A Combined Analytical and Numerical Approach for the Solution of an Edge Loaded Semi-Infinite Elastic Sheet

1996 ◽  
Author(s):  
Xin Sun ◽  
Dale G. Karr ◽  
Chunhui Han
Keyword(s):  
Fourier Transforms ◽  
Thin Sheet ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Order Theory ◽  
Thick Sheet ◽  
Approximate Theory ◽  
Loading Conditions ◽  
Elastic Sheet ◽  
Limit Solutions

Abstract Edge loading of an semi-infinite elastic sheet is of interest to many engineering applications. In this paper the penetration problem involving a rigid indentor and an elastic semi-infinite sheet of uniform thickness is addressed using a combined analytical and numerical approach. The tenth-order approximate theory of stretching of an isotropic sheet is applied to formulate the governing differential equations. Solutions are then obtained using Fourier transforms for various loading conditions and numerical schemes are employed to calculate the three dimensional state of stress throughout the sheet. The influence of the aspect ratio on the resulting stress state is studied. Limit solutions for thin sheet and thick sheet are presented. Finite element analyses of the same loading conditions are also performed. Results are compared with those of the tenth-order theory and the stress distribution assumptions of the tenth-order theory are examined.

Modeling and Assessment of the Produced Water Discharges from Offshore Petroleum Platforms

2007 ◽  
Vol 42 (4) ◽  
pp. 303-310 ◽  
Author(s):  
Zhi Chen ◽  
Lin Zhao ◽  
Kenneth Lee ◽  
Charles Hannath
Keyword(s):  
Random Walk ◽  
Produced Water ◽  
Model Development ◽  
Three Dimensional ◽  
Monitoring Program ◽  
Ecological Monitoring ◽  
Numerical Approach ◽  
Ocean Model ◽  
Scale Model ◽  
Water Stream

Abstract There has been a growing interest in assessing the risks to the marine environment from produced water discharges. This study describes the development of a numerical approach, POM-RW, based on an integration of the Princeton Ocean Model (POM) and a Random Walk (RW) simulation of pollutant transport. Specifically, the POM is employed to simulate local ocean currents. It provides three-dimensional hydrodynamic input to a Random Walk model focused on the dispersion of toxic components within the produced water stream on a regional spatial scale. Model development and field validation of the predicted current field and pollutant concentrations were conducted in conjunction with a water quality and ecological monitoring program for an offshore facility located on the Grand Banks of Canada. Results indicate that the POM-RW approach is useful to address environmental risks associated with the produced water discharges.

scholarly journals Microstructure and Mechanical Properties of Al-Mg-Si Similar Alloy Laminates Produced by Accumulative Roll Bonding

Materials ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4200
Author(s):  
Zhigang Li ◽  
Hao Jiang ◽  
Minghui Wang ◽  
Hongjie Jia ◽  
Hongjiang Han ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Accumulative Roll Bonding ◽  
Thin Sheet ◽  
Heterogeneous Materials ◽  
Thick Sheet ◽  
Subsequent Aging ◽  
Roll Bonding ◽  
Roll Casting ◽  
Promotive Effect ◽  
Similar Materials

As the applications of heterogeneous materials expand, aluminum laminates of similar materials have attracted much attention due to their greater bonding strength and easier recycling. In this work, an alloy design strategy was developed based on accumulative roll bonding (ARB) to produce laminates from similar materials. Twin roll casting (TRC) sheets of the same composition but different cooling rates were used as the starting materials, and they were roll bonded up to three cycles at varying temperatures. EBSD showed that the two TRC sheets deformed in distinct ways during ARB processes at 300°C. Major recrystallizations were significant after the first cycle on the thin sheet and after the third cycle on the thick sheet. The sheets were subject to subsequent aging for better mechanical properties. TEM observations showed that the size and distribution of nano-precipitations were different between the two sheet sides. These nano-precipitations were found to significantly promote precipitation strengthening, and such a promotive effect was referred to as hetero-deformation induced (HDI) strengthening. Our work provides a new promising method to prepare laminated heterogeneous materials with similar alloy TRC sheets.

