Volume 5, Issue 1

In this work a comparison is presented between elastic, plastic, and fracture analysis of the monumental arch bridge of Porta Napoli, Taranto (Italy). By means of a FEM model and applying the Mery’s Method, the behavior of the curved structure under service loads is verified, while considering the Safe Theorem approach byHeyman, the ultimate carrying capacity of the structure is investigated. Moreover, by using Fracture Mechanics concepts, the damage process which takes place when the conditions assessed through linear elastic analysis are no longer valid, and before the set-in of the conditions established by means of the plastic limit analysis, is numerically analyzed. The study of these transitions returns an accurate and effective whole service life assessment of the Porta Napoli masonry arch bridge.

This paper presents the first known vibration characteristics of moderately thick functionally graded carbon nanotube reinforced composite rectangular plates on Pasternak foundation with arbitrary boundary conditions and internal line supports on the basis of the firstorder shear deformation theory. Different distributions of single walled carbon nanotubes (SWCNTs) along the thickness are considered. Uniform and other three kinds of functionally graded distributions of carbon nanotubes along the thickness direction of plates are studied. The solutions carried out using an enhanced Ritz method mainly include the following three points: Firstly, create the Lagrange energy function by the energy principle; Secondly, as the main innovation point, the modified Fourier series are chosen as the basic functions of the admissible functions of the plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges; Lastly, solve the natural frequencies as well as the associated mode shapes by means of the Ritz-variational energy method. In this study, the influences of the volume fraction of CNTs, distribution type of CNTs, boundary restrain parameters, location of the internal line supports, foundation coefficients on the natural frequencies and mode shapes of the FG-CNT reinforced composite rectangular plates are presented.

This paper proposes an assumption that the fibre is elastic material and polymer matrix is viscoelastic material so that the energy dissipation depends only on the polymer matrix in dynamic response process. The damping force vectors in frequency and time domains, of FRP (Fibre-Reinforced Polymer matrix) laminated composite plates, are derived based on this assumption. The governing equations of FRP laminated composite plates are formulated in both frequency and time domains. The direct inversion method and direct time integration method for nonviscously damped systems are employed to solve the governing equations and achieve the dynamic responses in frequency and time domains, respectively. The computational procedure is given in detail. Finally, dynamic responses (frequency responses with nonzero and zero initial conditions, free vibration, forced vibrations with nonzero and zero initial conditions) of a FRP laminated composite plate are computed using the proposed methodology. The proposed methodology in this paper is easy to be inserted into the commercial finite element analysis software. The proposed assumption, based on the theory of material mechanics, needs to be further proved by experiment technique in the future.

In the present paper, the active vibration control of a composite beam using piezoelectric actuator is investigated. The space state equation is determined using system identification technique based on the structure input output response provided by ANSYS APDL finite element package. The Linear Quadratic (LQG) control law is designed and integrated into ANSYS APDL to perform closed loop simulations. Numerical examples for different types of excitation loads are presented to test the efficiency and the accuracy of the proposed model.

In this paper, an efficient and unified approach for free vibration analysis of the moderately thick functionally graded carbon nanotube reinforced composite annular sector plate with general boundary supports is presented by using the Ritz method and the first-order shear deformation theory. For the distribution of the carbon nanotubes in thickness direction, it may be uniform or functionally graded. Properties of the composite media are based on a refined rule of the mixture approach which contains the efficiency parameters. A modified Fourier series is chosen as the basic function of the admissible function to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. To establish the general boundary supports of the annular sector plate, the artificial spring boundary technique is implemented at all edges. The desired solutions are obtained through the Ritz-variational energy method. Some numerical examples are considered to check the accuracy, convergence and reliability of the present method. In addition, the parameter studies of the functionally graded carbon nanotube reinforced composite annular sector plate are carried out as well.

