• Steel and Composite Structures
• /
• v.32 no.5
• /
• pp.595-610
• /
• 2019

This paper deals with the static and dynamic behavior of Functionally Graded Carbon Nanotubes (FG-CNT)-reinforced porous sandwich (PMPV) polymer plate. The model of nanocomposite plate is investigated within the first order shear deformation theory (FSDT). Two types of porous sandwich plates are supposed (sandwich with face sheets reinforced / homogeneous core and sandwich with homogeneous face sheets / reinforced core). Functionally graded Carbon Nanotubes (FG-CNT) and uniformly Carbon Nanotubes (UD-CNT) distributions of face sheets or core porous plates with uniaxially aligned single-walled carbon nanotubes are considered. The governing equations are derived by using Hamilton's principle. The solution for bending and vibration of such type's porous plates are obtained. The detailed mathematical derivations are provided and the solutions are compared to some cases in the literature. The effect of the several parameters of reinforced sandwich porous plates such as aspect ratios, volume fraction, types of reinforcement, number of modes and thickness of plate on the bending and vibration analyses are studied and discussed. On the question of porosity, this study found that there is a great influence of their variation on the static and vibration of porous sandwich plate.

• Steel and Composite Structures
• /
• v.29 no.6
• /
• pp.749-758
• /
• 2018

This article derived a hybrid coupling technique using the higher-order displacement polynomial and three soft computing techniques (teaching learning-based optimization, particle swarm optimization, and artificial bee colony) to predict the optimal stacking sequence of the layered structure and the corresponding frequency values. The higher-order displacement kinematics is adopted for the mathematical model derivation considering the necessary stress and stain continuity and the elimination of shear correction factor. A nine noded isoparametric Lagrangian element (eighty-one degrees of freedom at each node) is engaged for the discretisation and the desired model equation derived via the classical Hamilton's principle. Subsequently, three soft computing techniques are employed to predict the maximum natural frequency values corresponding to their optimum layer sequences via a suitable home-made computer code. The finite element convergence rate including the optimal solution stability is established through the iterative solutions. Further, the predicted optimal stacking sequence including the accuracy of the frequency values are verified with adequate comparison studies. Lastly, the derived hybrid models are explored further to by solving different numerical examples for the combined structural parameters (length to width ratio, length to thickness ratio and orthotropicity on frequency and layer-sequence) and the implicit behavior discuss in details.

• Earthquakes and Structures
• /
• v.16 no.1
• /
• pp.109-118
• /
• 2019

This study, analyses the seismic response for a rigid massless square foundation resting on a viscoelastic soil layer limited by rigid bedrock. The foundation is subjected either to externally applied forces or to obliquely incident seismic body or surface harmonic seismic waves P, SV and SH. A 3-D frequency domain BEM formulation in conjunction with the thin layer method (TLM) is adapted here for the solution of elastodynamic problems and used for obtained the seismic response. The mathematical approach is based on the method of integral equations in the frequency domain using the formalism of Green's functions (Kausel and Peck 1982) for layered soil, the impedance functions are calculated by the compatibility condition. In this study, The key step is the characterization of the soil-foundation interaction with the input motion matrix. For each frequency the impedance matrix connects the applied forces to the resulting displacement, and the input motion matrix connects the displacement vector of the foundation to amplitudes of the free field motion. This approach has been applied to analyze the effect of soil-structure interaction on the seismic response of the foundation resting on a viscoelastic soil layer limited by rigid bedrock.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.12 no.1
• /
• pp.645-656
• /
• 2020

In this study (Part II), the empirical formulation of corrosion model of a ship's ballast tank was developed to predict nonlinear time-dependent corrosion wastage based on the advanced data processing technique proposed by Part I. The detail on how to propose generalised mathematical formulation of corrosion model was precisely documented in the previous paper (Part I). The statistical scatter of corrosion data at any exposure time was investigated by the refined method and formulated based on a 2-parameter Weibull distribution which selected the best fit PDF. Throughout the nine (9) steps, empirical formulation of the ship's seawater ballast tank was successfully proposed and four (4) key step results were also obtained. The proposed method in Part I was verified and confirmed by this application of seawater ballast tank, thus making it possible to predict accurate behaviours of nonlinear timedependent corrosion. Developed procedures and obtained corrosion damage model for ship's seawater ballast tank can be used for development of engineering software.

• Journal for History of Mathematics
• /
• v.33 no.6
• /
• pp.303-314
• /
• 2020

Extending the method of extractions of square and cube roots in Jiuzhang Suanshu, Jia Xian introduced zengcheng kaifangfa in the 11th century. The process of zengcheng kaifangfa is exactly the same with that in Ruffini-Horner method introduced in the 19th century. The latter is based on the synthetic divisions, but zengcheng kaifangfa uses the binomial expansions. Since zengcheng kaifangfa is based on binomial expansions, traditional mathematicians in East Asia could not relate the fact that solutions of polynomial equation p(x) = 0 are determined by the linear factorization of p(x). The purpose of this paper is to reveal the difference between the mathematical structures of zengcheng kaifangfa and Ruffini-Honer method. For this object, we first discuss the reasons for zengcheng kaifangfa having difficulties to connect solutions with linear factors. Furthermore, investigating multiple solutions of equations constructed by tianyuanshu, we show differences between two methods and the structure of word problems in the East Asian mathematics.

