An analytical solution is launched for Twin-cell Composite Box Beam (TCCBB) considering the impact of shear lag effects of concrete slab and twin-cell steel girder. To in-depth explore its mechanical mechanism, a new warping displacement mode of wide flange is chosen to meet the essential deformation feature of this TCCBB model by authors. Combining the virtual work principle with the thin-walled beam theory, its governing equations and boundary conditions are established for the TCCBB model. Closed form solutions for longitudinal strain and its shear lag coefficients are also derived under concentrated loads. What's more, experiment investigation and related parameter impact analysis are carried out for this established TCCBB model. Through this research, it shows that the proposed method can be applied to describe and predict shear lag behaviors for this type of composite structure. That further suggests that it provides a certain reference value for engineering design and its late reinforcement and maintenance in the composite structure.

Acceleration-factor (AF) equations have been developed to rapidly predict product lifetime, and the most widely used equation is Norris-Landzberg (N-L) equation. In recent years, some researchers have found that the current AF equation does not accurately predict the experimental results for thermal cyclic loading at high ramp rates; indeed, it may yield the opposite results, due to the changing effect of the solder strain rate at different ramp rates. Modifying the current AF equation to better assess product reliability has thus become an important task for researchers.

In this study, a novel AF equation was developed from a wafer level chip-scale package (WLCSP) under different thermal cyclic loadings. The frequency term used in the N-L equation was replaced with a new term in the proposed AF equation to distinguish between the effects of ramp rate and dwell time under thermal cyclic loading conditions. Proposed AF equation showed a high level of correlation with the simulation and test results for various thermal cyclic loadings. In addition, the proposed AF equation was validated by confirming the consistency of its results with experimental data on a range of packages and thermal-cycling profiles reported in the literature.

In the present paper, the low-velocity impact of an elastic rod with a flat end upon a viscoelastic Timoshenko type beam has been considered. Viscoelastic properties of the beam out of the contact zone are described by the standard linear solid model with integer derivatives, while inside this zone they are governed by the fractional derivative standard linear solid model. The contact force for a concrete target has been defined experimentally at the concrete age of 7, 14, 28, 56, and 91 days. It has been found that an average maximum of the contact force increases with concrete age, whereas the contact duration decreases. Moreover, the most remarkable changes of both, contact force and contact time, occur at the concrete age earlier than 14 days, after that the rate of changes slows down. Experimental results have a good coincidence with theoretical expectations.

A general series solution to the problem of interacting circular inclusions in plane elastostatics is presented in this paper. The analysis is based on the use of the complex stress potentials of Muskhelishvili and the theorem of analytical continuation. The general forms of the complex potentials are derived explicitly for the circular inhomogeneities under arbitrary plane loading. Using the alternation technique, these general expressions were subsequently employed to treat the problem of an infinitely extended matrix containing two arbitrarily located inhomogeneities. The major contribution of the present proposed method is shown to be capable of yielding approximate closed-form solutions for multiple inclusions, thus providing the explicit dependence of the solution on the pertinent parameters. The result shows that the dislocation has a stable equilibrium position at a certain combination of material constants. The case of an inhomogeneity interacting with a circular hole under a remote uniform load is also investigated.

With the aid of the Green's function method and complex function method, the scattering problem of SH-wave by a cylindrical inclusion and a semi-cylindrical hollow in the bi-material half space is considered to obtain the steady state response. Firstly, by the means of the image method, the essential solution of displacement field as well as Green's function is constructed which satisfies the stress free on the horizontal boundary in a right-angle space including a cylindrical inclusion and a semi-cylindrical hollow and bearing a harmonic out-plane line source force at any point on the vertical boundary. Secondly, the bi-material half space is divided into two parts along the vertical interface, and the first kind of Fredholm integral equations containing undetermined anti-plane forces at the linking section is established by “the conjunction method” and “the crack-division method”, the integral equations are reduced to the algebraic equations consisting of finite items by effective truncation. Finally, dynamic stress concentration factor around the edge of cylindrical inclusion and dynamic stress intensity factor at crack tip are calculated, and the influences of effect of interface and different combination of material parameters, etc. on dynamic stress concentration factor and dynamic stress intensity factor are discussed.