Demands for water transportation modes are continuously increasing as rapid economic and industrial growths in the recent decade. Ship as representative of the water transportation is generally needed to carry various products from one location to another. Besides as product carrier, ship also acts as public facility to transport human across islands for number of reasons, such as tourism and vehicle. Considering its importance, structural damage due to accidental loads or so-called impact can cause unacceptable casualties which threat ship passenger, shipping industry and maritime environment in same time. The most frequent impact phenomena occur in forms of collision and grounding, which are targeting side structure and double bottom consecutively. However, since responses of the impacts on structure are highly nonlinear and vary due to development of ship structures, sustainable analysis as an update of pioneer calculation can be beneficial as rational reference for improving safety and navigational instruments. This work aims to assess failures of the side structures subjected to penetration of striking bow in ship-ship collision scenario. Locations of impact are idealized to happen on after-end, midsection and fore-end to provide complete assessment. Striking bow is to be deployed by varying input velocity to observe significance of the fractures on the side structure. This configuration is implemented on the designed collision scenario, and later calculated using nonlinear finite element method (NLFEM). Summary of the solution indicated that the midsection produced the highest resistance against side collision. Breaching of the inner shell was successfully avoided on the fore-end, but the critical damage to the cargo was observed during bow penetration to the after-end region. This location was recommended to be added by longitudinal framing to increase its resistance against ship collision.

Desktop 3D FDM (Fused Deposition Modelling) printers are usually employed for the production of nonstructural objects. In recent years, the present authors tried to use this technology also to produce structural elements employed in the construction of small UAVs (Unmanned Aerial Vehicles). Mechanical stresses are not excessive for small multirotor UAVs. Therefore, the FDM technique combined with polymers, such as the ABS (Acrylonitrile Butadiene Styrene) and the PLA(Poly Lactic Acid), can be successfully employed to produce structural components. The present new work is devoted to the production and preliminary structural analysis of sandwich configurations. These new lamination schemes could lead to an important weight reduction without significant decreases of mechanical properties. Therefore, it could be possible, for the designed application (e.g., a multifunctional small UAV produced via FDM), to have stiffener and lighter structures easy to be manufactured with a low-cost 3D printer. The new sandwich specimens here proposed are PLA sandwich specimens embedding a PLA honeycomb core produced by means of the same extruder, multilayered specimens with ABS external layers and an internal homogeneous PLA core using different extruders for the two materials, sandwich specimens with external ABS skins and an internal PLA honeycomb core using different extruders for the two materials, and sandwich specimens where two different extruders have been employed for PLA material used for skins and for the internal honeycomb core. For all the proposed configurations, a detailed description of the production activity is given.Moreover, several preliminary results about three-point bending tests, different mechanical behaviors and relative delamination problems for each sandwich configuration will be discussed in depth.

In this paper, a unified solution for vibration analysis of the functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical panels with general elastic supports is carried out via using the Ritz method. The excellent accuracy and reliability of the present method are compared with the results of the classical boundary cases found in the literature. New results are given for vibration characteristics of FG-CNTRC cylindrical panels with various boundary conditions. The effects of the elastic restraint parameters, thickness, subtended angle and volume fraction of carbon nanotubes on the free vibration characteristic of the cylindrical panels are also reported.

A hybrid-mixed functionally graded material (FGM) piezoelectric four-node solid-shell element through the sampling surfaces (SaS) method is proposed. The SaS formulation is based on choosing inside the shell N SaS parallel to the middle surface in order to introduce the displacements and electric potentials of these surfaces as fundamental shell unknowns. Such choice of unknowns with the use of Lagrange polynomials of degree N-1 in through-thickness interpolations of the displacements, strains, electric potential, electric field and material properties leads to a robust FGM piezoelectric shell formulation. The inner SaS are located at Chebyshev polynomial nodes that make it possible to minimize uniformly the error due to Lagrange interpolation. To implement the effective analytical integration throughout the element, the extended assumed natural strain (ANS) method is employed. As a result, the piezoelectric four-node solid-shell element exhibits a superior performance in the case of coarse meshes. To circumvent shear and membrane locking, the hybrid stress-strain solid-shell formulation via the Hu-Washizu variational principle is employed. The developed solid-shell element could be useful for the 3D stress analysis of FGMstructures because the SaS method allows obtaining the solutions with a prescribed accuracy, which asymptotically approach the exact solutions of electroelasticity as the number of SaS tends to infinity.

