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Within the framework of three-dimensional (3D) nonlocal elasticity theory, the authors develop an asymptotic theory to investigate the free vibration characteristics of simply supported, single-walled carbon nanotubes (SWCNTs) non-embedded or embedded in an elastic medium using the multiple time scale method. Eringen’s nonlocal constitutive relations are adopted to account for the small length scale effect in the formulation. The interactions between the SWCNT and its surrounding medium are modeled as a two-parameter Pasternak foundation model. After performing a series of mathematical processes, including nondimensionalization, asymptotic expansion, and successive integration, etc., the authors obtain recurrent sets of motion equations for various order problems. The nonlocal classical shell theory (CST) is derived as a first-order approximation of the current 3D nonlocal elasticity problem, and the equations of motion for higher-order problems retain the same differential operators as those of the nonlocal CST, although with different nonhomogeneous terms. The current asymptotic solutions for the natural frequency parameters of non-embedded or embedded SWCNTs and their corresponding through-thickness modal stress and displacement component distributions are obtained to assess the accuracy of various nonlocal shell and beam theories available in the literature.

In conjunction with the Reissner's mixed variational theorem and nonlocal Timoshenko beam theory, we develop a finite element method for the geometrically nonlinear bending analysis of a mu...

This paper presents a three-dimensional finite deformation theory for the geometric nonlinear analysis of both the curved and twisted beams using the meshfree method based on the Timoshenko beam hypothesis. The theory presented is simple, but it is capable of solving the stability, postbuckling, snap-through, and large deformation problems effectively. Clear physical meanings will be revealed in derivation of the three-dimensional finite deformation theory. A meshfree method based on the differential reproducing kernel (DRK) approximation collocation method combined with the Newton–Raphson method is employed to solve the strong forms of the geometrically nonlinear problems. Numerical examples are given to illustrate the validity of the method presented.

An innovative efficient and fast neural networks in which hidden neurons are constructed based on Fourier series expansions (FSNN), half-range cosine (FCSNN) and sine expansions (FSSNN) are proposed and tested for linear and nonlinear regulation problems. The results of numerical examples using FSNN are compared with those obtained from traditional linear regression (LP), nonlinear regression (NLP), backward propagation neural networks (BPANN) and radial basis function neural networks (RBFNN). The results obtained from FSNN agree well with those obtained from LP, NLP, BPANN and RBFNN and show global approximation features to the fitting data. Only a few hidden neurons are required to obtain very good and fast convergence of regression as compared with BPANN and RBFNN.

This paper presents classification of linearly separable and non-separable problems using neural networks in which hidden neurons are constructed based on double Fourier series expansions (FSNN). The results of numerical examples including classification problems of logical AND, logical XOR, cows and wolves, as well as 3-category problem such as IRIS classification. All the FSNN results are compared with those obtained from backward propagation neural networks (BPANN) and radial basis function neural networks (RBFNN). Root mean squared errors (RMSE) of the algorithms during the training process are also compared. The classification results obtained from FSNN agree well with those obtained from BPANN and RBFNN. Only a few hidden neurons in FSNNs are required for very good and fast convergence of training as compared with BPANN and RBFNN.

Epithelial ovarian cancer (EOC) is the seventh most common cancer among women worldwide. The 5-year survival rate for women with EOC is only 30%-50%, which is largely due to the typically late diagnosis of this condition. EOC is difficult to detect in its early stage because of its asymptomatic nature. Recently, near-infrared fluorescent (NIRF) imaging has been developed as a potential tool for detecting EOC at the molecular level. In this study, a NIRF-sensitive probe was designed to detect matrix metalloproteinase (MMP) activity in ovarian cancer cells. A cyanine fluorochrome was conjugated to the amino terminus of a peptide substrate with enzymatic specificity for MMP-3. To analyze the novel MMP-3 probe, an in vivo EOC model was established by subcutaneously implanting SKOV3 cells, a serous-type EOC cell line, in mice. This novel MMP-3-sensitive probe specifically reacted with only the active MMP-3 enzyme, resulting in a significantly enhanced NIRF emission intensity. Histological analysis demonstrated that MMP-3 expression and activity were enhanced in the stromal cells surrounding the ovarian cancer cells. These studies establish a molecular imaging reporter for diagnosing early-stage EOC. Additional studies are required to confirm the early-stage activity of MMP-3 in EOC and its diagnostic and prognostic significance.