The numerical stability of the explicit precise algorithm, which was developed for the viscoplastic materials, was analyzed. It was found that this algorithm is not absolutely stable. A necessary but not sufficient condition for the numerical stability was deduced. It showed that the time step in numerical calculation should be less than a certain value to guarantee the stability of explicit precise algorithm. Through a series of numerical examples, the stability analysis on the explicit precise algorithm was proved to be reliable. At last, an iterative algorithm was presented for viscoplastic materials. Both of the theoretical and numerical results showed that the iterative algorithm is unconditionally stable and its convergence rate is rapid. In practice, the explicit precise algorithm and iterative algorithm can be combined to obtain reliable results with the minimum computing costs.

In this study, a methodology to design frame-like periodic solids for isotropic symmetry by appropriate sizing of unit-cell struts is presented. The methodology utilizes the closed-form effective elastic constants of 2D frame-like periodic solids with square symmetry and 3D frame-like periodic solids with cubic symmetry, derived using the homogenization method based on equivalent strain energy. By using the closed-form effective elastic constants, an equation to enforce isotropic symmetry can be analytically constructed. Thereafter, the equation can be used to determine relative unit-cell strut sizes that are required for isotropic symmetry. The methodology is tested with 2D and 3D frame-like periodic solids with some common unit-cell topologies. Satisfactory results are observed.

In the present study, assuming that the thermo-elastic creep response of the material is governed by Norton's law, an analytical solution has been developed for the purpose of time-dependent creep response for isotropic thick-walled cylindrical pressure vessels. To study the creep response, the first-order shear deformation theory (FSDT) is applied. To the best of the researchers’ knowledge, in the literature, there is no study carried out into FSDT for time-dependent creep response of cylindrical pressure vessels. The novelty of the present work is that it seeks to investigate creep life of the vessels made of 304L austenitic stainless steel (304L SS) using Larson-Miller Parameter (LMP) based on FSDT. Using this analytical solution, stress rates are calculated followed by an iterative method using initial thermo-elastic stresses at zero time. When the stress rates are known, the stresses at any time are obtained and then using LMP, creep life of the vessels are investigated. The Problem is also solved, using the finite element method (FEM), the result of which are compared with those of the analytical solution and good agreement was found. It is found that the temperature gradient distribution has significant influence on the creep life of the cylinder, so that the maximum creep life is located at the outer surface of the cylinder where the minimum value of temperature is located.

In this paper, the effective properties of particle-reinforced composites with a weakened interphase are investigated. The particle and interphase are regarded as an equivalent-inclusion, and the interphase zone around the particle is modeled as a linear elastic spring layer. A modified micro-mechanics model is proposed to obtain the effective elastic modulus. Moreover, a statistical debonding criterion is proposed to characterize the varying probability of the evolution of interphase debonding. Numerical examples are considered to illustrate the effect of imperfect interphases on the effective properties of particle-reinforced composites. It is found that the effective elastic properties obtained in the present work are in a good agreement with the existing data from the literatures.

Resonant micro-biochemical sensors play important roles in a wide range of emerging applications to detect biochemical molecules. As the resonators of micro-biochemical sensors, the vibration characteristics of circular sensor diaphragms are important for the design of diaphragm-based resonant micro-biochemical sensors. In this paper, the influence of residual stresses on the vibration of a circular sensor diaphragm with surface effects is analyzed. Based on the Kirchhoff's plate theory and surface elasticity theory, the governing equation is presented. The material characteristic lengths for different surface effects are obtained. The influences of residual stresses on the effective flexural rigidity and natural frequency of the diaphragm with surface effects are discussed. Results show that the influence of residual stresses on the effective flexural rigidity becomes obvious with the increasing of residual stresses. The first order natural frequency increases rapidly when the tension parameter is larger than 30 for the stiffened surfaces, while for the softened surfaces the value is 10. Moreover, surface effects can influence the transition range of diaphragm from the plate behavior to membrane behavior in terms of the tension parameter. The transition range can be enlarged by the stiffened surface and be shortened by the softened surface. The analysis and results are helpful for the design of sensor diaphragm-based resonant micro-biochemical sensors and some related researches.

