• Structural Engineering and Mechanics
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• v.52 no.4
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• pp.663-686
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• 2014

This paper deals with free vibration analysis of bidirectional functionally graded annular plates resting on a two-parameter elastic foundation. The formulations are based on the three-dimensional elasticity theory. This study presents a novel 2-D six-parameter power-law distribution for ceramic volume fraction of 2-D functionally graded materials that gives designers a powerful tool for flexible designing of structures under multi-functional requirements. Various material profiles along the thickness and in the in-plane directions are illustrated by using the 2-D power-law distribution. The effective material properties at a point are determined in terms of the local volume fractions and the material properties by the Mori-Tanaka scheme. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The fast rate of convergence of the method is shown and the results are compared against existing results in literature. Some new results for natural frequencies of the plates are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The interesting results indicate that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional 1-D functionally graded materials.

• Steel and Composite Structures
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• v.28 no.6
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• pp.735-748
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• 2018

In this study, the semi-analytical finite strip method is adopted to examine the free vibration of cylindrical shells made up of functionally graded material. The properties of functionally graded shells are assumed to be temperature-dependent and vary continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of ceramic and metal. The material properties of the shells and stiffeners are assumed to be continuously graded in the thickness direction. Theoretical formulations based on the smeared stiffeners technique and the classical shell theory with first-order shear deformation theory which accounts for through thickness shear flexibility are employed. The finite strip method is applied to five different shell theories, namely, Donnell, Reissner, Sanders, Novozhilov, and Teng. The approximate procedure is compared favorably with three-dimensional finite elements. Finally, a detailed numerical study is carried out to bring out the effects of power-law index of the functional graded material, stiffeners, and geometry of the shells on the difference between various shell theories. Finally, the importance of choosing the shell theory in simulating the functionally graded cylindrical shells is addressed.

• Carbon letters
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• v.9 no.4
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• pp.289-293
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• 2008

Naphtha Cracking Bottom (NCB) oil was heat reformed at various reforming temperature and time, and the volatile extracts were characterized including yields, molecular weight distributions, and representative compounds. The yield of extract increased as the increase of reforming temperature ($360{\sim}420^{\circ}C)$ and time (1~4 hr). Molecular weight of the as-received NCB oil was under 200, and those of extracts were distributed in the range of 100-250, and far smaller than those of precursor pitches of 380-550. Naphtalene-based compounds were more than 70% in the as-received NCB oil, and most of them were isomers of compounds bonding functional groups, such as methyl ($CH_{3^-}$) and ethyl ($C_2H_{5^-}$). When the as-received NCB oil was reformed at $360^{\circ}C$ for 1 hr, the most prominent compound was 1,2-Butadien, 3-phenyl- (24.57%), while naphthalene became main component again as increasing the reforming temperature.

• Earthquakes and Structures
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• v.4 no.3
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• pp.241-264
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• 2013

Since the beginning of the twentieth century, the progressive and rapid spread of reinforced concrete (RC) has led to the adoption of mixed masonry-RC solutions, such as the confined masonry. However, together with structures conceived with a definite role for earthquake behaviour, the spreading of RC technology has caused the birth of mixed solutions inspired more by functional aspects than by structural ones, such as: internal masonry walls replaced by RC frames, RC walls inserted to build staircases or raising made from RC frames. Usually, since these interventions rise from a spontaneous build-up, any capacity design or ductility concepts are neglected being designed only to bear vertical loads: thus, the vulnerability assessment of this class becomes crucial. To investigate the non-linear seismic response of these structures, suitable models and effective numerical tools are needed. Among the various modelling approaches proposed in the literature and codes, the authors focus their attention on the equivalent frame model. After a brief description of the adopted model and its numerical validation, the authors aim to point out some specific peculiarities of the seismic response of mixed masonry-RC structures and their repercussions on safety verification procedures (referring in particular way to the non-linear static ones). In particular, the results of non-linear static analyses performed parametrically to various configurations representative of different interventions are discussed.

• Advances in concrete construction
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• v.9 no.6
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• pp.569-576
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• 2020

Employment of the wave propagation approach with the combination of Pasternak foundation equation gives birth to the shell frequency equation. Mathematically, the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. A cylindrical shell is placed on the elastic foundation of Pasternak. For isotropic materials, the physical properties are same everywhere, whereas the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. The influence of the elastic foundation, wave number, length and height-to-radius ratios is investigated with different boundary conditions. The frequencies of length-to-radius and height-to-radius ratio are counter part of each other. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down for the variations of wave number. It is found that due to inducting the elastic foundation of Pasternak, the frequencies increases. It is also exhibited that the effect of frequencies is investigated by varying the surfaces with stainless steel and nickel as a constituent material. MATLAB software is utilized for the vibration of functionally graded cylindrical shell with elastic foundation of Pasternak and the results are verified with the open literature.

