Vietnam Journal of Mechanics

Study on the velocity of droplet at steady state in contraction microchannels by numerical simulation

Thanh Tung Nguyen — 2023-12-05

The droplet-based microfluidic system is increasingly advancing and widely applied in various fields of analytical techniques and experiments. To optimize and advance this system, droplet dynamics is of utmost concern. The velocity of droplets is highly significant as it aids in precise droplet control and manipulation, ultimately leading to the optimization of device design and performance. This paper utilizes numerical simulations to explore the influence of flow characteristics, fluid properties, and geometric parameters of the contraction microchannel on the velocity of droplets while they are in a stable state. The findings indicate that the droplet velocity is influenced by factors such as viscosity ratio (λ), capillary number (Ca), and contraction ratio (C).

Exact receptance function of a tapered AFG beam with nonlinearly varying ratios of beam properties carrying concentrated masses

Thao Thi Bich Dao — 2023-12-31

This paper presents a method for establishing the exact receptance function of a tapered axially functionally graded (AFG) beam with nonlinear ratios of properties using the Adomian method. In current papers, the Adomian method was applied for linearly tapered beams where the geometric series was used conveniently. However, for nonuniform AFG beams with nonlinearly varying ratios of properties, the geometric series cannot be used, thus the other type of power series needs to be established and applied. In this paper, the derivation of the power series applied for obtaining the exact receptance function of a nonuniform AFG beam with nonlinearly varying ratios of properties is presented. Numerical simulation results of the receptance function of a tapered AFG beam with nonlinearly varying ratios of beam properties carrying concentrated masses are conducted and provided. The influences of the concentrated masses and the varying ratios of properties of beam on the receptance matrix are also investigated and presented.

Adhesive contact between two-dimensional anisotropic elastic bodies

Nguyen Dinh Duc — 2023-12-28

Adhesion plays a vital role in the design of smart and intelligent high-tech devices such as modern optical, microelectromechanical, and biomedical systems. However, in the literature, adhesive contact is mostly considered for contact of rigid substrates and transversely isotropic and isotropic elastic materials. The composite materials are increasingly used in the mart and intelligent high-tech devices. Since the composite materials are generally anisotropic and contact bodies are all deformable, it is more practical to consider the adhesive contact of two anisotropic elastic materials. In this paper, an adhesive contact model of anisotropic elastic bodies is established, and the closed-form solutions for two-dimensional adhesive contact of two anisotropic elastic bodies are derived. The full-field solutions and the relation for the contact region and applied force are developed using the Stroh complex variable formalism, the analytical continuation method, and concepts of the JKR adhesive model. We will show that the frictionless contact of two anisotropic elastic materials is just a special case of the present contact problem, and its solutions can be obtained by setting the work of adhesion equal to zero. In addition, we also show that our present solutions are valid for the problems of indentation by a rigid punch on an elastic half-space through a proper placement of the contact radius and the corresponding material constant. Numerical results are provided to demonstrate the accuracy, applicability, and versatility of the developed solutions.

Proportional Topology Optimization algorithm with virtual elements for multi-material problems considering mass and cost constraints

Minh Tuan Tran — 2023-12-31

This paper presents an extension of the Proportional Topology Optimization (PTO) with virtual elements for multi-material problems with mass and cost constraints. In particular, the linear virtual element method (VEM) is constructed on unstructured polygonal meshes. The linear VEM is desirable in the sense that numerical integration is not explicitly required, significantly reducing the computational effort. Furthermore, the unstructured polygonal mesh naturally eliminates the issue of one-node connections encountered by the usual quadrilateral mesh. A feature of PTO is that it does not require sensitivity information, i.e., the derivative of the objective function with respect to design variables. Instead, the amount of material distributed into each element is determined proportionally to the contribution of that element to the objective function. For multi-material problems, the Ordered Solid Isotropic Material with Penalization (Ordered SIMP) technique is integrated into the PTO framework. Compared to other techniques for problems that involve multiple materials, Ordered SIMP has the advantage that computational cost does not depend on the number of materials. Furthermore, for the first time, the PTO approach is extended to consider two types of constraints: mass and cost simultaneously. The feasibility and efficiency of the proposed method are demonstrated via several benchmark examples and comparisons with the existing approach.

Wave propagation analysis in transversely isotropic piezoelastic medium based on nonlocal strain gradient theory

Trinh Thi Thanh Hue — 2023-12-31

The purpose of this research is to study the propagation of surface waves in transversely isotropic piezoelastic medium based on nonlocal strain gradient theory. A characteristics equation for the existence of surface waves is discussed. This equation could be easily reduced to the ones of the gradient strain theory, nonlocal theory, and classical theory. It has also been concluded that there exist cut-off frequency for the wave propagating in size-dependent materials based on the nonlocal strain gradient theory. The dispersion equation which surface wave speed satisfies is derived from the free traction condition on the surface of half-space with consideration of electrically open circuit conditions. The effect of the nonlocal parameter, the strain gradient parameter on the existence of surface waves as well as the Rayleigh wave propagation is illustrated through some numerical examples.