Chaos theory has been seen as an efficient tool for studying the turbulent flow, the findings of attractor were also important and made in the study to investigate the wake flow behind the bluff body. Here, the fractal dimension value would then be found by Hurst analysis. According to the results found, the Hurst empirical formula derived by the self-similar laceration of vortex plane would be applied by self-similar property to decide the band of the frequency variations in the vortex shedding process. The three kinds of flow mode with their individual attractors and characteristics could be decomposed and shown as following: self-similar laceration, energy input and white noise band. Finally, the energy ratio for the three kinds of flow mode had been confirmed. Hence, these findings would be helpful to further study the wake flow in the vortex shedding process.

The hygrothermal-mechanical behavior of a quad flat non-lead (QFN) package without a chip inside is investigated experimentally and numerically. The present study is focused on understanding the effect of the inherent hygrothermal behaviors of epoxy molding compound (EMC) on the deformations of QFN package. Prior to studying the package, the coefficient of moisture expansion for the EMC is measured experimentally. Full-field moiré and Twyman-Green interferometries are used for measuring the real-time in-plane and out-of-plane deformations of the specimen, respectively, under thermal and moisture loading. In addition, the finite element and theoretical analyses are adopted for validating the experimental observations and further understanding the hygrothermal mechanics of the specimen. The coefficient of moisture expansion of the EMC was experimentally obtained to be about 0.2. The experimental results of the full-field deformations of the specimen, due to temperature, moisture and a combination of both, are presented. The experimental observations are validated by the finite element and theoretical analyses. It was observed that the maximum moisture-induced deformation (strain) can be up to as large as 50% of the thermal deformation (strain) caused by ΔT = 50°C for the specimen. As a result, neglecting moisture-induced deformations (strains) would cause the significant amount of error in thermal deformation (strain) measurement of plastic packages. Furthermore, the present study has laid down the fundamental mechanics and approaches for the QFN packaging structural design and analysis in terms of hygrothermal effects.

In this study, a simplified method for evaluating amount of deflection for the tooth of worm and worm gear under loading is proposed. In a previous study, the plate theory was used for the approximation. However, it was found that the deflection of gear tooth using the plate theory was far from the actual value, and that the values from 3D FE analyses were closer to the actual value than from the plate theory. However, the FE analysis process starting from the CAD model to the final analysis results is complicated and too time-consuming. Therefore, the form factors are needed to facilitate simple but accurate results for the design purpose. In this study, the equations of form factors obtained from the results of plate theory and the 3D FEM, are developed. Since the worm gear assembly has various tooth geometries, the moment of inertia and the deflection of tooth geometry are different. Therefore, tooth geometries with trapezoid and involute forms are investigated.

The normal function of the knee relies upon a complicated and delicate mechanical interaction between the force-bearing structures, including muscles, ligaments and articular surfaces. Injury or damage to any of these structures will lead to the degradation or loss of joint function. Stair locomotion is one of the most common forms of motion in daily living. The purposes of the study were to analyze forces transmitted by the force-bearing structures of the knee during normal stair ascent and descent and to evaluate their mechanical differences. Compared to stair descent, higher peak patellar tendon forces, peak flexor forces, posterior cruciate ligament (PCL) forces and contact forces were required during stair ascent. In contrast, the anterior cruciate ligament (ACL) trended to bear higher forces during stair descent. It is suggested that one should be cautious in the use of stair ascent and descent as a rehabilitation exercise for patients with injuries or diseases of the cruciate ligaments and articular surfaces. The results of the study will be helpful for the understanding of the normal mechanics of the knee during stair locomotion, contributing to the design and evaluation of rehabilitation programs for patients with knee problems such as ACL injury and osteoarthritis.