The evaluation of the stress field within a nonlocal version of the displacement-based finite element method is addressed. With the aid of two numerical examples it is shown as some spurious oscillations of the computed nonlocal stresses arise at sections (or zones) of macroscopic inhomogeneity of the examined structures. It is also shown how the above drawback, which renders the stress numerical solution unreliable, can be viewed as the so-called locking in FEM, a subject debated in the early seventies. It is proved that a well known remedy for locking, i.e. the reduced integration technique, can be successfully applied also in the nonlocal elasticity context.

This paper deals with the bending analysis of exponentially graded material (EGM) plates resting on two-parameter elastic foundations according to a trigonometric shear deformation plate theory (TPT) using Navier’s technique. The normal and shear deformations are both includes. The present TPT does not need a shear correction factors. The material properties of plate like, Lamé’s coefficients convert exponentially in a given constant orientation. The equilibrium equations according to the EG plate resting on Pasternak foundations are presented. Numerical results for the EG thick plate on elastic foundations are presented. A good comparison of results with those being in the literature. The influences played by Winkler and Pasternak parameters, side-to-thickness ratio, inhomogeneity parameter and aspect ratio on the bending responses of EG plates are debated.

Effect of geometric nonlinearity onfree vibration behaviour of a non-uniform in-plane inhomogeneousplate on elastic foundation is carried out with an emphasis on mode switching phenomenon. The formulation is semianalytic displacement based and it is carried out in two distinct steps. First, the static problem is solved to find out the unknown displacement field by using minimum total potential energy principle. Secondly, subsequent dynamic problem is set up as an eigenvalue problem on the basis of the known displacement field. The governing set of equations in dynamic problem is obtained by using Hamilton’s principle. In static analysis, unknown co-efficient of the governing equations are solved using an iterative method, which is direct substitution with relaxation method. The dynamic problem is solved with the help of intrinsic Matlab solver. The results of the present method are validated with existing data. Backbone curve corresponding to different combinations of systemparameters are presented in non-dimensional plane.Mode switching is observed to occur in certain specific situation. The linear and nonlinear mode shapes are also furnished to support the presence of switching phenomenon.

During ship collision, hull crashworthiness is an important data which needs to be assessed as rapid development of hull structure has taken into consideration since several notable dangerous events. After catastrophic accidents cause both tragic loss of life and destruction of maritime environment, double skin system is applied for almost all ships, including RoRo passengers. This work aimed to assess effects of selected internal parameters to crashworthiness criteria, considering a passenger vessel as the target of a series of impact loads. A set of collision scenario was numerically designed using finite element (FE) method by involving single and double skin structures, target location and material grade to obtained estimation of hull crashworthiness. Assessment was focussed on the energy absorption, crushing force, stress level and failure strain of the target ship after experiencing side collisions. It was obtained from the analyses regarding role of the inner skin on tendency of the energy absorption. Failure progress on the proposed structures was successfully quantified based on stress expansion. Minimum value of material strength was concluded in final discussion to reduce more massive failure.

Bending of functionally graded plate with two reverse simply supported edges is studied based upon a refined quasi three-dimensional (quasi-3D) shear and normal deformation theory using a third-order shape function. The present theory accounts for the distribution of transvers shear stresses that satisfies the free transverse shear stresses condition on the upper and lower surfaces of the plate. Therefore, the strain distribution does not include the unwanted influences of transverse shear correction factor. The effect of transverse normal strain is included. Unlike the traditional normal and shear deformation theories, the present theory have four unknowns only. The equilibrium equations are derived by using the principle of virtual work. The influence of material properties, aspect and side-to-thickness ratios, mechanical loads and inhomogeneity parameter are discussed. The efficiency and correctness of the present theory results are established by comparisons with available theories results.