On the basis of Reissner’s mixed variational theorem (RMVT), rather than the principle of virtual displacement (PVD), the authors presented a nonlocal Timoshenko beam theory (TBT) for the g...

A meshless collocation method is developed for the static analysis of plane problems of functionally graded (FG) elastic beams and plates under transverse mechanical loads using the differential reproducing kernel (DRK) interpolation, in which the DRK interpolant is constructed by the randomly distributed nodes. A point collocation method based on this DRK interpolation is developed for the plane stress and strain problems of homogeneous and FG elastic beams and plates. It is shown that the present DRK interpolation-based collocation method is indeed a truly meshless approach with excellent accuracy and has a fast convergence rate.

A meshless collocation (MC) and an element-free Galerkin (EFG) method, using the differential reproducing kernel (DRK) interpolation, are developed for the quasi-three-dimensional (3D) analysis of simply supported, multilayered composite and functionally graded material (FGM) plates. The strong and weak formulations of this 3D static problem are derived on the basis of the Reissner mixed variational theorem (RMVT) where the strong formulation consists of the Euler–Lagrange equations of the problem and its associated boundary conditions, and the weak formulation represents a weighted-residual integral in which the differentiation is equally distributed among the primary field variables and their variations. The early proposed DRK interpolation is used to construct the primary field variables where the Kronecker delta properties are satisfied, and the essential boundary conditions can be readily applied, exactly like the implementation in the finite element method. The system equations of both the RMVT-based MC and EFG methods are obtained using these strong and weak formulations, respectively, in combination with the DRK interpolation. In the illustrative examples, it is shown that the solutions obtained from these methods are in excellent agreement with the available 3D solutions, and their convergence rates are rapid.

A Hermite differential reproducing kernel (DRK) interpolation-based collocation method is developed for solving fourth-order differential equations where the field variable and its first-order derivatives are regarded as the primary variables. The novelty of this method is that we construct a set of differential reproducing conditions to determine the shape functions of derivatives of the Hermite DRK interpolation, without directly differentiating it. In addition, the shape function of this interpolation at each sampling node is separated into a primitive function possessing Kronecker delta properties and an enrichment function constituting reproducing conditions, so that the nodal interpolation properties are satisfied for the field variable and its first-order derivatives. A weighted least-squares collocation method based on this interpolation is developed for the static analyses of classical beams and plates with fully simple and clamped supports, in which its accuracy and convergence rate are examined, and some guidance for using this method is suggested.

A differential reproducing kernel (DRK) interpolation-based collocation method is developed for solving partial differential equations governing a certain physical problem. The novelty of this method is that we construct a set of differential reproducing conditions to determine the shape functions of derivatives of the DRK interpolation function, without directly differentiating the DRK interpolation function. In addition, the shape function of the DRK interpolation function at each sampling node is separated into a primitive function processing Kronecker delta properties and an enrichment function constituting reproducing conditions, so that the nodal interpolation properties are satisfied. A point collocation method based on the present DRK interpolation is developed for the analysis of one-dimensional bar problems, two-dimensional potential problems, and plane problems of elastic solids. It is shown that the present DRK interpolation-based collocation method is indeed a truly meshless approach, with excellent accuracy and fast convergence rate.

