A semi-analytic method is proposed for two problem settings for a Kirchhoff plate containing an absolutely rigid circular inclusion and undergoing a transverse point force. The settings differ by the location (within and out of inclusion) of the force application point. In both cases, the plate's stress-strain state is simulated with a boundary value problem for the biharmonic equation stated over a doubly connected region whose inner contour represents the edge of the inclusion. Boundary conditions imposed on the inner contour bring some parameters which are found via the equations of static equilibrium of the inclusion. A modification of the Kupradze's method of functional equations is proposed for obtaining influence functions of a point force for such plates. Green's functions of the biharmonic equation for appropriately shaped simply connected regions are employed. Numerical differentiation is never required in the computing of stress components and the latter are subsequently found with accuracy level comparable with that attained for the deflection function.

In this paper, a constitutive equation of steady creep rates:

is derived based on a liaison of the theory of irreversible thermodynamics of continuous media with internal state variables (ISV); and the deformation kinetics. In steady creep, only one ISV is used, whose evolution equation is derived by the concepts of deformation kinetics, in which micromotions are generated by a group of atoms climbing over a tilted potential barrier of the highest height ε0.

Applications of the constitutive equation in the cases of some Sn/Pb solder alloys-63Sn/37Pb, 60Sn/40Pb and 97.5Pb/2.5Sn under shear creep tests; and 98Pb/2Sn under tensile creep tests, show that the theoretical results can describe the experimental data quite well. These results pave the way for future research in the comparisons of creep resistance among solders with various Sn/Pb compositions and in the generalization of three-dimensional constitutive equation.

In this paper, elastic analysis for a collinear crack problem in antiplane elasticity of functionally graded materials (FGMs) is present. An elementary solution is obtained, which represents the traction applied at a point “x” on the real axis caused by a point dislocation placed at a point “t” on the same real axis. The Fourier transform method is used to derive the elementary solution. After using the obtained elementary solution, the singular integral equation is formulated for the collinear crack problem. Furthermore, from the solution of the singular integral equation the stress intensity factor at the crack tip can be evaluated immediately. In the solution of stress intensity factor, influence caused by the materials property “α” is addressed. Finally, numerical solutions are presented.

Numerical simulations based on molecular statics are carried out to study nano-scale plastic deformation behavior in thin metal films. Particular attention is devoted to correlating the overall mechanical response and the underlying crystal defect mechanisms during mechanical loading. The simulations are within the two-dimensional framework involving pair molecular interactions in singlecrystal materials. Special modeling features are utilized for studying the formation of dislocations, interface characteristics, and defect interactions. Specific problems investigated in this work include: plastic deformation and tensile fracture in a free-standing film, interface-constrained plasticity in substrate-bonded films, and homogeneous nucleation of dislocations during nanoindentation.

With the concrete treated as unconfined, semi-empirical equations for curvature ductility ratios of doubly reinforced beam sections were derived. Based on the resulted semi-empirical equations, design formulas for curvature ductility ratios, which take into account the effect of tension and compression reinforcement ratios and strengths of reinforcement and concrete, are established and calibrated. The proposed design formulas are fairly simple with reasonable accuracy. The proposed design formulas enable the designer to design beam sections for selected ductility ratios, and, consequently, to acquire better control of concrete spalling during major earthquakes. From the aspect of performance based design, the proposed formulas can facilitate beam design for concrete spalling limit state.

This study investigates the flow bifurcation and transition between stable states in the gap between two concentric rotating spheres. A continuation method is used together with linear stability analysis to investigate the bifurcation structure of the discretized governing equations and to determine the stability of the calculated states. The constructed bifurcation diagram is used to illustrate the restricted range of Reynolds number within which each equilibrium state exists. The diagram also identifies the permissible transitions between these states and indicates their terminative states. In the present study, it is shown how appropriate control of the angular velocity of the outer sphere results in the evolution of the flow state through a series of permitted stable states. The time-dependent transitions between these states are investigated by means of a backwards-Euler time stepping formulation. The terminate state of transition process can also be used to confirm the stability of the flow. The flow evolution between each transition is illustrated by means of temporal sequences of the meridional streamlines and transition curves. The present results indicate that all the flow transitions in a gap between two rotating spheres are produced symmetrically with respect to the equator.

This paper describes a computational model based on the dual reciprocity boundary element method (DRBEM) for the solution of two-dimensional incompressible viscous flow problems. The model is based on the Navier-Stokes equations in velocity-vorticity variables. The model includes the solution of vorticity transport equation for vorticity whose solenoidal vorticity components are obtained by solving Poisson equations involving the velocity and vorticity components. Both the Poisson equations and the vorticity transport equations are solved iteratively using DRBEM and combined to determine the velocity and vorticity vectors. In DRBEM, all source terms, advective terms and time dependent terms are converted into boundary integrals and hence the computational domain of the problem reduces by one. Internal points are considered wherever solution is required. The model has been applied to simulate two-dimensional incompressible viscous flow problems with low Reynolds (Re) number in a typical square cavity. Results are obtained and compared with other models. The DRBEM model has been found to be reasonable and satisfactory.

