A Perfectly Transparent Spectral Shell for Unsteady Wave-Body Interactions

2002 ◽  
Author(s):  
J. Andrew Hamilton ◽  
Ronald W. Yeung
Keyword(s):  
Boundary Condition ◽  
Solution Method ◽  
Outer Boundary ◽  
Outer Region ◽  
Interior Solution ◽  
Function Solution ◽  
Solution Methods ◽  
Matching Procedure ◽  
Surface Green Function ◽  
Unsteady Problems

A general outer boundary condition for time-dependent wave-body interaction problems is developed. The technique is based on domain decomposition and the unsteady free-surface Green function solution of the flow in an outer region. The boundary condition results in a shell condition which may be applied to a variety of interior solution methods. When the interior solution method is a boundaryintegral method, an implicit matching can be done. When a volume-discretization method is used in the interior region, a newly developed explicit matching procedure is performed. Demonstrations of the transparent properties of this shell are made for several unsteady problems.

Spectral Shell and Perfectly Transparent Open-Boundary Condition for Unsteady Wave-Body Interactions

2003 ◽  
Vol 125 (1) ◽  
pp. 9-16 ◽  
Author(s):  
J. Andrew Hamilton ◽  
Ronald W. Yeung
Keyword(s):  
Boundary Condition ◽  
Outer Region ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Open Boundary ◽  
Interior Solution ◽  
Open Boundary Condition ◽  
Solution Methods ◽  
Surface Green Function ◽  
Unsteady Problems

This work, presented in the OMAE-2002 Special Symposium in honor of John V. Wehausen, is dedicated to him, an admirable teacher, colleague, and scholar. A general open boundary condition for time-dependent wave-body interaction problems is developed. The technique is based on domain decomposition and a use of the unsteady free-surface Green function in an outer region. The boundary condition results in a shell condition which may be applied to a variety of interior solution methods. When the interior solution method is a boundary-integral method, an implicit matching can be done. When a volume-discretization method is used in the interior region, a newly developed explicit matching procedure is performed. Demonstrations of the transparent properties of this shell are made for several types of unsteady problems.

scholarly journals Solution of Contact Problems for Nonlinear Gao Beam and Obstacle

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
J. Machalová ◽  
H. Netuka
Keyword(s):  
Solution Method ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Contact Problems ◽  
Beam Model ◽  
Contact Conditions ◽  
Beam Elements ◽  
Solution Methods ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

Contact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler’s type in some distance under the beam. The problem is static without a friction and modeled either using Signorini conditions or by means of normal compliance contact conditions. The problems are then reformulated as optimal control problems which is useful both for theoretical aspects and for solution methods. Discretization is based on using the mixed finite element method with independent discretization and interpolations for foundation and beam elements. Numerical examples demonstrate usefulness of the presented solution method. Results for the nonlinear Gao beam are compared with results for the classical Euler-Bernoulli beam model.

scholarly journals Computational Methods for Production-Based Asset Pricing Models with Recursive Utility

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Eric Mark Aldrich ◽  
Howard Kung
Keyword(s):  
Asset Pricing ◽  
Solution Method ◽  
Value Function ◽  
Polynomial Solution ◽  
Dsge Models ◽  
Recursive Utility ◽  
Solution Quality ◽  
Global Method ◽  
Asset Pricing Models ◽  
Solution Methods

Abstract We compare local and global polynomial solution methods for DSGE models with Epstein- Zin-Weil utility. We show that model implications for macroeconomic quantities are relatively invariant to choice of solution method but that a global method can yield substantial improvements for asset prices and welfare costs. The divergence in solution quality is highly dependent on parameters which affect value function sensitivity to TFP volatility, as well as the magnitude of TFP volatility itself. This problem is pronounced for calibrations at the extreme of those accepted in the asset pricing literature and disappears for more traditional macroeconomic parameterizations.