Optical lithography is one of the most extensively used technologies in the fabrication of a printed circuit board (PCB) or a semiconductor device. In recent years, as the demand for smaller sized electronic appliances increases and the cost of the stripping agents keeps escalating, higher standard and requirement on existing photoresist stripping technology is demanded for the semiconductor industry. In conventional techniques, photoresists can be removed by simple hydroxides based stripping agents. Proprietary stripping agents which are predominantly based on amine chemistry have attracted much attention because of their proven ability to make the photoresist film particulate into small features thus to show faster and improved stripping efficiency. However, the photoresist stripping ability of known stripping agents is insufficient to tackle the newly developed fine process and short time treatment in the production of semiconductor devices and liquid crystal display panels. Moreover, these known stripping agents are reported to show negative effect on the PCB production process with problems such as high metal corrosion rates which can lead to tin transfer and etch retardation. Therefore, it has been a high demand for further improvement of the stripping ability. Up to date, the stripping agents we used are capable of dry films removal processes within a short period of time. However, the existing stripping agents are not powerful enough to clean the liquid photoresists efficiently. The liquid photoresists removal process performs much worse with high level of residues which requires a second exposure and lead to unacceptable scrap rates after etching. Furthermore, corrosive attack on copper substrate by these existing stripping agent results in an uneven wire width after gold plating. In order to resolve such issues, development of the next generation of photoresist stripping agent which can be applied to both dry and wet film with minimal attack on the metal base is an urgent issue in the immediate future. In this paper, a photoresist stripping agent containing a combination of amine compounds in aqueous alkaline based solutions is proposed. By using this new photoresist stripping agent, the circuit appears to have been fully stripped of all dry film with increasing stripping rate and the production was increased by 60%. New product is also capable of completely removing the liquid photoresists without secondary processes, and the production was increased by 25%. The use of new formulation avoids any undesirable metal attack. In addition, the cost of the new formulation is much less than the existing stripping agent. With the advantages of lower cost, better stripping ability and increase of production rates, the new stripping agent is aimed to replace the older stripping agent in order to produce high quality product.

Heat conduction in circular cylinders of functionally graded materials and laminated composites is studied with emphasis on the end effects. By means of matrix algebra and eigenfunction expansion, the decay length that characterizes the end effects on the thermal filed is evaluated and the 2D solution as a useful approximation assessed.

A state space approach to heat conduction in a cylindrically anisotropic circular tube of functionally graded materials (FGM) is presented. A power-law type of the radial inhomogeneity for the FGM is considered. By means of eigenfunction expansion and matrix algebra, analytic solutions for transient and steady-state heat conduction in the FGM tube under general thermal boundary conditions are derived.

When an elastic medium containing an elliptic inclusion with a sliding interface is subjected to a remote pure shear, it was found that the inclusion behaves like a cavity. Since a circle is a special case of an ellipse, the solution should be applicable to a circular inclusion as well. However, it breaks down when the ellipse degenerates into a circle. This implies that the solution is questionable. In this paper the problem is examined by considering a rigid elliptic inclusion in an elastic medium with sliding interface between them. By taking account of a large rotation of the inclusion instead of a small rotation, we obtain a uniformly valid solution applicable to a circular inclusion as well as to an elliptic inclusion. The solution reveals a remarkable snapping behavior of the inclusion under a critical load. A simple condition for its occurrence is derived.

We present a state space approach to extension, torsion, bending, shearing and pressuring of laminated composite tubes. One of the novel features is that we have formulated the basic equations of anisotropic elasticity in the cylindrical coordinate system into a state equation by a judicious arrangement of the displacement and stress variables so that the system matrix is independent of r. The formulation suggests a systematic way using matrix algebra and the transfer matrix to determine the stress and deformation in a multilayered cylindrically anisotropic tube under applied loads that do not vary in the axial direction. An exact analysis of the tube subjected to uniform surface tractions, an axial force, a torque and bending moments is presented. The solution consists of an axisymmetric state due to extension, torsion, uniform pressuring and shearing, and an asymmetric state due to bending. The formalism indicates that extension, torsion and pressuring interact; uniform shearing causes pure shears in the laminated tube, regardless of the number of layers. These deformations are uncoupled with bending of the tube.

