Papers by Keyword: Boundary Condition

Abstract: This work presents a two-dimensional numerical analysis of a wave channel. The goal is to investigate a methodology that uses transient velocity data as means to impose velocity boundary condition for generating numerical waves. To do so, a numerical wave channel was simulated using irregular waves. These waves were obtained using the WaveMIMO methodology, which converts sea data from a spectral model into time series of free surface elevation, and then converts this elevation into transient discrete wave velocity data. For the numerical analysis, computational fluid dynamics ANSYS Fluent software was employed, which is based on the finite volume method. The computational domain and mesh were generated using GMSH software, and the nonlinear multiphase model volume of fluid (VOF) was applied to tackle water-air interaction. In general, the results obtained through the use of discrete data as velocity boundary condition presented a good agreement with free surface elevation converted from the spectral model, and the tests performed provided further insight into the parameters which affect this methodology. Since many studies use regular waves, the proposed investigation stands out for its capacity to improve the use of realistic sea state data in numerical simulations of wave energy converters.

Abstract: This paper describes an approach extended from Ritz method to analyze the free vibration of thin isotropic annular plates in good accuracy, and presents comprehensive lists of natural frequencies of the plate for all possible sets of classical boundary conditions. Analytical process is developed to introduce the boundary index that allows to accommodate any sets of free, simple supported and clamped edges along inner and outer boundary of the plate. Convergence and comparison studies are made to demonstrate numerical accuracy in the frequency parameters. Results are summarized for nine sets of boundary conditions and six different ratios of (inner radius)/(outer radius), and are intended to serve for uses of design data and comparison in relevant future papers.

Abstract: The size-dependent bending and static stability characteristics of nanobeams made of bi-directional functionally graded materials (2D-FGMs) under different boundary conditions are comprehensively investigated. Based on the modified couple stress theory and surface elasticity theory, the size-dependent model is formulated for 2D-FG Euler-Bernoulli beam. The material properties of the beam smoothly change along both the axial and thickness directions according to power-law distribution. The continuous spatial variations of the single material length scale parameter and the three surface constants are incorporated to describe the effects of microstructure and surface energy, respectively. This model accounts for the axial and transverse displacements, the exact position of the physical neutral plane, and Poisson’s effect. To obtain the static response of the present model, Ritz method is employed by approximating the axial and transverse displacements in terms of polynomial forms. Different boundary conditions, i.e., Simply-simply (S-S), Clamped-clamped (C-C), Clamped-simply (C-S), and Clamped-free (C-F), are considered and satisfied by adding auxiliary functions to the displacement functions. Numerical results with various cases of boundary conditions are performed with an insight to explore the effects of gradient indices in thickness and length directions, surface energy, material length scale parameter, slenderness ratio, and thickness on the static deflection and buckling responses of 2D-FG nanobeams. Results disclose that, the material properties, the surface energy, and microstructure effects have a significant effect on the bending, and buckling responses of 2D-FG nanobeams. Hence, this study can be helpful in the design and optimization of 2D-FG nanobeams in bending and buckling responses.

Abstract: We applied the dielectric function method to solve analytically L-NL-L structure problems with negative Kerr nonlinearity. A damped wave in linear and a periodic standing wave in non-linear media had to be matched at boundaries. We gave a formulation of boundary conditions that did not explicitly include a film thickness. The boundary-value of a dielectric function can be expressed through the constant of non-trivial integral of motion. Using it, one generates a family of matched solutions satisfying boundary conditions. Then arbitrary film thickness can be checked against this family of solutions in search of matches. As a result, all fitted solutions are determined straightforwardly.

