• Steel and Composite Structures
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• v.33 no.3
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• pp.463-472
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• 2019

Initial thermo-elastic and steady state creep deformation of a rotating functionally graded simple blade is studied using first-order shear deformation theory. A variable thickness model for cantilever beam has been considered. The blade geometry and loading are defined as functions of length so that one can define his own blade profile and loading using any arbitrary function. The blade is subjected to a transverse distributed load, an inertia body force due to rotation and a distributed temperature field due to a thermal gradient between the tip and the root. All mechanical and thermal properties except Poisson's ratio are assumed to be longitudinally variable based on the volume fraction of reinforcement. The creep behaviour is modelled by Norton's law. Considering creep strains in stress strain relation, Prandtl-Reuss relations, Norton' law and effective stress relation differential equation in term of effective creep strain is established. This differential equation is solved numerically. By effective creep strain, steady state stresses and deflections are obtained. It is concluded that reinforcement particle size and form of distribution of reinforcement has significant effect on the steady state creep behavior of the blade.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.4
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• pp.123-135
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• 1995

A numerical procedure is described for predicting steady drift forces an multiple three-dimensional bodies of arbitrary shape freely floating in waves. The developed numerical approach is based on combination of a three-dimensional source distribution method, wave interaction theory art the far-field method using momentum theory. Numerical results are compared with the experimental or numerical ones, which are obtained in the literature, of steady drift forces on 33(3 by 11) floating composite vertical cylinders in waves. The results of comparison confirmed the validity of the proposed approach. Finally, the interaction effects are examined in the case of an array of 40(4 by 10) freely floating rectangular bodies in shallow water.

• Steel and Composite Structures
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• v.39 no.3
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• pp.275-290
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• 2021

The main purpose of this research work is to investigate the critical buckling load of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement using generalized differential quadrature (GDQ) method at thermal condition. It is supposed that the GPL nanofillers and the porosity coefficient vary continuously along the plate thickness direction. Generally, the thermal distribution is considered to be nonlinear and the temperature changing continuously through the thickness of the nanocomposite plates according to the power-law distribution. To model closed cell FG porous material reinforced with GPLs, Halpin-Tsai micromechanical modeling in conjunction with Gaussian-Random field scheme are used, through which mechanical properties of the structures can be extracted. Based on the third order shear deformation theory (TSDT) and the Hamilton's principle, the equations of motion are established and solved for various boundary conditions (B.Cs). The fast rate of convergence and accuracy of the method are investigated through the different solved examples and validity of the present study is evaluated by comparing its numerical results with those available in the literature. A special attention is drawn to the role of GPLs weight fraction, GPLs patterns through the thickness, porosity coefficient and distribution of porosity on critical buckling load. Results reveal that the importance of thermal condition on of the critical load of FGP-GPL reinforced nanocomposite plates.

• Steel and Composite Structures
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• v.29 no.5
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• pp.579-590
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• 2018

Size-dependent free vibration responses and magneto-electro-elastic bending results of a three layers piezomagnetic curved beam rest on Pasternak's foundation are presented in this paper. The governing equations of motion are derived based on first-order shear deformation theory and nonlocal piezo-elasticity theory. The curved beam is containing a nanocore and two piezomagnetic face-sheets. The piezomagnetic layers are imposed to applied electric and magnetic potentials and transverse uniform loadings. The analytical results are presented for simply-supported curved beam to study influence of some parameters on vibration and bending results. The important parameters are spring and shear parameters of foundation, applied electric and magnetic potentials, nonlocal parameter and radius of curvature of curved beam. It is concluded that the increase in radius of curvature tends to an increase in the stiffness of curved beam and consequently natural frequencies increase and bending results decrease. In addition, it is concluded that with increase of nonlocal parameter of curved beam, the stiffness of structure is decreased that leads to decrease of natural frequency and increase of bending results.

• International Journal of Naval Architecture and Ocean Engineering
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• v.12 no.1
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• pp.531-540
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• 2020

The whirl and generated forces of rotating cylinders with different diameters placed in still water and in flow are studied experimentally. For the rotating cylinders in still water, the Same Frequency Whirl (SFW) and Different Frequency Whirl (DFW) have been identified and illustrated. The corresponding SFW and DFW areas are divided. The Root Mean Square (RMS) values of the generated force coefficient dramatically increase in the defined ranges of Resonance I and Resonance II. For the rotating cylinders in flow, the hydrodynamics, SFW and DFW are illustrated. The hydrodynamic, SFW and DFW areas are divided. The RMS values of the generated forces in the range of Resonance II are much smaller than those in still water due to the generated lift forces. The discussion suggests that the frequency of the DFW may equal multiple times or one-multiple times that of the rotating frequency: the whirl direction of the DFW with multiple times the frequency of the rotating frequency is the same as the rotating direction. The whirl direction of the DFW with one-multiple times frequency of the rotating frequency is opposite to the rotating direction.