On the basis of the Hellinger–Reissner (H–R) principle, an asymptotic finite strip method (FSM) for the analysis of doubly curved laminated shells is presented by means of perturbation. In the formulation the displacements and transverse stresses are taken as the functions subject to variation. Imposition of the stationary condition of the H–R functional, the weak formulation associated with the Euler–Lagrange equations of three-dimensional (3D) elasticity is obtained. Upon introducing a set of appropriate dimensionless scaling and bringing the transverse shear deformations to the stage at the leading-order level, the weak formulation is asymptotically expanded as a series of weak-form equations for various orders. An asymptotic FSM according to the present formulation is then developed where the field variables are interpolated as a finite series of products of trigonometric functions and crosswise polynomial functions independently. Through successive integration, the present formulation turns out that three mid-surface displacement degrees-of-freedom (DOF) and two rotation DOF for each node in a strip element are taken as the independent unknowns in the system equations for various orders. The solution procedure for the leading-order level can be repeatedly applied level-by-level in a consistent and hierarchic way. Application of the asymptotic FSM to a benchmark problem is demonstrated.

This paper develops a finite element scheme to generate the spatial- and time-dependent absorbing boundary conditions for unbounded elastic-wave problems. This scheme first calculates the spatial- and time-dependent wave speed over the cosine of the direction angle using the Higdon's one-way first-order boundary operator, and then this operator is used again along the absorbing boundary in order to simulate the behaviour of unbounded problems. Different from other methods, the estimation of the wave speed and directions is not necessary in this method, since the wave speed over the cosine of the direction angle is calculated automatically. Two- and three-dimensional numerical simulations indicate that the accuracy of this scheme is acceptable if the finite element analysis is appropriately arranged. Moreover, only the displacements along absorbing boundary nodes need to be set in this method, so the standard finite element method can still be used. Copyright © 2001 John Wiley & Sons, Ltd.

Stress decay in laminates due to edge boundary effects are studied through a state space formulation. A self-equilibrium eigenstress field accounting for the multilayer construction of the laminate is derived using the state variables and the transfer matrix method. The eigenvalue determination requires only the solution of 6×6 determinants irrespective of the number of laminae. Through combinations of the eigenstress field and the interior stress field a complete solution valid in the boundary layer as well as in the interior region of the laminate can be obtained. For verification, the formulation is first applied to determining the eigenstress in a homogeneous anisotropic layer, and then the free edge stress decay in laminates under uniform extension is examined.

A general theory for multilayered anisotropic elastic shells is developed in an asymptotic variational framework of 3-D elasticity. The generic shell continuum considered is heterogeneous through the thickness. It is shown that the classical laminated shell theory based on Love's assumption arises naturally as the first-order approximation to the 3-D theory. Higher-order corrections can be determined by solving the 2-D shell equations hierarchically. The associated edge conditions at each level of approximation are derived. Various types of shells such as shells of revolution, conical shells, spherical shells, circular cylindrical shells can be treated within the context.

An asymptotic finite element model for anisotropic inhomogeneous and laminated plates is developed within the framework of three-dimensional elasticity. The formulation begins with a Hellinger-Reissner functional in which the displacements and transverse stresses are taken to be the functions subject to variation. By means of asymptotic expansion the H—R functional for the problem is decomposed into functionals of various orders from which the asymptotic finite element equations are derived. In the multilevel computations the transverse stresses and displacements may be interpolated independently, and the midplane displacements are the only unknown nodal degree of-freedoms (DOF) in the system equations, thus the total DOF at each level is less than that of a homogeneous Kirchhoff plate. The stiffness matrix remains unchanged; the one generated at the leading-order level is always used at subsequent levels. The formulation is three-dimensional yet requires only two-dimensional finite element discretization with no need of interpolation in the thickness direction. The through-thickness effect can be accounted for in a consistent and hierarchical manner. Numerical comparisons with the benchmark solutions show that the method is effective in modeling of multilayered composite plates.

On the basis of three-dimensional elasticity without a priori assumptions, we develop an asymptotic theory for the thermoelastic analysis of anisotropic inhomogeneous plates subject to general temperature variations and under the action of lateral loads. The inhomogeneities considered are in the thickness direction, and the laminated plate represents an important special case. Through reformulation of the basic equations and nondimensionalization of the field variables, we find that the method of asymptotic expansions is well suited for the problem. Upon using the asymptotic expansion, we obtain sets of recurrence equations that can be integrated successively to determine the solution for a problem. We show that the classical laminated plate theory (CLT) is merely the leading-order approximation in the asymptotic theory. Furthermore, the higher-order equations are essentially the same as the CLT equations, only with nonhomogeneous terms that are completely determined from the lower-order solutions. As a r...