In this paper, Differential Quadrature Method (DQM) is applied to investigate free vibration of Single Walled Carbon Nanotubes (SWCNTs) with exponentially varying stiffness based on non-local Euler-Bernoulli beam theory. Application of DQ method in the governing differential equation converts the problem to a generalized eigenvalue problem and its solution gives frequency parameters. Convergence of the results show that DQM solutions converge fast. In this article, a detailed investigation has been reported and MATLAB code has been developed to analyze the numerical results for different scaling parameters as well as for four types of boundary conditions. Present results are compared with other available results and are found to be in good agreement.

A systematic investigation is carried out on how different parameters influence stress and strain concentration factors (SCF and SNCF) in a composite plate with a hole under uniaxial tension. Flat and singly curved composite plates have been modelled in ANSYS 15.0. The governing parameter includes: (i) size, shape and eccentricity of hole, (ii) number of plies, (v) fiber orientation and (vi) plate curvature. It is observed that different parameters influence the SCF and SNCF with varying degrees. For example, SCF may be as high as 7.16 for a square shaped hole. Also, SCF and SNCF are found to be approximately same in most of the cases. Finally, simplified design formulas are developed for evaluation of SCF for a wide range of hole size, eccentricity and fiber orientation.

The analysis of monolithic and sandwich plates is illustrated for those cases where the boundary conditions are not uniform along the thickness direction, and run at a given position along the thickness direction. For instance, a sandwich plate constrained at the bottom or top face can be considered. The approach relies upon a sublaminate formulation,which is applied here in the context of a Ritz-based approach. Due to the possibility of dividing the structure into smaller portions, viz. the sublaminates, the constraints can be applied at any given location, providing a high degree of flexibility in modeling the boundary conditions. Penalty functions and Lagrange multipliers are introduced for this scope. Results are presented for free-vibration and bending problems. The close matching with highly refined finite element analyses reveals the accuracy of the proposed formulation in determining the vibration frequencies, as well as the internal stress distribution. Reference results are provided for future benchmarking purposes.

Inclined, shallow, elastic cables under static 3D loads, arbitrarily distributed, are studied. Cables having natural length both larger or smaller than the distance between the supports (i.e. suspended or taut cables, respectively), are considered. Kinematically exact equations are derived, and projected onto an orthonormal basis intrinsic to the chord. A perturbation procedure is proposed, which extrapolates the solution relevant to the taut string, up to the desired order, and leads to a closed-form solution. Lower-order solutions are consistent with the hypotheses normally adopted in technical environment. Emphasis is given to the mechanical interpretation of the cable behavior. The asymptotic solution is compared to the explicit (not in closed-form) solution of the literature.

In this article, free vibration of SingleWalled Carbon Nanotube (SWCNT) resting on exponentially varying Winkler elastic foundation is investigated by using Differential Quadrature Method (DQM). Euler-Bernoulli beam theory is considered in conjunction with the nonlocal elasticity theory of Eringen. Step by step procedure is included and MATLAB code has been developed to obtain the numerical results for different scaling parameters as well as for four types of edge conditions. Obtained results are validated with known results in special cases showing good agreement. Further, numerical as well as graphical results are illustrated to show the effects of nonuniform parameter, nonlocal parameter, aspect ratio,Winkler modulus parameter and edge conditions on the frequency parameters.

In the present paper, rotary inertia and small size effects on the free vibration response of single-walled carbon nanotubes are examined. The equations in motion and associated boundary conditions are obtained by using Hamilton’s principle on the basis of modified couple stress and Rayleigh beam theories. The size effect is taken into account by modified couple stress theory while the rotary inertia effect is considered by Rayleigh beam theory. The resulting equations are analytically solved by implementing Navier’s solution technique for pinned-pinned carbon nanotubes. Influences of slenderness ratio, length scale parameter and rotary inertia on the natural frequencies of single-walled carbon nanotubes are studied in detail.