Simulation of small-angle scattering curves by numerical Fourier transformation

2007 ◽  
Vol 40 (1) ◽  
pp. 16-25 ◽  
Author(s):  
Klaus Schmidt-Rohr
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Fourier Transformation ◽  
Three Dimensional ◽  
Power Laws ◽  
Numerical Approach ◽  
Peak Position ◽  
Two Dimensions ◽  
Correlation Peak ◽  
Scattering Intensity

A simple numerical approach for calculating theq-dependence of the scattering intensity in small-angle X-ray or neutron scattering (SAXS/SANS) is discussed. For a user-defined scattering density on a lattice, the scattering intensityI(q) (qis the modulus of the scattering vector) is calculated by three-dimensional (or two-dimensional) numerical Fourier transformation and spherical summation inqspace, with a simple smoothing algorithm. An exact and simple correction for continuous rather than discrete (lattice-point) scattering density is described. Applications to relatively densely packed particles in solids (e.g.nanocomposites) are shown, where correlation effects make single-particle (pure form-factor) calculations invalid. The algorithm can be applied to particles of any shape that can be defined on the chosen cubic lattice and with any size distribution, while those features pose difficulties to a traditional treatment in terms of form and structure factors. For particles of identical but potentially complex shapes, numerical calculation of the form factor is described. Long parallel rods and platelets of various cross-section shapes are particularly convenient to treat, since the calculation is reduced to two dimensions. The method is used to demonstrate that the scattering intensity from `randomly' parallel-packed long cylinders is not described by simple 1/qand 1/q4power laws, but at cylinder volume fractions of more than ∼25% includes a correlation peak. The simulations highlight that the traditional evaluation of the peak position overestimates the cylinder thickness by a factor of ∼1.5. It is also shown that a mix of various relatively densely packed long boards can produceI(q) ≃ 1/q, usually observed for rod-shaped particles, without a correlation peak.

scholarly journals Modelling of Applied Magnetic Field and Thermal Radiations Due to the Stretching of Cylinder

Processes ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 1077
Author(s):  
Muhammad Tamoor ◽  
Muhammad Kamran ◽  
Sadique Rehman ◽  
Aamir Farooq ◽  
Rewayat Khan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Boundary Layer Equations ◽  
Convective Parameter ◽  
Momentum And Heat Transfer ◽  
Dimensional Boundary

In this study, a numerical approach was adopted in order to explore the analysis of magneto fluid in the presence of thermal radiation combined with mixed convective and slip conditions. Using the similarity transformation, the axisymmetric three-dimensional boundary layer equations were reduced to a self-similar form. The shooting technique, combined with the Range–Kutta–Fehlberg method, was used to solve the resulting coupled nonlinear momentum and heat transfer equations numerically. When physically interpreting the data, some important observations were made. The novelty of the present study lies in finding help to control the rate of heat transfer and fluid velocity in any industrial manufacturing processes (such as the cooling of metallic plates). The numerical results revealed that the Nusselt number decrease for larger Prandtl number, curvature, and convective parameters. At the same time, the skin friction coefficient was enhanced with an increase in both slip velocity and convective parameter. The effect of emerging physical parameters on velocity and temperature profiles for a nonlinear stretching cylinder has been thoroughly studied and analyzed using plotted graphs and tables.

scholarly journals A Numerically Supported Investigation of the 3D Flow in Centrifugal Impellers: Part I — The Validation Base

1996 ◽  
Author(s):  
Ch. Hirsch ◽  
S. Kang ◽  
G. Pointel
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Boundary Layer Separation ◽  
Numerical Approach ◽  
Secondary Flows ◽  
Pump Impeller ◽  
High Loss ◽  
Leakage Flows ◽  
Fine Mesh ◽  
Radial Pump