scholarly journals Numerical Solution of Continuation Problem for 3D Steady-State Diffusion in Cylindrically Layered Medium

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Magira Kulbay ◽  
Saule Maussumbekova ◽  
Balgaisha Mukanova
Keyword(s):  
Steady State ◽  
Layered Medium ◽  
Outer Boundary ◽  
Cauchy Data ◽  
Piecewise Constant Function ◽  
Piecewise Constant ◽  
State Diffusion ◽  
Solution Methods ◽  
Continuation Problem ◽  
Steady State Diffusion

This work is based on the application of Fourier and quasi-solution methods for solving the continuation inverse problem for 3D steady-state diffusion model inside a cylindrical layered medium. The diffusion coefficient is supposed to be a piecewise constant function, Cauchy data are given on the outer boundary of the cylinder, and we seek to recover the temperature at the inner boundary of the cylinder. Numerical experiments are investigated and show the capacity of proposed method only for smooth boundary condition. Under the suitable choice of regularization parameters we recover the distribution of temperature on the inner boundary with satisfactory quality for noisy data.

scholarly journals EVALUATION OF SEVERAL NONREFLECTING COMPUTATIONAL BOUNDARY CONDITIONS FOR DUCT ACOUSTICS

1995 ◽  
Vol 03 (04) ◽  
pp. 327-342 ◽  
Author(s):  
WILLIE R. WATSON ◽  
WILLIAM E. ZORUMSKI ◽  
STEVE L. HODGE
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Sound Propagation ◽  
Sparse Matrix ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Substantial Reduction ◽  
Sound Attenuation ◽  
Interior Solution ◽  
Duct Acoustics

Several nonreflecting computational boundary conditions that meet certain criteria and have potential applications to duct acoustics are evaluated for their effectiveness. The same interior solution scheme, grid, and order of approximation are used to evaluate each condition. Sparse matrix solution techniques are applied to solve the matrix equation resulting from the discretization. Modal series solutions for the sound attenuation in an infinite duct are used to evaluate the accuracy of each nonreflecting boundary condition. The evaluations are performed for sound propagation in a softwall duct, for several sources, sound frequencies, and duct lengths. It is shown that a recently developed nonlocal boundary condition leads to sound attenuation predictions considerably more accurate than the local ones considered. Results also show that this condition is more accurate for short ducts. This leads to a substantial reduction in the number of grid points when compared to other nonreflecting conditions.

INVESTIGATING THE EFFECT OF SLOSHING ON THE ENERGY ABSORPTION OF TANK WAGONS CRASH

2015 ◽  
Vol 39 (2) ◽  
pp. 187-200 ◽  
Author(s):  
Reza Razaghi ◽  
Majid Sharavi ◽  
Mohammad Mahdi Feizi
Keyword(s):  
Energy Absorption ◽  
Solution Method ◽  
Crash Test ◽  
Test Results ◽  
Software Simulation ◽  
Fluid Sloshing ◽  
Mass Spring Model ◽  
Solution Methods ◽  
Height Increase ◽  
Mass Spring

One of the main fluid mechanics phenomena is fluid sloshing which is originated from the free surface of fluid and should be taken into account in design of fluid structures such as fuel tank wagons, ships and so on. The aim of this paper is to investigate the effect of tank fluid sloshing on energy absorption and reducing tank acceleration during the tank wagon impact. For this purpose, methods of software simulation and dynamics solution methods are accomplished. The assumed wagon includes a tank with the approximate volume of 95 m3 and capacity of 65 tons of fluid. Using finite element method, the tank impact is simulated based on the corresponding standards for different heights of fluid in the tank. Obtained results show fluid height increase has an inappropriate effect on energy absorption among impact however the more fluid in tank, the more time would be consumed for energy absorption in general. At the end, by using crash test results for a tank with aforementioned scale, validity of impact software simulation and dynamic solution method considering the tank fluid as mass-spring model are checked.