The improved numerical approach is implemented with preconditioned Navier-Stokes solver on arbitrary three-dimensional (3-D) structured multi-block complex flowfield. With the successful application of time-derivative preconditioning, present hybrid finite volume solver is performed to obtain the steady state solutions in compressible and incompressible flows. This solver which combined the adjective upwind splitting method (AUSM) family of low-diffusion flux-splitting scheme with an optimally smoothing multistage scheme and the time-derivative preconditioning is used to solve both the compressible and incompressible Euler and Navier-Stokes equations. In addition, a smoothing procedure is used to provide a mechanism for controlling the numerical implementation to avoid the instability at stagnation and sonic region. The effects of preconditioning on accuracy and convergence to the steady state of the numerical solutions are presented. There are two validation cases and three complex cases simulated as shown in this study. The numerical results obtained for inviscid and viscous two-dimensional flows over a NACA0012 airfoil at free stream Mach number ranging from 0.1 to 1.0E-7 indicates that efficient computations of flows with very low Mach numbers are now possible, without losing accuracy. And it is effectively to simulate 3-D complex flow phenomenon from compressible flow to incompressible by using the advanced numerical methods.

Narrow micromachined bilayer cantilevers, which are broadly used to determine different thin film material properties, have rarely been used to characterize the Poisson's ratio. It is difficult to be determined from the tip deflection, and thus the Poisson's ratio, of the narrow bilayer cantilever. In this paper, the tip deflections of ultra-wide micromachined bilayer cantilevers carry the needed information for finding the Poisson's ratio of thin-film materials. The measurement process and its corresponding model, based on the plate theory, is introduced and tested. The Poisson's ratio of the thin film is determined by comparing the tip deflections of the bilayer cantilever before and after the deposition of the upper layer. Because the fabrication processes are widely used in surface micromachining, the method can be easily implemented.

An experimental investigation of heat transfer carried out for a semiannular enclosure. Inner and outer walls of the enclosure were kept at different but constant temperatures. The semiannular enclosure was filled with a CuSO4 - H2SO4 - H2O solution. An electrochemical method has been used for the mass transfer. The purpose of this study is to investigate flows resulting from buoyancy due to a combination of both temperature and concentration gradients in the enclosure. The flow structure in the enclosure was visualized by the shadowgraph technique. Flow visualization photograph showed interesting multi-cell flow structures in the enclosure for the cooperating and opposing thermal and solutal buoyancy. An optical technique is based on the idea that the intensity of the light beam absorbed by the copper sulphate solution is proportional to the solution concentration when the light beam passes through the solution. For each flow regime the mass transfer coefficient across the enclosure was also measured. The ranges of the dimensionless parameters studied in the experimental were Ar = 0.23, k = 2.5, Sc = 1700∼2300, Pr = 6.5 ∼ 7.3, Grt = 104 ∼ 106, N = −15.44 ∼ 6.16, θ = 45°∼90°.

The Saint Venant equations are often merged into a single equation for being easily solvable. By doing so, the most general form of the single equation is formulated in this study if all terms are preserved. As a result, the generalized model (GM) results and contains several unexpected nonlinear terms that may impose a great limitation on model analyses. In order to identify these redundant terms, this paper discusses the employment of the linearized Saint Venant equations (LSVE) governing subcritical flow in prismatic channels. The LSVE is solved by a new procedure that separates, in the Laplace frequency domain, the governing equation of water depth from that of flow velocity and thus enables us to consider two independent equations rather than two coupled ones. This allows us to obtain analytical solutions in a much easier way. Comparisons of the response functions of LSVE and the linearized generalized model (LGM) show that the two equations provide identical solutions if the redundant terms embedded in LGM are neglected. It then follows that the response function of LGM can be utilized as a replacement for solving the analytical solution of LSVE that is valid for prismatic channels of any shape. Validity of the analytical solution is verified by repeatedly comparing with the corresponding numerical solutions of finite difference method or Crump's algorithm [1], depending on whether the flow domain is finite or semi-infinite. It is clearly demonstrated in this paper that LSVE serves as an excellent substitution for LGM whose variants have been employed for quite a few years.

This paper explores a novel design of an encapsulated and integrated device, which employs an oscillatory fluid flow to cool micro spots in micro systems. The oscillatory flow can be induced by two thermal bubbles that form and expand in turn on two micro line heaters at both ends of a sealed fluid channel. Compared with those using outside connecting channels and pumps, this design benefits from its much smaller size. A numerical calculation indicates that the heat transfer enhancement is independent of the Wormersely number, but depends on the Peclet number, Pe, and the cooling capacity of channel walls. The heat transfer rate increases dramatically as Pe increases from 30 to 100.