The Lekhnitskii complex potential approach of anisotropic elasticity is extended to include the thermal effect. A concise formulation of the thermal stress problem of an anisotropic elastic body with a hole or a rigid inclusion in generalized plane deformation or generalized plane stress condition is presented. Special attention is paid to the systematic determination of the general forms of the complex potentials for the thermoelastic field that satisfies the prescribed boundary conditions at the interior contour. Both the Dirichlet and the Neumann type of boundary conditions arc considered. Using these general forms of solution, thermal stresses for the generalized plane problems of anisotropic body with a hole or a rigid inclusion can be determined in a simple and systematic manner. Applications of the solution method to several illustrative examples are given.

Green’s function solutions are presented for the generalized plane problems of a point force and an edge dislocation located in the general anisotropic elastic medium with a hole or with a rigid inclusion. The Lekhnitskii’s complex potential approach is used and a general expression of the solutions is obtained. Particular attention is paid to the determination of appropriate mapping functions that map the exterior of the hole or the inclusion onto the exterior of a unit circle. The conditions under which the conformal mapping is possible are explored. Examples using the Green’s functions for the solution of notch problem are given.

A fundamental solution for an anisotropic medium with a notch or a rigid inclusion of arbitrary shape is derived based on the complex potential formulation of anisotropic elasticity. The solutions for a crack, for a circular hole or inclusion, and for a half plane are obtained as special cases. The solution can be applied to the analysis of crack, notch and inclusion problems of anisotropic materials.

The fundamental solutions for boundary element analysis of torsionai problems of a cylindrical anisotropic medium are presented. The particular form of cylindrical anisotropy considered in this paper is the most general kind possible for axisymmetric torsion deformation. A suitable change of variables is suggested to reduce the governing equation to a simple form which is amenable to Hankel transforms. The explicit form of the fundamental solution for infinite space subjected to an axisymmetric ring of uniformly applied tangential forces is then derived. An existing solution for an isotropic medium is recovered. In addition, simple half‐space fundamental solutions for the torsion of a transversely isotropic medium are determined. The kernel functions obtained herein are readily implemented in the boundary element formulation of the axisymmetric torsionai problems.

The fundamental problem of a point force acting in the interior of an unbounded transversely isotropic elastic space is reconsidered and formulated in cylindrical coordinates (r, θ, z). Navier‐Cauchy equations are solved by Fourier transform with respect to θ in conjunction with the Hankel transforms of appropriate order with respect to r. A closed‐form solution is obtained with the well‐known Kelvin solution as a special case. The direct and systematic derivation can be easily extended to other problems of interest.

The fundamental solutions required in boundary element analysis‐of torsionai problems of nonhomogeneous transversely isotropic media are derived in this paper. The elastic constants of the nonhomogeneous medium are assumed to be variables as functions of cylindrical coordinates in the forms rα exp (λz) and rα (z+c) β . The displacement resulting from an axisymmetric ring of tangential forces applied in the interior of a infinite space and of a half‐space are obtained. The effects of nonhomogeneity are compared and discussed.

The objective of this work is to express the overall property of multiphase composites in terms of the properties, volume concentrations and geometric arrangement of its constituents. A differential scheme for multiphase composites is developed and specific formulations are made for isotropic and transversely isotropic multiphase composites containing ellipsoidal inclusions. The elastic moduli obtained by this scheme lie between the Hashin‐Shtrikman bounds. The scheme is evaluated favorably in comparison with other schemes.

The differential scheme developed in Part I of this work is applied to the calculation of thermal expansion coefficients and conductivities of isotropic and transversely isotropic multiphase composites. The results obtained herein are compared with the existing experimental results as well as those by other schemes. The effect of the inclusion shape on the overall property of the composites is investigated. The inclusions of disk shape produce the most pronounced effect, followed by inclusions of needle shape and spherical shape.