Abstract: FRP laminates are used in several industries such as automobile, aircraft’s, spacecraft’s, defense and etc.., where high strength-to-weight ratio is the primary criteria. FRP laminates offer high design and material tailoring properties but are highly susceptible to delamination and debonding under out-of-plane low velocity impact which induces barely visible impact damage (BVID) inside the structures. A lot of research investigation is going on related to damage resistance behavior of FRP laminates under out-of-plane impact loading. But very less concentration is paid to the FRP laminates behavior under in-plane low impact loading. In this numerical analysis in-plane low velocity impact loading is carried out on a bidirectional plain woven glass fiber reinforced epoxy laminate (GFRP) using LS-DYNA. A hemispherical impactor of mass 5kg and diameter of 10mm is impacted at 0.5, 1.0 and 1.5m/sec velocity on [(0⁰/90⁰)/(+45⁰/-45⁰)/(+45⁰/-45⁰)/(0⁰/90⁰)]_S layup design. Two boundary conditions complete edge and corner constraining boundary conditions are considered for numerical analysis. Force vs. time, energy vs. time, displacement vs. time plots are used to evaluate the analysis.

Abstract: Free and forced longitudinal oscillations of homogeneous rods of constant cross section are considered. Analytical and numerical methods for solving problems are used. With free vibration, numerical examples are shown for a rod with a jammed and free end and for a rod with a concentrated non-deformable mass at the end, due to which the mathematical model accordingly changes. Forced oscillations are considered for distributed and concentrated loads. The eigenmodes of oscillations characteristic for continually discrete sisites are obtained.

Abstract: In this paper, we consider the influence of the conditions for fixing a wavy plate lying on an elastic foundation on its stressed-deformed state. The profiled plates are widely used in construction practice as fencing structures, for siding works, for roofing and others. The stress-strain state of the wavy plates varies depending on geometry, materials mechanical properties, foundation characteristics and boundary condition. Steel with polymer coatings, which make the sheets a decorative material, is increasingly used in individual and low-rise buildings. The elastic foundation is considered as Winkler base, so we suppose that the reaction of the base is directly proportional to the deflection of the plate at each point. The Bubnov-Galerkin method is used to determine the stress-strain state of the plate. To solve the problem, we use special orthogonal Legendre polynomials satisfying the boundary conditions: simply supported and clamped edges. The results of the calculations were compared for different types of fixation.

Abstract: Boundary condition is an important factor for the impact behavior of fabrics. In the present work, the effect of boundary condition on the impact behavior of fabrics was investigated modeling the impact conditions in a finite element software program. In the numerical simulations, fabric boundary condition and impact velocity were used as variable parameters and their effects were discussed in terms of fabric deformation and energy absorption capacity. Based on the study, the significance of boundary condition gradually diminishes as impact velocity increases. However, at low velocities, fabrics with free edges provide enhanced energy absorption performance in comparison to those with fixed edges. In addition, fabric deformation turns to local scale increasing impact velocity however, at low velocities, deformation is extended over a wider area on the fabrics.

Abstract: This paper presents boundary conditions for lateral buckling of the H-shaped beams connected to columns by flush end plates which fall into the lateral buckling following the out of plane plastic deformations of the flush end plates. The study is conducted by the following procedure: First, the behavior of the connection is researched by the no buckling experiment under the cyclic loading. As a result, it is found that the relationship between the out of plane plastic deformations of the endplates and the bending moment at the beam end can be predicted. Next, the FEM analyses of the rigid-frame structures consist of the slender beams having flush end plates connection and the structures consist of the beams having rigid connection are conducted to research the stress conditions in the tension flanges and the compression flanges of the beams during falling into lateral buckling. As a result, it is found that the rigid connection is restraining warping of the beam more tightly than the flush end plates connection, then the maximum bending moment strength against lateral buckling of the beams connected by rigid connections is higher than those of the beams connected by flush endplate. We recommend that the boundary conditions for the lateral buckling of the beams connected by flush end plates should be regarded to be different from those of the beams connected by the rigid connections.

Abstract: The planar flow of a Newtonian incompressible fluid in a T-shaped channel is investigated. Three fluid interaction models with solid walls are considered: no slip boundary condition, Navier slip boundary condition and slip boundary condition with slip yield stress. The fluid flow is provided by uniform pressure profiles at the boundary sections of the channel. The problem is numerically solved using a finite difference method based on the SIMPLE procedure. Characteristic flow regimes have been found for the described models of liquid interaction with solid walls. The estimation of the influence of the Reynolds number, pressure applied to the boundary sections and the parameters of these models on the flow pattern was performed. The criterial dependences describing main characteristics of the flow under conditions of the present work have been demonstrated.