• Steel and Composite Structures
• /
• v.35 no.2
• /
• pp.249-260
• /
• 2020

The main purpose of this research work is to investigate the free vibration of conical shell structures reinforced by graphene platelets (GPLs) and the elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. To this end, a shell model is developed based on Donnell's theory. To solve the problem, the analytical Galerkin method is employed together with beam mode shapes as weighting functions. Due to importance of boundary conditions upon mechanical behavior of nanostructures, the analysis is carried out for different boundary conditions. The effects of boundary conditions, semi vertex angle, porosity distribution and graphene platelets on the response of conical shell structures are explored. The correctness of the obtained results is checked via comparing with existing data in the literature and good agreement is eventuated. The effectiveness and the accuracy of the present approach have been demonstrated and it is shown that the Donnell's shell theory is efficient, robust and accurate in terms of nanocomposite problems.

• Smart Structures and Systems
• /
• v.5 no.6
• /
• pp.613-632
• /
• 2009

The present paper is concerned with the design of a proper patch actuator network in order to track a desired displacement of the sidewalls of a one-storey frame structure; both, for the static and the dynamic case. Weights for each patch of the actuator network found in our previous work were based on beam theory; in the present paper a refinement of these weights by modeling the sidewalls of the frame structure as thin plates is presented. For the sake of calculating the refined weights approximate solutions of the plate equations are calculated by an extended Galerkin method. The solutions based on the analytical plate model are compared with three-dimensional Finite Element results computed in the commercially available code ANSYS. The patch actuator network is put into practice by means of four piezoelectric patches attached to each of the two sidewalls of the frame structures, to which electric voltages proportional to the analytically refined patch weights are applied. Analytical and numerical results coincide very well over a broad frequency range.

• Journal of the Society of Naval Architects of Korea
• /
• v.31 no.3
• /
• pp.119-128
• /
• 1994

Deflection estimation at engine room upper deck panel is performed for the actual ship structure. These deflection behaviours are basically investigated from not only the data based on the full series results of nonlinear analysis using Incremental Galerkin's Method but also actual deflection data measured from damaged ship under construction in dry dock. The effects of residual stress, initial deflection and static loading are also included. The computed estimation results of upper deck plate panel including theme effects are shown that upper deck platings of new ship expected less deflection magnitude than damaged ship.

• Structural Engineering and Mechanics
• /
• v.71 no.4
• /
• pp.351-361
• /
• 2019

Present article deals with the static stability analysis of compositionally graded nanocomposite beams reinforced with graphene oxide powder (GOP) is undertaken once the beam is subjected to an induced force caused by nonuniform magnetic field. The homogenized material properties of the constituent material are approximated through Halpin-Tsai micromechanical scheme. Three distribution types of GOPs are considered, namely uniform, X and O. Also, a higher-order refined beam model is incorporated with the dynamic form of the virtual work's principle to derive the partial differential motion equations of the problem. The governing equations are solved via Galerkin's method. The introduced mathematical model is numerically validated presenting a comparison between the results of present work with responses obtained from previous articles. New results for the buckling load of GOP reinforced nanocomposites are presented regarding for different values of magnetic field intensity. Besides, other investigations are performed to show the impacts of other variants, such as slenderness ratio, boundary condition, distribution type and so on, on the critical stability limit of beams made from nanocomposites.

• Nuclear Engineering and Technology
• /
• v.51 no.6
• /
• pp.1479-1486
• /
• 2019

The purpose of the present study is to develop the 3D static and noise simulator based on Galerkin Finite Element Method (GFEM) using the unstructured hexahedral elements. The 3D, 2G neutron diffusion and noise equations are discretized using the unstructured hexahedral by considering the linear approximation of the shape function in each element. The validation of the static calculation is performed via comparison between calculated results and reported data for the VVER-1000 benchmark problem. A sensitivity analysis of the calculation to the element type (unstructured hexahedral or tetrahedron elements) is done. Finally, the neutron noise calculation is performed for the neutron noise source of type of variable strength using the Green function technique. It is shown that the error reduction in the static calculation is considerable when the unstructured tetrahedron elements are replaced with the hexahedral ones. Since the neutron flux distribution and neutron multiplication factor are appeared in the neutron noise equation, the more accurate calculation of these parameters leads to obtaining the neutron noise distribution with high accuracy. The investigation of the changes of the neutron noise distribution in axial direction of the reactor core shows that the 3D neutron noise analysis is required instead of 2D.