This paper presents a new approach to simulate the propagation of elastic and cohesive cracks under mode-I loading based on the vector form intrinsic finite element method. The proposed approach can handle crack propagation without requiring global stiffness matrices and extra weak stiffness elements. The structure is simulated by mass particles whose motions are governed by the Newton's second law. Elastic and cohesive crack propagation are simulated by proposed VFIFE-J-integral and VFIFE-FCM methods, respectively. The VFIFE-J-integral method is based on vector form intrinsic finite element (VFIFE) and J-integral methods to calculate the stress intensity factors at the crack tips, and the VFIFE-FCM method combines VFIFE and fictitious crack models (FCM). When the stress state at the crack tip meets the fracture criterion, the mass particle at the crack tip is separated into two particles. The crack then extends in the plate until the plate splits into two parts. The proposed VFIFE-J-integral method was validated by elastic crack simulation of a notched plate, and the VFIFE-FCM method by cohesive crack propagation of a three point bending beam. As assembly of the global stiffness matrix is avoided and each mass particle motion is calculated independently, the proposed method is easy and efficient. Numerical comparisons demonstrate that the present results predicted by the VFIFE method are in agreement with previous analytical, numerical and experimental works.

In recent years, compact camera modules (CCMs) have been widely used in consumer electrical and electronic products. CCMs with low cost specially are necessary for portable devices. Therefore, the present group recently developed a miniaturized open-loop controlled camera module with low cost for cellphone applications, in which the Lorentz force is balanced by a magnetic restoring force. To enhance the performance of the camera module, this article reports a pattern structure to modify the linearity of the magnetic restoring force. We fabricated a CCM prototype with the dimensions of 8.5 mm × 8.5 mm × 5 mm and demonstrated the usefulness of the pattern structure with the CCM prototype. Its potential applications are foreseeable in portable devices, such as cellphones, web cameras, personal digital assistants and other commercial electronics.

The effects of various parameters, such as thermal properties of substrates, thermal interface materials (TIMs) and heat sinks on the thermal performance of the light emitting diode (LED) light bars and backlight module are investigated experimentally and numerically in terms of junction temperature (Tj) and thermal resistances from junction to air (Rj-a). The results show that the measured Rj-a of the light bars by powering-on five LEDs in the test is different from one by powering-on only one LED, resulting from the extra heat coming from the adjacent LED packages affecting the Tj for the case of powering-on five LEDs. For the modules, Rj-a is significantly reduced by using the heat sinks for all backlight modules, and aluminum and iron heat sinks do not show any obvious difference in heat dissipation along with any substrates and TIMs. Furthermore, both experimental and simulation results show that the thermal conductivity of the substrates are more important and dominant than TIM and heat sink for the Rj-a of the backlight modules concerned, and also demonstrate that the thermal field for the local model can represent the one in full-scale backlight module.

Reducers are extensively used in many machines for reducing the speeds of mechanism. This paper proposed a new design of speed reducers to meet the performance requirements in high rigidness and large speed-reduction ratios. The movements of the reducer are designed based on the principles of differential displacements of the deceleration gear rings. The geometric models of the related components were designed using CAD software. The motions of mechanism were simulated for identifying the feasibility of designing including acquiring the kinematic properties. The mathematical models of structural stresses analysis were proposed so that the bending and contact stresses of the gear rings could be evaluated, accordingly. Finite element methods (FEM) were also used to analyze the structural stresses of the reducer. The studied results showed that the bending fracture of the gear rings would prior to its contacting fracture. The allowable loading of the reducer was then established according to the analyzed results of the maximum stresses on various transmitted torques. The methods of reliability evaluation were reported for considering the strength variation and calculating the reliabilities of the reducer at various loadings. The studied results are useful in structural design, stress analysis and reliability evaluation for developing high speed-reduction mechanisms.

The natural boundary integral equation (NBIE) is developed to calculate potential derivatives for potential problems with anisotropic media. Firstly, the governing equation of the two-dimensional anisotropic potential problem is transformed into standard Laplace equation by a coordinate transformation method. Then a potential derivative boundary integral equation named as NBIE is extended to solve the anisotropic potential problem. The most important virtue of the NBIE is that the singularity of the integral kernel function is reduced by one order in comparison with the conventional potential derivative boundary integral equation(CDBIE). Therefore the new potential derivative boundary integral equation only contains strongly singular integrals rather than hyper-singular integrals. Thus the NBIE can calculate more accurate potential derivative results for both boundary nodes and interior points. Moreover, in combination with the analytical integral regularization algorithm of nearly singular integrals, the NBIE can obtain more accurate potential derivatives of interior points very close to the boundary than the CDBIE. Numerical examples on heat conduction in anisotropic media demonstrate the accuracy and efficiency of the NBIE.