This paper is concerned with linear and buckling analyses of composite beams with partial shear connection (partial composite beams) using the finite element method. Two elements derived from different types of shape functions are proposed in this study. The first element, referred to as exact, is based on the exact shape functions obtained by solving the differential equations governing the transverse displacement and the slip of the shear connector layer of a partial composite beam. The second element, referred to as approximate, is based on the conventional linear and cubic shape functions used in conventional axial and beam elements. By making use of these two types of shape functions, the elastic and geometric stiffness matrices can be derived explicitly from the strain energy and the load potential, respectively. Both types of elements can be used to carry out linear static and buckling analyses. As expected, the exact element is more accurate than the approximate element if the same discretization is adopted. However, the approximate element has the advantage of easy implementation since the expressions of its elastic and geometric stiffness matrices are very simple. Also, the solutions obtained from the approximate element converge very fast; with reasonable discretization, say 8 elements per member, very accurate solutions can be obtained.

The shear failure probabilities of reinforced concrete beam-column joints have been investigated by Monte Carlo method. The theoretical shear strength of joints is based on the softened strut-and-tie model proposed by Hwang and Lee (2002). The random variables included in this study are the strengths of concrete, the ultimate compression strain of concrete, the strengths of reinforcement, the dimensions of cross-section, and the model error of theoretical shear strength of joints. The shear failure probabilities of joints with SD 280 flexural reinforcement in the beams designed using the ACI Code are all higher than 0.04. The joints designed according to the softened strut-and-tie model are safer than those designed according to the ACI Code. The shear failure probabilities of exterior joints are higher than those of interior joints. The shear failure probabilities of joints with SD 280 flexural reinforcement in the beams are higher than those of joints with SD 420 flexural reinforcement.

Numerical properties of the Newmark explicit method in the solution of nonlinear systems are explored. It is found that the upper stability limit is no longer equal to 2 for the Newmark explicit method for nonlinear systems. In fact, it is enlarged for stiffness softening and is reduced for stiffness hardening. Furthermore, its relative period error increases with the increase of the step degree of nonlinearity for a given value of the product of the natural frequency and the time step. It is also verified that the viscous damping determined from an initial stiffness is effective to reduce displacement response in the solution of a nonlinear system as that for solving a linear elastic system. All the theoretical results are confirmed with numerical examples.

The mixing behavior of a two-channel micromixer with a circular mixing chamber at four different chamber depths and six different flow rates had been investigated. Experiments were implemented with the mixings of two fluids. An image inspection method using the variance of the image gray level contrast as the measurement parameter to determine the mixing efficiency distribution in these mixers. The steady, three-dimensional and laminar flow fields inside the micromixers were also simulated numerically with a finite volume discretization. Through the numerical integration over the chamber depth, the three-dimensional numerical prediction could be compressed into a two-dimensional result, which could be directly used to compare with the experimental measurements. Experimental results show that the measured mixing efficiency is raised with the increase of chamber depth. The numerical prediction of mixing efficiency agreed qualitatively with those obtained from the experimental measurements, while the ratio of the depth to diameter of the mixing chamber is big enough to eliminate the viscosity effect.

Creep is the time-dependent, viscoelastic strain observed in materials under constant stress. Creep can increase structural strains/deformations to non-serviceable levels or alter the stress distribution among structural components. While stress redistribution can be helpful in composite materials by relieving the stress on one component, it might have a detrimental effect on another, especially if it leads to overstressing.

A step-by-step in time approach for modeling creep in quasi-brittle materials such as concrete and masonry is utilized, and a new continuum damage model based on Weibull's failure rate distribution is introduced. A multiplicative approach to integrate the creep and damage effects within the step-by-step in time analysis is invoked. The significance of the proposed approach is exemplified through analysis of a clay masonry column filled with grout and subjected to concentric axial load. It is shown that the proposed approach can provide insights on the stress evolution in both components of the composite material that might not be inferred using classical methods of analysis.

The flow of a viscous fluid disturbed by an oscillating plate of arbitrary initial phase is studied in present note. The exact solutions of the velocity and the shear stress are solved using a Laplace transform method. The velocity is derived in terms of complementary error functions and the shear stress on the boundary is given in the form of Fresnel integrals. Since the steady-state solutions are well known, our discussions are focused on the transient solutions. The transient state will disappear faster for the wall stress than that for the velocity field. Comparing the results corresponding to different initial phases, the cosine case reaches to the steady state more rapidly than the sine case.