• Structural Engineering and Mechanics
• /
• v.70 no.5
• /
• pp.623-637
• /
• 2019

This paper analyzes the non-stationary vibration and super-harmonic resonances in nonlinear dynamic motion of viscoelastic nano-resonators. For this purpose, a new coupled size-dependent model is developed for a plate-shape nano-resonator made of nonlinear viscoelastic material based on modified coupled stress theory. The virtual work induced by viscous forces obtained in the framework of the Leaderman integral for the size-independent and size-dependent stress tensors. With incorporating the size-dependent potential energy, kinetic energy, and an external excitation force work based on Hamilton's principle, the viscous work equation is balanced. The resulting size-dependent viscoelastically coupled equations are solved using the expansion theory, Galerkin method and the fourth-order Runge-Kutta technique. The Hilbert-Huang transform is performed to examine the effects of the viscoelastic parameter and initial excitation values on the nanosystem free vibration. Furthermore, the secondary resonance due to the super-harmonic motions are examined in the form of frequency response, force response, Poincare map, phase portrait and fast Fourier transforms. The results show that the vibration of viscoelastic nanosystem is non-stationary at higher excitation values unlike the elastic ones. In addition, ignoring the small-size effects shifts the secondary resonance, significantly.

• Structural Engineering and Mechanics
• /
• v.70 no.5
• /
• pp.525-534
• /
• 2019

An analytical research on buckling of simply supported thin plate with variable thickness under bi-axial compression is presented in this paper. Combining the perturbation technique, Fourier series expansion and Galerkin methods, the linear governing differential equation of the plate with arbitrary thickness variation under bi-axial compression is solved and the analytical expression of the critical buckling load is obtained. Based on that, numerical analysis is carried out for the plates with different thickness variation forms and aspect ratios under different bi-axial compressions. Four different thickness variation forms including linear, parabolic, stepped and trigonometric have been considered in this paper. The calculated critical buckling loads and buckling modes are presented and compared with the published results in the tables and figures. It shows that the analytical expressions derived by the theoretical method in this paper can be effectively used for buckling analysis of simply supported thin plates with arbitrary thickness variation, especially for the stepped thickness that used in engineering widely.

• Computers and Concrete
• /
• v.24 no.5
• /
• pp.445-452
• /
• 2019

In this paper, dynamic stress, strain and deflection analysis of concrete pipes conveying nanoparticles-water under the seismic load are studied. The pipe is buried in the soil which is modeled by spring and damper elements. The Navier-Stokes equation is used for obtaining the force induced by the fluid and the mixture rule is utilized for considering the effect of nanoparticles. Based on refined two variables shear deformation theory of shells, the pipe is simulated and the equations of motion are derived based on energy method. The Galerkin and Newmark methods are utilized for calculating the dynamic stress, strain and deflection of the concrete pipe. The influences of internal fluid, nanoparticles volume percent, soil medium and damping of it as well as length to diameter ratio of the pipe are shown on the dynamic stress, strain and displacement of the pipe. The results show that with enhancing the nanoparticles volume percent, the dynamic stress, strain and deflection decrease.

• Ocean Systems Engineering
• /
• v.11 no.1
• /
• pp.59-81
• /
• 2021

The nonlinear formulation using the principle of virtual work-energy for free vibration of a large-sag extensible catenary riser in two dimensions is presented in this paper. A support at one end is hinged and the other is a free-sliding roller in the horizontal direction. The catenary riser has a large-sag configuration in the static equilibrium state and is assumed to displace with large amplitude to the motion state. The total virtual work of the catenary riser system involves the virtual strain energy due to bending, the virtual strain energy due to axial deformation, the virtual work done by the effective weight, and the inertia forces. The nonlinear equations of motion for two-dimensional free vibration in the Cartesian coordinate system is developed based on the difference between the Euler's equations in the static state and the displaced state. The linear and nonlinear stiffness matrices of the catenary riser are obtained and the eigenvalue problem is solved using the Galerkin finite element procedure. The natural frequencies and mode shapes are obtained. The results are validated with regard to the reference research addressing the accuracy and efficiency of the proposed nonlinear formulation. The numerical results for free vibration and the effect of the nonlinear behavior for catenary riser are presented.

• Smart Structures and Systems
• /
• v.30 no.2
• /
• pp.121-133
• /
• 2022

An analytical approach for the free vibration behavior of a sandwich cylindrical shell with a functionally graded (FG) core is presented. It is considered that the FG distribution is in the direction of thickness. The material properties are temperature-dependent. The sandwich cylindrical shell with a FG core is considered with two cases. In the first model, i.e., Ceramic-FGM-Metal (CFM), the interior layer of the cylindrical shell is rich metal while the exterior layer is rich ceramic and the FG material is located between two layers and for the second model i.e., Metal-FGM-Ceramic (MFC), the material distribution is in reverse order. This study develops Carrera's Unified Formulation (CUF) to analyze sandwich cylindrical shell with an FG core for the first time. Considering the Principle of Virtual Displacements (PVDs) according to the CUF, the dependent boundary conditions and governing equations are obtained. The coupled governing equations are derived using Galerkin's method. In order to validate the present results, comparisons are made with the available solutions in the previous researches. The effects of different geometrical and material parameters on the free vibration behavior of a sandwich cylindrical shell with an FG core are examined.