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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.

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.

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 (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.

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.

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.

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.