The three-dimensional flow in centrifugal impellers is investigated on the basis of a detailed analysis of the results of numerical simulations. In order to gain confidence in this process, an in-depth validation is performed, based on computations of Krain’s centrifugal compressor and of a radial pump impeller, both with vaneless diffusers. Detailed comparisons with available experimental data provide high confidence in the numerical tools and results. The appearance of a high loss ‘wake’ region results from the transport of boundary layer material from the blade surfaces to the shroud region and its location depends on the balance between secondary and tip leakage flows and is not necessarily connected to 3D boundary layer separation. Although the low momentum spots near the shroud can interfere with 3D separated regions, the main outcome of the present analysis is that these are two distinct phenomena. Part I of this paper focuses on the validation base of the numerical approach, based on fine mesh simulations, while Part II presents an analysis of the different contributions to the secondary flows and attempts to estimate their effect on the overall flow pattern.

scholarly journals A hypoplastic macroelement for single vertical piles in sand subject to three-dimensional loading conditions

2015 ◽  
Vol 11 (2) ◽  
pp. 373-390 ◽  
Author(s):  
Zheng Li ◽  
Panagiotis Kotronis ◽  
Sandra Escoffier ◽  
Claudio Tamagnini
Keyword(s):  
Three Dimensional ◽  
Loading Conditions

Thermal jet drilling of granite rock: a numerical 3D finite-element study

2021 ◽  
Vol 379 (2196) ◽  
pp. 20200128
Author(s):  
Timo Saksala ◽  
Reijo Kouhia ◽  
Ahmad Mardoukhi ◽  
Mikko Hokka
Keyword(s):  
Finite Elements ◽  
Numerical Study ◽  
Thermal Flux ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Mass Scaling ◽  
Granite Rock ◽  
Fracture Dynamics ◽  
Rock Heterogeneity ◽  
Thermal Drilling

This paper presents a numerical study on thermal jet drilling of granite rock that is based on a thermal spallation phenomenon. For this end, a numerical method based on finite elements and a damage–viscoplasticity model are developed for solving the underlying coupled thermo-mechanical problem. An explicit time-stepping scheme is applied in solving the global problem, which in the present case is amenable to extreme mass scaling. Rock heterogeneity is accounted for as random clusters of finite elements representing rock constituent minerals. The numerical approach is validated based on experiments on thermal shock weakening effect of granite in a dynamic Brazilian disc test. The validated model is applied in three-dimensional simulations of thermal jet drilling with a short duration (0.2 s) and high intensity (approx. 3 MW m −2 ) thermal flux. The present numerical approach predicts the spalling as highly (tensile) damaged rock. Finally, it was shown that thermal drilling exploiting heating-forced cooling cycles is a viable method when drilling in hot rock mass. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

Computational Investigation of Thrust Production of a Dolphin at Various Swimming Speeds

2021 ◽  
Author(s):  
Junshi Wang ◽  
Vadim Pavlov ◽  
Zhipeng Lou ◽  
Haibo Dong
Keyword(s):  
Surface Pressure ◽  
Swimming Performance ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Immersed Boundary ◽  
Reconstruction Method ◽  
Force Coefficient ◽  
Speed Increase ◽  
Generation Mechanisms ◽  
Thrust Production

Abstract Dolphins are known for their outstanding swimming performance. However, the difference in flow physics at different speeds remains elusive. In this work, the underlying mechanisms of dolphin swimming at three speeds, 2 m/s, 5 m/s, and 8 m/s, are explored using a combined experimental and numerical approach. Using the scanned CAD model of the Atlantic white-sided dolphin (Lagenorhynchus acutus) and virtual skeleton-based surface reconstruction method, a three-dimensional high-fidelity computational model is obtained with time-varying kinematics. A sharp-interface immersed-boundary-method (IBM) based direct numerical simulation (DNS) solver is employed to calculate the corresponding thrust production, wake structure, and surface pressure at different swimming speeds. It is found that the fluke keeps its effective angle of attack at high values for about 60% of each stroke. The total pressure force coefficient along the x-axis converges as the speed increase. The flow and surface pressure analysis both show considerable differences between lower (2 m/s) and higher (5 m/s and 8 m/s) speeds. The results from this work help to bring new insight into understanding the force generation mechanisms of the highly efficient dolphin swimming and offer potential suggestions to the future designs of unmanned underwater vehicles.

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