• Steel and Composite Structures
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• v.23 no.1
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• pp.1-16
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• 2017

This paper is presented to solve the buckling problem of functionally graded truncated conical shells subjected to displacement-dependent pressure which remains normal to the shell middle surface throughout the deformation process by the semi-analytical finite strip method. Material properties are assumed to be temperature dependent, and varied continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of a ceramic and metal. The governing equations are derived based on first-order shear deformation theory which accounts for through thickness shear flexibility with Sanders-type of kinematic nonlinearity. The element linear and geometric stiffness matrices are obtained using virtual work expression for functionally graded materials. The load stiffness also called pressure stiffness matrix which accounts for variation of load direction is derived for each strip and after assembling, global load stiffness matrix of the shell which may be un-symmetric is formed. The un-symmetric parts which are due to load non-uniformity and unconstrained boundaries have been separated. A detailed parametric study is carried out to quantify the effects of power-law index of functional graded material and shell geometry variations on the difference between follower and non-follower lateral buckling pressures. The results indicate that considering pressure stiffness which arises from follower action of pressure causes considerable reduction in estimating buckling pressure.

• Geomechanics and Engineering
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• v.14 no.1
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• pp.91-98
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• 2018

Length of a vehicle is an important variation to generate different variants of an automotive platform. This parameter is usually adjusted by embedding dimensional flexibility into different components of the Body in White (BIW) including the floor pan. Due to future uncertainties, it is not necessarily possible to define certain values of wheelbase for the future products of a platform. This work is performed to add flexibility into the design process of a length-variable floor pan. By means of this analysis, the cost and time consuming process of optimization is not necessary to be performed for designing the different variants of a product family. Stiffness and mass of the floor pan are two important functional requirements of this component which directly affect the occupant comfort, dynamic characteristics, fuel economy and environmental protection of the vehicle. A combination of Genetic algorithm, GMDH-type of artificial neural networks and TOPSIS methods is used to optimally design the floor pan associated with arbitrary length of the variant in the defined system range. The correlation between the optimal results shows that for a constant mass of the floor pan, the first natural frequency decreases by increasing the length of this component.

• Earthquakes and Structures
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• v.14 no.2
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• pp.117-128
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• 2018

In this research work, free vibrations of simply supported functionally graded plate resting on a Winkler-Pasternak elastic foundation are investigated by a new shear deformation theory. The influence of alternative micromechanical models on the macroscopic behavior of a functionally graded plate based on shear-deformation plate theories is examined. Several micromechanical models are tested to obtain the effective material properties of a two-phase particle composite as a function of the volume fraction of particles which continuously varies through the thickness of a functionally graded plate. Present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. The energy functional of the system is obtained using Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. Finally, the numerical results are provided to reveal the effect of explicit micromechanical models on natural fundamental frequencies.

• Computers and Concrete
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• v.25 no.5
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• pp.411-425
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• 2020

In this paper, the shell material has been taken as functionally graded material and their material quantity is located by the exponential volume fraction law. Moreover, the impact of ring supports around the shell circumference has been examined for their various positions along the shell axial length. These rings support restraints the radial displacement in the transverse direction. While the axial modal deformation functions have been estimated by characteristic beam functions and nature of materials used for construction of cylindrical shells. The fundamental natural frequency of cylindrical shell of parameter versus ratios of length- and height-to-radius for a wide range has been reported and investigated through the study. In addition, by increasing height-to-radius ratio resulting frequencies also increase and frequencies decrease on ratio of length-to-radius. Though the trends of frequency values of both ratios are converse to each other with three different boundary conditions. Also it is examined the position of ring supports with length-to radius ratio, height-to-radius ratio and varying the exponent of volume fraction. MATLAB software package has been utilized for extracting shell frequency spectra. The obtained results are confirmed by comparing with available literature.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.111-112
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• 2006

A new MR cylinder with built-in valves using Magneto - Rheological fluid (MR valve) is proposed for fluid power control systems. The MR fluid is a newly developed functional fluid whose obvious viscosity is controlled by the applied magnetic field intensity. This MR cylinder, which is composed of cylinder with small clearance and piston with electromagnet, has the characteristics of simple, compact and reliable structure. This paper presents a method to control the pressure of MR cylinder by using Generalized Predictive Control (GPC) algorithm. The differential pressure is controlled by applying magnetic field intensity to MR fluid. The use of GPC controller is to generate a control sequence by minimizing a cost function in such a way that the future system output is driven close to reference over finite prediction horizons. Experimental results from real time control using GPC method compared with conventional PID control method are also shown in this paper.