This paper presents an analytical study on the buckling of cylindrical shells with arbitrary circumferential thickness variations under external pressure. Firstly, based on the thin shell theory and separation of variables, corresponding ordinary differential equations of laterally pressured cylinders are obtained. Secondly, the general asymptotic formula of buckling load, which is in terms of thickness variation parameter up to arbitrary order, is derived by combining the perturbation method and Fourier series expansion. Thirdly, the effects of uniform and circumferential modal thickness variations on the buckling of cylindrical shells under external pressure are investigated, respectively, and the results agree well with those available in literature. Particularly, the buckling load reduction of cylinders with circumferential modal thickness variation obtained by the proposed method coincides with the numerical results presented by Gusic et al. This analytical method is applicable for evaluating the stability of laterally pressured cylindrical shells with arbitrary circumferential thickness variations, once the thickness variation is known.

This paper is devoted to the analytical solution of three-dimensional hyperbolic heat conduction equation in a finite solid medium with rectangular cross-section under time dependent and non-uniform internal heat source. The closed form solution of both Fourier and non-Fourier profiles are introduced with Eigen function expansion method. The solution is applied for simple simulation of absorption of a continues laser in biological tissue. The results show the depth of laser absorption in tissue and considerable difference between the Fourier and Non-Fourier temperature profiles. In addition the solution can be applied as a verification branch for other numerical solutions.

Presently, physical limitations are restricting the development of the microelectronic industry driven by Moore's law. To achieve high-performance, small form factor, and lightweight applications, new electronic packaging methods have exceeded Moore's law. This research proposes a double-chip stacking structure in an embedded fan-out wafer-level packaging with double-sided interconnections. The overall reliability of the solder joints and redistributed lines is assessed through finite element analysis. The application of soft lamination material and selection of a carrier material whose coefficient of thermal expansion (CTE) is close to that of the printed circuit board can effectively enhance the reliability of solder joints over more than 1,000 cycles. A trace/pad junction whose direction is parallel to the major direction of the CTE mismatch is recommended, and the curved portion of trace lines can absorb the expansion of metal lines and filler material. Design-on-simulation methodology is necessary to develop novel packaging structures in the electronic packaging industry.

This attempt addresses the peristaltic transport of Jeffrey fluid in a curved channel. Heat transfer is discussed employing convective condition at the channel walls. Effects of radial applied magnetic field and Joule heating are retained. Convective boundary conditions at both walls with different temperature are also accounted. The relevant equations are modeled in view of lubrication approach. Closed form expression for stream function is constructed. Numerical solution of stream function, velocity and temperature is obtained via shooting method in Mathematica with the help of NDSolve command. It is observed that curvature has opposite effects on the lower and upper walls of channel. However temperature is an increasing function of curvature parameter. Temperature also decreases in presence of heat transfer convective parameter naturally the Biot number.

The present article proposes the closed-form solution for analytical prediction of stability lobes in internal turning process. The passively damped boring bar is modeled as a cantilevered Euler-Bernoulli beam with constant cross sectional properties in which a Tuned Mass Damper (TMD) is embedded for the purpose of chatter suppression. The non-dimensional equations of motion are derived, assuming that the boring bar dynamics is well-represented by the fundamental mode of vibration. The stability of equivalent two-DOF dynamic model, i.e. boring bar with TMD, is analyzed in frequency domain. The closed- form expressions for critical depth of cut and spindle speed are presented in terms of boring bar and TMD characteristics. The proposed solution considers the effects of boring bar's structural damping and cutting geometry of insert on the stability behavior of passively damped cutting tool. An unconstrained optimization method is utilized to compute the most optimal set of tuning parameters for anti-chatter TMD. In order to improve the boundary of stability in a global sense, maximization of minimum critical depth of cut is selected as the objective of optimization. The superior performance of anti-chatter TMD is compared to H∞ and H2 TMDs for a wide range of applications. Moreover, the achieved results show a remarkable improvement of stability boundary compared to recent research works.