• International Journal of Advanced Culture Technology
• /
• v.10 no.3
• /
• pp.339-345
• /
• 2022

In this paper, the effect of porosity on the acoustic phase velocity of the 3D printed Kelvin closed-cell structure was investigated using the spectral phase analysis. Since Kelvin cells bring about the large amount of scattering, acoustic pulses in ultrasonic measurements undergoes a distortion of waveforms due to the dispersion effect. In order to take account on the dispersion, mathematical expressions for calculating the phase velocity of longitudinal waves propagating normal to the plane of the Kelvin structure are suggested by introducing a complex wave number based on Fourier transform. 3D Kelvin structure composed of identical unit-cells, a polyhedron of 14 faces with 6 quadrilateral and 8 hexagonal faces, was developed and fabricated by 3D CAD and 3D printer to represent the micro-structure of porous materials such as aluminum foam and cancellous bone. Total nine samples of 3D Kelvin structure with different porosity were made by changing the thickness of polyhedron. Ultrasonic pulse of 1MHz center frequency was applied to the Kelvin structures for the measurement of the phase velocity of ultrasound using the TOF(time-of-flight) and the phase spectral method. From the experimental results, it was found that the acoustic phase velocity decreased linearly with the porosity.

• Steel and Composite Structures
• /
• v.43 no.6
• /
• pp.689-706
• /
• 2022

Thin-walled square concrete-filled double steel tubular (CFDST) columns composed of the inner circular tube filled with concrete can be used to carry the large axial loads or strengthen existing CFST columns in composite constructions. This paper reports an experimental program carried out on short square CFDST columns loaded concentrically. The influences of important column parameters on the post-buckling performance of such columns are investigated. Test results exhibit that the inner circular tube significantly improves the ultimate loads and the ductility of such columns compared to conventional concrete-filled steel tubular (CFST) and double-skin CFST (DCFST) columns with an inner void. A mathematical model developed is used to simulate the ultimate strengths and load-strain curves of such columns loaded axially. Furthermore, the ultimate strengths of such columns are predicted using existing codified design models for conventional CFST columns as well as the formulas proposed by previous researchers and compared against a large database comprising 500 CFDST columns. Lastly, an accurate artificial neural network model is developed for the practical applications of such columns under axial loading.

• Smart Structures and Systems
• /
• v.29 no.3
• /
• pp.395-420
• /
• 2022

A new hybrid quasi-3D and 2D high-order shear deformation theory is studied in this mathematical formulation, for an investigation of the bending, free vibrations and buckling influences on a functionally graded material plate. The theoretical formulation has been begun by a displacement field of five unknowns, governing the transverse displacement across the thickness of the plate by bending, shearing and stretching. The transverse shear deformation effect has been taken into consideration, satisfying the stress-free boundary conditions, especially on plate free surfaces as parabolic variation through its thickness. Thus, the mechanical properties of the functionally graded plate vary across the plate thickness, following three distributions forms: the power law, exponential form and the Mori-Tanaka scheme. The mechanical properties are used to develop the equations of motion, obtained from the Hamilton principle, and solved by applying the Navier-type solution for simply supported boundary conditions. The results obtained are compared with other solutions of 2D, 3D and quasi-3D plate theories have been found in the literature.

• Smart Structures and Systems
• /
• v.29 no.4
• /
• pp.577-588
• /
• 2022

Oil refineries' Fluid Catalytic Cracking Units (FCCU) when in full operation may exhibit strong fluid dynamics caused by turbulent flow in the piping system that may induce vibrations in other mechanical and structural components of the Unity. This paper reports on the experimental-theoretical-computational program performed to get the vibration properties and the dynamic response amplitudes to find out alternative solutions to attenuate the excessive vibrations that were causing fatigue fractures in components of the bottle like reactor-regenerator of an FCC unit in operation in an existing oil refinery in Brazil. Solutions to the vibration problem were sought with the aid of a 3D finite element model calibrated with the results obtained from experimental measurements. A short description of the found solutions is given and their effectiveness are shown by means of numerical results. The solutions were guided by the concepts of structural stiffening and dynamic control performed by a nonlinear pendulum controller whose mechanical design was based on parameters determined by means of a parametric study carried out with 2D and 3D mathematical models of the coupled pendulum-structure system. The effectiveness of the proposed solutions is evaluated in terms of the fatigue life of critical welded connections.

• Steel and Composite Structures
• /
• v.43 no.2
• /
• pp.229-240
• /
• 2022

The main objective of this work is presenting a mathematical model for the concrete slab with fiber reinforced polymer (FRP) layer under the impact load. Impacts are assumed to occur normally over the top slab and the interaction between the impactor and the structure is simulated using a new equivalent three-degree-of-freedom (TDOF) spring-mass-damper (SMD) model. The structure is assumed viscoelastic based on Kelvin-Voigt model. Based on the sinusoidal shear deformation theory (SSDT), energy method and Hamilton's principle, the motion equations are derived. Applying DQM, the dynamic deflection and contact force of the structure is calculated numerically so that the effects of mass, velocity and height of impactor, boundary conditions, FRP layer, structural damping and geometrical parameters of structure are shown on the dynamic deflection and contact force of system. Results show that considering structural damping leads to lower dynamic deflection and contact force. In addition, increasing the impact velocity of impactor yields to increases in the maximum contact force and deflection while the contact duration is decreased. The result shows that the contact force and the central deflection of the structure decreases and the contact time decreases with assuming FRP layer.