Exact three-dimensional analysis for static torsion of piezoelectric rods

Based on the theory of elasticity, exact analytical and numerical solutions of piezoelectric rods under static torsion are studied. In this paper, direct solution method is used. The main scope is to check the extension of validity of assumptions in previous papers that had been made based on linear distribution of electric potential through the cross section and their influences on deflection and the angle of rotation. Stress and electric induction functions are employed to obtain the exact solution of the static and electrostatic equilibrium equations under torsional loading. It is shown that previous assumptions are valid only in some types of piezoelectric materials, while in other types these assumptions lead to considerable deviations from accurate modeling. The present analytical solutions are compared with three-dimensional finite element analysis results and absolute agreements are found. At the end of this article, torsional rigidity, shape-effects on induced piezoelectric deformation and the range of valid region for linear distribution of electric potential assumption have been studied.     

Tea-industry waste activated carbon, as a novel adsorbent, for separation, preconcentration and speciation of chromium

Activated carbon was produced from tea-industry wastes (TIWAC) and employed as a low cost and effective solid phase material for the separation, preconcentration and speciation of chromium species without using a complexing agent, prior to determination by flame atomic absorption spectrometry (FAAS). The characterization of TIWAC was performed by utilizing several techniques such as Fourier Transform Infrared (FTIR) Spectroscopy, Scanning Electron Microscopy (SEM), and elemental analysis. The adsorption experiments were conducted in a batch adsorption technique. Under the experimental conditions, Cr(VI) adsorption amount was nearly equal to zero, however the adsorption percentage of Cr(III) was in the range of 95–100%. Therefore total chromium was determined after the reduction of Cr(VI) to Cr(III) and Cr(VI) was calculated by subtracting Cr(III) concentration from total chromium concentration. The suitable conditions for adsorption and speciation processes were evaluated in terms of pH, eluent type and volume, TIWAC concentration, adsorption and desorption contact time, etc. Adsorption capacity of TIWAC was found to be 61.0 mg g⁻¹. The detection limit for Cr(III) was found to be 0.27 μg L⁻¹ and the preconcentration factor was 50 for 200 mL of sample volume. The procedure was applied to the determination and speciation of chromium in stream, tap and sea water. Also, the proposed method was applied to total chromium preconcentration in microwave digested tobacco and dried eggplant samples with satisfactory results. The method was validated by analyzing certified reference materials (CRM-TMDW-500 Drinking Water and CRM-SA-C Sandy Soil C) and the results were in good agreement with the certified values.     

Fiber Remodeling During Torsion of a Fiber Reinforced Hyperelastic Cylinder��Unloading Behavior

Previous studies introduced a constitutive theory for fiber reinforced hyperelastic materials that allows the fibers to undergo microstructural changes. In this theory, increasing deformation of the matrix leads to increasing stretch of the fibers that causes their gradual dissolution. The dissolving fibers reassemble in the direction of maximum principal stretch of the matrix. The implications of the constitutive theory were first studied for two homogeneous deformations: uniaxial extension along the fibers and simple shear in the direction normal to the fibers. The constitutive theory was then used in treatment of the non-homogeneous deformation of combined axial stretch and twisting. The emphasis was on the determination of the influence of increasing axial stretch and twist on the spatial distribution of fiber dissolution and reassembly within the cylinder and also on the axial force and torque applied to the end faces of the cylinder. The present work is concerned with another aspect of combined axial stretch and twisting of the cylinder, namely unloading following dissolution and reassembly of some of the fibers. In this case, the cylinder is given an initial twist until there is an inner core of original fiber/matrix material and an outer sheath of remodeled fiber/matrix material. A condition is established that determines the combinations of axial stretch and twist that cause no additional dissolution and reassembly of fibers during unloading. It is also shown that there is a residual axial stretch and twist if the axial force and torque become zero. A numerical example illustrates this for a particular choice of matrix and fiber properties.     

Iterative Methods for Triple Hierarchical Variational Inequalities in Hilbert Spaces

In this paper, we consider a variational inequality with a variational inequality constraint over a set of fixed points of a nonexpansive mapping called triple hierarchical variational inequality. We propose two iterative methods, one is implicit and another one is explicit, to compute the approximate solutions of our problem. We present an example of our problem. The convergence analysis of the sequences generated by the proposed methods is also studied.     