The Role of the Outer Boundary Condition in Accretion Disk Models: Theory and Application

2000 ◽  
Vol 537 (1) ◽  
pp. 236-244 ◽  
Author(s):  
Feng Yuan ◽  
Qiuhe Peng ◽  
Ju‐fu Lu ◽  
Jianmin Wang
Keyword(s):  
Boundary Condition ◽  
Accretion Disk ◽  
Outer Boundary

Investigations: Vehicles for Learning and Doing Mathematics

1996 ◽  
Vol 178 (2) ◽  
pp. 35-49 ◽  
Author(s):  
Carole Greenes
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Solution Method ◽  
Professional Organizations ◽  
Mathematical Concepts ◽  
Educational Benefits ◽  
Problem Situations ◽  
Mathematics Educators ◽  
Solution Methods ◽  
Problem Solving Strategies

Professional organizations of mathematics educators and mathematicians are calling for major reforms in the teaching and learning of mathematics. Among those reforms are a shift in emphasis in curriculum from mastery of lists of unrelated mathematical concepts and skills to exploration of rich mathematical topics and problem situations, and a shift in learning from memorizing and replicating algorithmic procedures to investigating and solving complex problems. To help students achieve proficiency in solving problems, the curriculum must focus on development of the major concepts of mathematics, the enhancement and enlargement of students' repertoires of problem-solving strategies and reasoning methods, and the refinement of communication and collaboration skills. Because they present intriguing problems whose solutions or solution methods are not immediately obvious, and require the application of concepts from different areas of mathematics, and, in some instances, knowledge from other content areas, investigations are powerful vehicles for helping students achieve expertise in solving problems. The nature of investigations and their educational benefits are described. Three types of investigations, whimsical, real, and mathematical, are defined and illustrated. For each investigation, the mathematical content and problem-solving strategies are identified, and a solution method is presented. The responsibilities of the teacher, before, during and after an investigation are described.

Preparation and properties of polyimide-polysiloxane hybrid materials by the sol-gel process

1994 ◽  
Vol 6 (2) ◽  
pp. 95-107 ◽  
Author(s):  
Yoshitake Iyoku ◽  
Masa-aki Kakimoto ◽  
Yoshio Imai
Keyword(s):  
Solution Method ◽  
Sol Gel ◽  
Mechanical Analysis ◽  
Methanol Solution ◽  
Heating Process ◽  
Hybrid Films ◽  
Polyamic Acid ◽  
Sol Gel Process ◽  
Solution Methods ◽  
Polyimide Matrix

Polyimide-poly(methylsiloxane) hybrid films were successfully prepared by the sol-gel process with methyltriethoxysilane (MTES) and/or dimethyldiethoxysilane (DMDES) in the polymer solution. Two methods were used for making hybrid films. First, MTES and/or DMDES were dissolved in the N,N-dimethylacetamide (DMAc) solution of the polyamic acid (polyimide precursor) prepared from 4,4'-diaminodiphenyl ether (ODA) and pyromellitic dianhydride (PMDA). During the heating process at 300°C the polyamic acid was converted to polyimide and the sol-gel reaction, which consists of hydrolysis and condensation of MTES and/or DMDES, proceeded simultaneously. Second, methanol was used as the solvent to make the hybrid films by using the triethylamine salt of polyamic acid. The IR spectra proved that the sol-gel reactions started from MTES and DMDES readily proceeded in the polymer matrix. The hybrid films prepared in methanol were more transparent than those prepared in DMAc. Measurement by dynamic mechanical analysis indicated that the polystloxane was dispersed homogeneously in the polyimide matrix even after the heat treatment at 300°C, in the case of both DMAc and methanol solution methods. With respect to the tensile properties, the tensile strength and the elongation at break of the hybrid films prepared by the methanol solution method were higher than those by the DMAc solution method. The modulus of the obtained hybrid films decreasing with increasing DMDES ratio in the silicone unit in both cases.

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