approach towards development of a methodology for optimization of first-ply failure index (FI) in unidirectional fibrous laminates using Genetic-Algorithms (GA) under quasi-static loading. The GAs, by the application of its operators like reproduction, cross-over, mutation and elitist strategy, optimize the ply-orientations in laminates so as to have minimum FI of Tsai-Wu first-ply failure criterion. The GA optimization procedure has been implemented in MATLAB and interfaced with commercial software ABAQUS using python scripting. FI calculations have been carried out in ABAQUS with user material subroutine (UMAT). The GA's application gave reasonably well-optimized ply-orientations combination at a faster convergence rate. However, the final optimized sequence of ply-orientations is obtained by tweaking the sequences given by GA's based on industrial practices and experience, whenever needed. The present study of conversion of an all metallic structure to partial CFC structure has led to 12% of weight reduction. Therefore, the approach proposed here motivates designer to use CFC with a confidence.

Finite Element, Boundary Element, Finite Volume, and Finite Difference Analysis are all commonly used in nearly all engineering disciplines to simplify complex problems of geometry and change, but they all tend to oversimplify. This paper shows a more recent computational approach developed initially for problems in solid mechanics and electro-magnetic field analysis. It is an algebraic approach, and it offers a more accurate representation of geometric and topological features.

This paper presents an analytical solution for nonlinear free and forced vibration response of smart laminated nano-composite beams resting on nonlinear elastic foundation and under external harmonic excitation. The structure is under a temperature change and an electric excitation through the piezoelectric layers. Different distribution patterns of the single walled aligned and straight carbon nanotubes (SWCNTs) through the thickness of the beam are considered. The beam complies with Euler-Bernoulli beam theory and von Kármán geometric nonlinearity. The nonlinearity is due to the mid-plane stretching of the beam and the nonlinear stiffness of the elastic foundation. The Multiple Time Scales perturbation scheme is used to perform the nonlinear dynamical analysis of functionally graded carbon nanotube-reinforced beams. Analytical expressions of the nonlinear natural frequencies, nonlinear dynamic response and frequency response of the system in the case of primary resonance have been presented. The effects of different parameters including applied voltage, temperature change, beam geometry, the volume fraction and distribution pattern of the carbon nanotubes on the nonlinear natural frequencies and frequency-response curves are presented. It is found that the volume fractions of SWCNTs as well as their distribution pattern significantly change the behavior of the system.

In this paper free vibration behavior of laminated composite stiffened elliptic parabolic shell has been analyzed in terms of natural frequency and mode shape. Finite element method has been applied using an eight-noded curved quadratic isoparametric element for shell with a three noded curved beam element for stiffener. Cross and angle ply shells with different edge conditions have been studied varying the size and position of the cutouts to arrive at a set of inferences of practical engineering significances.

A redesign of canard control-surface of an advanced all-metallic fighter aircraft was carried out by using carbon fibre composite (CFC) for ribs and panels. In this study ply-orientations of CFC structure are optimized using a Genetic-Algorithm (GA) with an objective function to have minimum failure index (FI) according to Tsai-Wu failure criterion. The redesigned CFC structure was sufficiently strong to withstand aerodynamic loads from stress and deflection points of view. Now, in the present work CFC canard structure has been studied for its buckling strength in comparison to existing metallic design. In this study, the existing metallic design was found to be weak in buckling. Upon a detailed investigation, it was revealed that there are reported failures in the vicinity of zones where initial buckling modes are excited as predicted by the finite element based buckling analysis. In view of buckling failures, the redesigned CFC structure is sufficiently reinforced with stringers at specific locations. After providing reinforcements against buckling, the twist and the camber variations of the airfoil are checked and compared with existing structure data. Finally, the modal analysis has been carried out to compare the variation in excitation frequency due to material change. The CFC structure thus redesigned is safe from buckling and aerodynamic aspects as well.

The Cell Method (CM) is a computational tool that maintains critical multi-dimensional attributes of physical phenomena in analysis. This information is neglected in the differential formulations of the classical approaches of finite element, boundary element, finite volume, and finite difference analysis, often leading to numerical instabilities and spurious results. This paper highlights the central theoretical concepts of the CM that preserve a more accurate and precise representation of the geometric and topological features of variables for practical problem solving. Important applications occur in fields such as electromagnetics, electrodynamics, solid mechanics and fluids. CM addresses non-locality in continuum mechanics, an especially important circumstance in modelling heterogeneous materials.

Strengthening the structural members of old buildings using advanced materials is a contemporary research in the field of repairs and rehabilitation. Many researchers used plain Glass Fiber Reinforced Polymer (GFRP) sheets for strengthening Reinforced Concrete (RC) beams. In this research work, rectangular corrugated GFRP laminates were used for strengthening RC beams to achieve higher flexural strength and load carrying capacity. Type and dimensions of corrugated profile were selected based on preliminary study using ANSYS software. A total of twenty one beams were tested to study the load carrying capacity of control specimens and beams strengthened with plain sheets and corrugated laminates using epoxy resin. This paper presents the experimental and theoretical study on flexural strengthening of Reinforced Concrete (RC) beams using corrugated GFRP laminates and the results are compared. Mathematical models were developed based on the experimental data and then the models were validated.

Analytical Strip Method is presented for the analysis of the bending-extension coupling problem of stiffened and continuous antisymmetric thin laminates. A system of three equations of equilibrium, governing the general response of antisymmetric laminates, is reduced to a single eighth-order partial differential equation (PDE) in terms of a displacement function. The PDE is then solved in a single series form to determine the displacement response of antisymmetric cross-ply and angle-ply laminates. The solution is applicable to rectangular laminates with two opposite edges simply supported and the other edges being free, clamped, simply supported, isotropic beam supports, or point supports.