The construction and operation of electronic speckle pattern interferometer (ESPI) applied to single-inserted sandwich plates have been earliest presented in this paper. Proposed ESPI has advantages of full-field and non-destructive testing, which can measures microscopic out-of-plane displacement in the elastic region without wasting specimen. For validation purpose, the finite element method (FEM) analysis was conducted. By comparing the results of ESPI and FEM displacement fields around the inserts that a convincing agreement is revealed. The effect of potting material diameter on the displacement of single-inserted sandwich plates was obtained by the ESPI and FEM.

In a series of three articles, fundamentals of a vector form intrinsic finite element procedure (VFIFE) are summarized. The procedure is designed to calculate motions of a system of rigid and deformable bodies. The motion may include large rigid body motions and large geometrical changes. Newton's law, or a work principle, for particle is assumed to derive the governing equations of motion. They are obtained by using a set of deformation coordinates for the description of kinematics. A convected material frame approach is proposed to handle very large deformations. Numerical results are calculated by using an explicit algorithm. In the first article, using the plane frame element as an example, basic procedures are described. In the accompanied articles, plane solid elements, convected material frame procedures and numerical results of patch tests are given.

Analytical closed-form solutions for the crack tip plastic zone shape have been derived for a semi-infinite crack in an isotropic elastic-perfectly plastic solid under both plane stress and plane strain conditions. Two yield criteria have been applied: the Von Mises and Tresca yield criteria. The solutions have been developed for crack modes I and III (mode II has been published previously). The results, which favorably compare to a limited number of existing experimental and analytical findings, indicate that the Tresca zone is larger in size than the Von Mises zone. Moreover, an interesting observation is that both zones are generally much larger than the ones predicted by classical Irwin and Dugdale-Barenblatt solutions.

Heat transfer and near-wall flow characteristics in an inherently swirling fan flow, containing rectangular-plate turbulators with 45° and 90° angles of attack, were experimentally investigated. The heat transfer characteristics for uniform flows with the turbulators were also investigated for comparison. Eight heated aluminum plates, installed along a bottom duct-wall, were used as the heat transfer surfaces, which allows the studies of heat transfer variations along the duct and the studies of the relations between the local fluid flows and heat transfer variations. Three-component mean and fluctuating velocities were measured using a laser Doppler velocimetry to obtain the near-wall flow parameters, including the axial mean velocity, axial vorticity and turbulent kinetic energy. The temperatures on the eight heat transfer surfaces were measured using thermocouples to obtain the Stanton number distributions. Results suggest that the rectangular-plate turbulators in fan flows may cause the increases in the near-wall flow parameters and, consequently, augment the heat transfer, especially around the flow reattachment regions. Also, the rectangular-plate turbulator effect on heat transfer augmentation in fan flows may be as attractive as that in uniform flows at the investigated X/H ranges.

In the second article of the series, the vector form intrinsic finite element is extended to formulate plane solid elements, a three-node triangular element and a four-node isoparametric element. Also, conceptual differences of the intrinsic element and traditional element based on variational formulation are discussed.

In the analysis of simple wire-driven platform (SWDP) mechanisms, the tension and the posture of each wire can be formulated, and expressed in an integrated screw representation naturally. In this study, a unified approach for analyzing the kinematics and kinetics of SWDP mechanisms based on the screw theory is proposed and developed, which includes the screw-based Jacobian, the static and dynamic equilibrium of wires and platform, and the singularity analysis. Via using the unified screw-based approach, the investigation on the characteristics of SWDP mechanisms, therefore, can be more efficient and simplified. An example is presented to demonstrate this unified approach.

Due to external loads, damage extension forces will drive mechanical and electrical damages to evolve in piezoelectric materials from the viewpoint of continuum damage mechanics, so it is important for understanding piezoelectric fracture mechanism and estimating the utilizing life and safety of a piezoelectric device to study the damage extension forces. Based on the static piezoelectric damage constitutive model established in our previously published papers, general expressions of the damage extension forces are given. The finite element method and the iterative procedure are utilized to calculate the extension forces at crack-tips in the samples for the experiments of Park and Sun's, and then the linear and nonlinear fracture criteria are presented. It is revealed from the list of the normalized mean square deviations that the nonlinear criterion is better.

Applying the principle of virtual work, the slice element method, and the variational method proposed in this paper, one can derive the governing equation and transversality conditions for the rupture surface of a sliding mass of retaining wall and shallow foundation under several external conditions. The governing equation, transversality, and boundary conditions can be solved by the finite difference method (FDM) proposed in this paper, so that the rupture surface and its associated earth pressure acting on the retaining wall or the ultimate bearing capacity acting on the foundation can be determined effectively. By comparison of our results with those of some well known earth pressure and bearing capacity estimating methods, it can be concluded that determining the earth pressure on a retaining wall or the ultimate bearing capacity of a shallow foundation by using the variational method and FDM proposed in this paper, a logical and reasonable result can be obtained without the necessity of guessing the rupture surface.