• Membrane and Water Treatment
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• v.7 no.1
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• pp.23-38
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• 2016

Batch adsorption of methyl orange (MO) from aqueous solution using three kinds of anion exchange membranes BI, BIII and DF-120B having different ion exchange capacities (IECs) and water uptakes ($W_R$) was investigated at room temperature. The FTIR spectra of anion exchange membranes was analysed before and after the adsorption of MO dye to investigate the intractions between dye molecules and anion exchange membranes. The effect of various parameters such as contact time, initial dye concentration and molarity of NaCl on the adsorption capacity was studied. The adsorption capacity found to be increased with contact time and initial dye concentration but decreased with ionic strength. The adsorption of MO on BI, BIII and DF-120B followed pseudo-first-order kinetics and the nonlinear forms of Freundlich and Langmuir were used to predict the isotherm parameters. This study demonstrates that anion exchange membranes could be used as useful adsorbents for removal of MO dye from wastewater.

• Structural Engineering and Mechanics
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• v.50 no.3
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• pp.403-417
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• 2014

The present paper addresses a general formulation for the thermo elastic analysis of a functionally graded cylindrical shell subjected to external loads. The shear deformation theory and energy method is employed for this purpose. This method presents the final relations by using a set of second order differential equations in terms of integral of material properties along the thickness direction. The proposed formulation can be considered for every distribution of material properties, whether functional or non functional. The obtained formulation can be used for manufactured materials or structures with numerical distribution of material properties which are obtained by using the experiments. The governing differential equation is applied for two well-known functionalities and some previous results are corrected with present true results.

• Structural Engineering and Mechanics
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• v.12 no.1
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• pp.85-100
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• 2001

In this paper, an analytical procedure for solving several static and dynamic problems of non-uniform beams is proposed. It is shown that the governing differential equations for several stability, free vibration and static problems of non-uniform beams can be written in the from of a unified self-conjugate differential equation of the second-order. There are two functions in the unified equation, unlike most previous researches dealing with this problem, one of the functions is selected as an arbitrary expression in this paper, while the other one is expressed as a functional relation with the arbitrary function. Using appropriate functional transformation, the self-conjugate equation is reduced to Bessel's equation or to other solvable ordinary differential equations for several cases that are important in engineering practice. Thus, classes of exact solutions of the self-conjugate equation for several static and dynamic problems are derived. Numerical examples demonstrate that the results calculated by the proposed method and solutions are in good agreement with the corresponding experimental data, and the proposed procedure is a simple, efficient and exact method.

• Smart Structures and Systems
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• v.26 no.1
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• pp.77-87
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• 2020

By employing a quasi-3D plate formulation, the present research studies static stability of magneto-electro-thermo-elastic functional grading (METE-FG) nano-sized plates. Accordingly, influences of shear deformations as well as thickness stretching have been incorporated. The gradation of piezo-magnetic and elastic properties of the nano-sized plate have been described based on power-law functions. The size-dependent formulation for the nano-sized plate is provided in the context of nonlocal elasticity theory. The governing equations are established with the usage of Hamilton's rule and then analytically solved for diverse magnetic-electric intensities. Obtained findings demonstrate that buckling behavior of considered nanoplate relies on the variation of material exponent, electro-magnetic field, nonlocal coefficient and boundary conditions.

• Coupled systems mechanics
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• v.5 no.4
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• pp.305-314
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• 2016

We utilize first-principles calculations within density-functional theory to investigate the possibility of strain engineering in the tuning of the band structure of two-dimensional $MoS_2$. We find that the band structure of $MoS_2$ monolayers transits from direct to indirect when mechanical strain is applied. In addition, we discuss the change in the band gap energy and the critical stains for the direct-to-indirect transition under various strains such as uniaxial, biaxial, and pure shear. Biaxial strain causes a larger change, and the pure shear stain causes a small change in the electronic band structure of the $MoS_2$ monolayer. We observe that the change in the interaction between molecular orbitals due to the mechanical strain alters the band gap type and energy.

• Advances in Computational Design
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• v.5 no.2
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• pp.147-175
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• 2020

To achieve appropriate stresses, two new rectangular elements are presented in this study. For reaching this aim, a complementary energy functional is used within an element for the analysis of plane problems. In this energy form, the Airy stress function will be used as a functional variable. Besides, some basic analytical solutions are found for the stress functions. These trial functions are matched with each element number of degrees of freedom, which leads to a number of equations with the anonymous constants. Subsequently, according to the principle of minimum complementary energy, the unknown constants can be expressed in terms of displacements. This system can be rewritten in terms of the nodal displacement. In this way, two new hybrid-rectangular triangular elements are formulated, which have 16 and 40 degrees of freedom. To validate the outcomes, extensive numerical studies are performed. All findings clearly demonstrate accuracies of structural displacements, as well as, stresses.

• Smart Structures and Systems
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• v.21 no.2
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• pp.187-194
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• 2018

This paper focuses on the $H_{\infty}$ filter design problem for offshore steel jacket platforms. Its objective is to design a full-order state observer for offshore platforms in presence of unknown disturbances. To make the method more practical, it is assumed that the measured variables are available at discrete-time instants with time-varying sampling time intervals. By modelling the sampling intervals as a bounded time-varying delay, the estimation error system is expressed as a time-delay system. As a result, the addressed problem can be transformed to the problem of stability of dynamic error between the system and the state estimator. Then, based on the Lyapunov-Krasovskii Functional (LKF), a stability criterion is obtained in the form of Linear Matrix Inequalities (LMIs). According to the stability criterion, a sufficient condition on designing the state estimator gain is obtained. In the end, the proposed method is applied to an offshore platform to show its effectiveness.

• Structural Engineering and Mechanics
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• v.13 no.2
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• pp.155-170
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• 2002

In this study, a new functional is obtained for folded plates with geometric (kinematic) and dynamic (natural) boundary conditions. This functional is the combination of two different functionals. Both functionals are obtained for thick plates which carry in-plane and lateral forces. A new mixed finite element is developed with $4{\times}13$ nodal parameters for folded plates (REC52). Forces and moments which are the necessary unknowns in engineering problems are obtained directly using the technique suggested here. The use of the global co-ordinate system causes time consuming operations and therefore the Lagrange multiplier method is used to relate the components of the parameters on the fold line. Numerical results are presented for folded plates and compared with experimental results.

• Structural Engineering and Mechanics
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• v.69 no.4
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• pp.427-437
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• 2019

In this study, an alternative solution procedure presented by using variational methods for analysis of shear deformable functionally graded material (FGM) beams with mixed formulation. By using the advantages of $G{\hat{a}}teaux$ differential approaches, a refined complex general functional and boundary conditions which comprises seven independent variables such as displacement, rotation, bending moment and higher-order bending moment, shear force and higher-order shear force, is derived for general thick-thin FGM beams via shear deformation beam theories. The mixed-finite element method (FEM) is employed to obtain a beam element which have a 2-nodes and total fourteen degrees-of-freedoms. A computer program is written to execute the analyses for the present study. The numerical results of analyses obtained for different boundary conditions are presented and compared with results available in the literature.

• Advances in Computational Design
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• v.9 no.2
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• pp.97-113
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• 2024

In this paper, we proposed a new class of stochastic neutral neural networks with uncertain and deterministic coefficients. Made the Sigmund activation and Lipschitz activation functions less conditional. The Lyapnov-Krasovskii functional is constructed. The linear matrix inequality (LMI) is constructed using Schur's lemma, and new criteria for the global asymptotic stability and global asymptotic robust stability of neural networks are obtained. Furthermore, we have verified that the method is effective and feasible through numerical examples.