Study of the Coordination Properties of 1,2-Bis(2,6-dimethphenylamino) Glyoxime and Determine the Stability Constant of Its Complexes with Ni(II), Cu(II) and Zn(II) Metal Ions in Solution

This study aims to investigate the nature and type of complexes formed in solution between 1,2-bis(2,6-dimethphenylamino) glyoxime (DPG) and the ions Ni²⁺, Cu²⁺ and Zn²⁺. Potentiometric titration was used to follow the formation of complexes.The complexes formed were studied through the determination of stability constants of these complexes in mixed ethanol–aqueous solution at 25±0.1?°C and ionic strength of 0.1 mol?dm^?3 NaCl. The basicity of the ligand was also assessed by the determination of the dissociation constants of the ligand. All of the constants were determined by computer refinement of pH–volume data using the SUPERQUAD program. The species distribution diagrams were also calculated.Comparison with other vic-dioximes was made to provide reliable support for the formation of the proposed complexes in solution.     

关于图的符号边全控制数

Let G = （V,E） be a graph.A function f ： E → {-1,1} is said to be a signed edge total dominating function （SETDF） of G if e ∈N（e） f（e ） ≥ 1 holds for every edge e ∈ E（G）.The signed edge total domination number γ st （G） of G is defined as γ st （G） = min{ e∈E（G） f（e）｜f is an SETDF of G}.In this paper we obtain some new lower bounds of γ st （G）.     

Reversibility of 1D Cellular Automata with Periodic Boundary over Finite Fields $\pmb{ {\mathbb{Z}}}_{p}$

The reversibility problem for linear cellular automata with null boundary defined by a rule matrix in the form of a pentadiagonal matrix was studied recently over the binary field ℤ₂ (del Rey and Rodriguez Sánchez in Appl. Math. Comput., 2011, doi:). In this paper, we study one-dimensional linear cellular automata with periodic boundary conditions over any finite field ℤ _p . For any given p≥2, we show that the reversibility problem can be reduced to solving a recurrence relation depending on the number of cells and the coefficients of the local rules defining the one-dimensional linear cellular automata. More specifically, for any given values (from any fixed field ℤ _p ) of the coefficients of the local rules, we outline a computer algorithm determining the recurrence relation which can be solved by testing reversibility of the cellular automaton for some finite number of cells. As an example, we give the full criteria for the reversibility of the one-dimensional linear cellular automata over the fields ℤ₂ and ℤ₃.     

Binomial sums involving harmonic numbers

This paper develops the approach to the evaluation of a class of infinite series that involve special products of binomial type, generalized harmonic numbers of order 1 and rational functions. We give new summation results for certain infinite series of non-hypergeometric type. New formulas for the number π are included.     

Probabilistic nonlinear analysis of CFR dams by MCS using Response Surface Method

This paper presents the probabilistic analysis of concrete-faced rockfill (CFR) dams according to the Monte Carlo Simulation (MCS) results which are obtained through the Response Surface Method (RSM). ANSYS finite element program is used to get displacement and principal stress components. First of all, some parametric studies are performed according to the simple and representative finite element model of dam body to obtain the optimum approximate model. Secondly, a sensitivity analysis is performed to get the most effective parameters on dam response. Then, RSM is used to obtain the approximate function through the selected parameters. After the performed analyses, star experimental design with quadratic function without mixed terms according to the k = 1 is determined as the most appropriate model. Finally, dam-foundation-reservoir interaction finite element model is constituted and probabilistic analyses are performed with MCS using the selected parameters, sampling method, function and arbitrary factor under gravity load for empty and full reservoir conditions. Geometrically and materially nonlinearity are considered in the analysis of dam-foundation-reservoir interaction system. Reservoir water is modeled by fluid finite elements based on the Lagrangian approach. Structural connections are modeled as welded contact and friction contact based on Coulomb’s friction law. Probabilistic displacements and stresses are presented and compared with deterministic results.     

A model updating approach based on design points for unknown structural parameters

Finite element analysis has become an essential tool to estimate structural responses under static and dynamic loads. However, there are a lot of uncertainties in structural properties. For this reason, in many cases, the outcomes of the theoretical and experimental modal analyses do not match. Therefore, the analytical models of the structures need to be updated according to the experimental test results. The commonly used method to get parameters for model updating is experimental modal analysis which provides structural dynamic characteristic (natural frequencies, mode shapes and modal damping ratio). There are many methods available for the updating process. This study addresses an updating algorithm to modify the numerical models by using the design points for unknown structural properties. The proposed method aims to minimize the difference between the analytical and experimental natural frequencies by updating uncertain parameters for each mode and combine them to get an optimum solution. The algorithm is tested on a column and a 2D frame models. These models are investigated by taking the connection rigidity and elasticity modulus as unknown parameters. It is observed that the proposed algorithm gives better results for unknown structural properties compared to the initial values.