• Steel and Composite Structures
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• v.37 no.6
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• pp.695-709
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• 2020

The buckling properties of a single-layered graphene sheet (SLGS) are examined using nonlocal integral first shear deformation theory (FSDT) by incorporating the influence of visco-Pasternak's medium. This model contains only four variables, which is even less than the conventional FSDT. The visco-Pasternak's medium is introduced by considering the damping influence to the conventional foundation model which modeled by the linear Winkler's coefficient and Pasternak's (shear) foundation coefficient. The nanoplate under consideration is subjected to compressive in- plane edge loads per unit length. The impacts of many parameters such as scale parameter, aspect ratio, the visco-Pasternak's coefficients, damping parameter, and mode numbers on the stability investigation of the SLGSs are examined in detail. The obtained results are compared with the corresponding available in the literature.

• Steel and Composite Structures
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• v.43 no.5
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• pp.603-623
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• 2022

This article is dedicated to predict the natural frequencies of joined conical shell structures made of Functionally Graded Material (FGM). The structure includes two conical segments. The equivalent material properties are found by using the rule of mixture based on Voigt model. In addition, three well-known patterns are employed for distribution of material properties throughout the thickness of the structure. The main objective of the present research is to propose a novel exponential pattern and obtain the related equivalent material properties. Furthermore, the Donnell type shell theory is used to obtain the governing equations of motion. Note that these equations are obtained by employing First-order Shear Deformation Theory (FSDT). In order to discretize the governing system of differential equations, well-known and efficient semi-analytical scheme, namely Generalized Differential Quadrature Method (GDQM), is utilized. Different boundary conditions are considered for various types of single and joined conical shell structures. Moreover, an applicable modification is considered for the continuity conditions at intersection position. In the first step, the proposed formulation is verified by solving some well-known benchmark problems. Besides, some new numerical examples are analyzed to show the accuracy and high capability of the suggested technique. Additionally, several geometric and material parameters are studied numerically.

• Steel and Composite Structures
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• v.43 no.1
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• pp.31-54
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• 2022

This paper is concerned with the buckling behavior of functionally graded graphene reinforced porous nanocomposite beams based on the finite element method (FEM) using two variables trigonometric shear deformation theory. Both Young's modulus and material density of the FGP beam element are simultaneously considered as grading through the thickness of the beam. The finite element approach is developed using a nonlocal strain gradient theory. The governing equations derived here are solved introducing a 3-nodes beam element, and then the critical buckling load is calculated with different porosity distributions and GPL dispersion patterns. After a convergence and validation study to verify the accuracy of the present model, a comprehensive parametric study is carried out, with a particular focus on the effects of weight fraction, distribution pattern of GPL reinforcements on the Buckling behavior of the nanocomposite beam. The effects of various structural parameters such as the dispersion patterns for the graphene and porosity, thickness ratio, boundary conditions, and nonlocal and strain gradient parameters are brought out. The results indicate that porosity distribution and GPL pattern have significant effects on the response of the nanocomposite beams, and the results allows to identify the most effective way to achieve improved buckling behavior of the porous nanocomposite beam.

• Steel and Composite Structures
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• v.43 no.1
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• pp.117-127
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• 2022

This study investigates the wave propagation in porous functionally graded (FG) sandwich plates subjected to hygrothermal environments. A new simple three-unknown first-ordershear deformation theory (FSDT) incorporating an integral term is utilized in this paper. Only three unknowns are used to formulate the governing differential equation by applying the Hamilton principle. The FG layer of the sandwich plate is modeled using the power-law function with evenly distributed porosities to represent the defects of the manufacturing process. The plate is subjected to nonlinear hygrothermal changes across the thickness. The effects of the power-law exponent, core to thickness ratios, porosity volume, and the relations between volume fraction and wave properties of porous FG plate under the hygrothermal environment are investigated. The results showed that the waves' phase velocities increase linearly with the waves number in the FGM plate. The porosity of the FG materials plate has a noticeable impact on the phase velocity when considering the high ratios of the core layer. It has a negligible effect on small core layers. Finally, it is observed that changing temperatures and moistures do not influence the relationship between the power law and the phase velocity.

• Steel and Composite Structures
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• v.41 no.6
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• pp.805-820
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• 2021

In this research, the buckling and free vibration of three-phase carbon nanotubes/ fiber/ polymer piezoelectric nanocomposite face sheet sandwich microbeam with microsensor and micro-actuator surrounded in elastic foundation based on modified couple stress theory (MCST) is investigated. Three types of porous materials are considered for sandwich core. Higher order (Reddy) and sinusoidal shear deformation beam theories are employed for the displacement fields. Sinusoidal surface stress effects are extracted for sinusoidal shear deformation beam theory. The equations of motion are derived by Hamilton's principle and then the natural frequency and critical buckling load are obtained by Navier's type solution. The determined results are in good agreement with other literatures. The detailed numerical investigation for various parameters is performed for this microsensor-microactuator. The results reveal that the microsensor-microactuator enhanced by increasing of Skempton coefficient, carbon nanotubes diameter length to thickness ratio, small scale factor, elastic foundation, surface stress constants and reduction in porous coefficient, micro-actuator voltage and CNT weight fraction. The valuable results can be expedient for micro-electro-mechanical (MEMS) and nano-electro-mechanical (NEMS) systems.