To determine fracture parameters of interfacial cracks in transverse isotropic magnetoelectroelastic composites, a displacement extrapolation formula was derived. The matrix-form formula can be applicable for both material components with arbitrary poling directions. The corresponding explicit expression of this formula was obtained for each poling direction normal to the crack plane. This displacement extrapolation formula is only related to the boundary quantities of the extended crack opening displacements across crack faces, which is convenient for numerical applications, especially for BEM. Meantime, an alternative extrapolation formula based on the path-independent J-integral and displacement ratios was presented which may be more adaptable for any domain-based numerical techniques like FEM. A numerical example was presented to show the correctness of these formulae.

A trigonometric beam theory (TBT) is developed for the bending analysis of laminated composite and sandwich beams considering the effect of transverse shear deformation. The axial displacement field uses trigonometric function in terms of thickness coordinate to include the effect of transverse shear deformation. The transverse displacement is considered as a sum of two partial displacements, the displacement due to bending and the displacement due to transverse shearing. Governing equations and boundary conditions are obtained by using the principle of virtual work. To demonstrate the validity of present theory it is applied to the bending analysis of laminated composite and sandwich beams. The numerical results of displacements and stresses obtained by using present theory are presented and compared with those of other trigonometric theories available in literature along with elasticity solution wherever possible.

The present study investigates whether an nthorder shear deformation theory is applicable for the composite laminates in cylindrical bending. The theory satisfies the traction free conditions at top and bottom surfaces of the plate and does not require problem dependent shear correction factor which is normally associated with the first order shear deformation theory. The well-known classical plate theory at (n = 1) and higher order shear deformation theory of Reddy at (n = 3) are the perticular cases of the present theory. The governing equations of equilibrium and boundary conditions are obtained using the principle of virtual work. A simply supported laminated composite plate infinitely long in y-direction is considered for the detail numerical study. A closed form solution for simply supported boundary conditions is obtained using Navier’s technique. The displacements and stresses are obtained for different aspect ratios and modular ratios.

The present paper considers the linear static thermal stress analysis of composite structures by means of a shell finite element with variable through-thethickness kinematic. The temperature profile along the thickness direction is calculated by solving the Fourier heat conduction equation. The refined models considered are both Equivalent Single Layer (ESL) and Layer Wise (LW) and are grouped in the Unified Formulation by Carrera (CUF). These permit the distribution of displacements, stresses along the thickness of the multilayered shell to be accurately described. The shell element has nine nodes, and the Mixed Interpolation of Tensorial Components (MITC) method is used to contrast the membrane and shear locking phenomenon. The governing equations are derived from the Principle of Virtual Displacement (PVD). Cross-ply plate, cylindrical and spherical shells with simply-supported edges and subjected to bi-sinusoidal thermal load are analyzed.Various thickness ratios and curvature ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions given in the literature and the analytical solutions obtained using the CUF and the Navier’s method. Finally, plates and shells with different lamination and boundary conditions are analyzed using high-order theories in order to provide FEM benchmark solutions.

The dynamic response of a deformable curved solid body is investigated as it interacts with a flow field. The fluid is assumed to be viscous and the flow is nearly incompressible. Fluid dynamics is predicted through a lattice Boltzmann solver. Corotational beam finite elements undergoing large displacements are adopted to idealize the submerged body, whose presence in the lattice fluid background is handled by the immersed boundary method. The attention focuses on the solid’s deformation and a numerical campaign is carried out. Findings are reported in terms of deformation energy and deformed configuration. On the one hand, it is shown that the solution of the problem is strictly dependent on the elastic properties of the body. On the other hand, the encompassing flow physics plays a crucial role on the resultant solid dynamics. With respect to the existing literature, the present problem is attacked by a new point of view. Specifically, the author proposes that the problem is governed by four dimensionless parameters: the Reynolds number, the normalized elastic modulus, the density and aspect ratii. The formulation and the solution strategy for curved solid bodies herein adopted are introduced for the first time in this paper.

In this paper, second order statistics of thermally induced post buckling response of elastically supported piezoelectric laminated composite plate using micromechanical approach is examined. A Co finite element has been used for deriving eigenvalue problem using higher order shear deformation theory (HSDT) with von-Karman nonlinearity. The uncertain system properties such as material properties of fiber and matrix of composite and piezoelectric, fiber volume fraction, plate thickness, lamination angle and foundation are modeled as random variables. The temperature field considered to be uniform temperature distributions through the plate thickness. A direct iterative based nonlinear finite element method combined with mean-centered second order perturbation technique (SOPT) is used to find the mean and coefficient of variance of the post buckling temperature. The effects of volume fraction, fiber orientation, and length to thickness ratio, aspect ratios, foundation parameters, position and number of piezoelectric layers, amplitude and boundary conditions with random system properties on the critical temperature are analysed. It is found that small amount of variations of uncertain system parameters of the composite plate significantly affect the initial and post buckling temperature of laminated composite plate. The results have been validated with independent Monte Carlo simulation (MCS) and those available in literature.

This paper presents a derivation of the Rayleigh- Betti reciprocity relation for layered curved composite beams with interlayer slip. The principle of minimum of potential energy is also formulated for two-layer curved composite beams and its applications are illustrated by numerical examples. The solution of the presented problems are obtained by the Ritz method. The applications of the Rayleigh-Betti reciprocity relation proven are illustrated by some examples.