scholarly journals Growth estimates in linear elasticity with a sublinear body force without definiteness conditions on the elasticities

1984 ◽  
Vol 27 (2) ◽  
pp. 223-228 ◽  
Author(s):  
Franca Franchi
Keyword(s):  
Wave Equation ◽  
Body Force ◽  
Displacement Vector ◽  
Fundamental Solutions ◽  
Existence Results ◽  
The Body ◽  
Heat Diffusion ◽  
Initial Value ◽  
Linear Elastic ◽  
Linear Elastic Body

In this paper, we study the boundary-initial value problem for a linear elastic body ina bounded domain, when the body force depends on the displacement vector u in asublinear way.Recently, much attention has been given to nonlinear body forces not only to studythe fundamental solutions of the equations governing linear elastodynamics, see e.g.Kecs [3], but also to derive global non existence results in abstract problems with directapplications to nonlinear heat diffusion or to the nonlinear wave equation, see e.g. Ball[1], Levine and Payne [10].

On the Motion of an Elastic Body Rolling/Sliding on an Elastic Substrate

1995 ◽  
Vol 117 (2) ◽  
pp. 308-314 ◽  
Author(s):  
A. Spector ◽  
R. C. Batra
Keyword(s):  
Elastic Body ◽  
Frictional Force ◽  
Three Dimensional ◽  
The Body ◽  
Elastic Substrate ◽  
Linear Elastic ◽  
Linear Elastic Body ◽  
Body Rolling ◽  
Applied Forces ◽  
Two Phases

The three-dimensional evolutionary problem of rolling/sliding of a linear elastic body on a linear elastic substrate is studied. The inertial properties of the body regarded as rigid are accounted for. By employing an asymptotic analysis, it is shown that the process can be divided into two phases: transient and quasistationary. An expression for the frictional force as a function of the externally applied forces and moments, and inertial properties of the body is derived. For an ellipsoid rolling/sliding on a linear elastic substrate, numerical results for the frictional force distribution, slip/adhesion subareas, and the evolution of the slip velocity are given.

Initiation, Propagation, and Kinking of an In-Plane Crack

1988 ◽  
Vol 55 (3) ◽  
pp. 587-595 ◽  
Author(s):  
Chien-Ching Ma
Keyword(s):  
Dynamic Stress Intensity Factor ◽  
Crack Tip ◽  
Fundamental Solutions ◽  
Constant Speed ◽  
Crack Face ◽  
Full Field ◽  
Linear Elastic ◽  
Linear Elastic Body ◽  
Infinite Linear ◽  
Original Crack

Consider an infinite linear elastic body containing a semi-infinite crack loaded by a longitudinal stress pulse parallel to the crack face. After the stress wave strikes the crack at time t = 0, the stress gradually intensifies at the crack tip. At some finite delay time tt, the crack begins to extend straight ahead with constant speed vo. At some later time tb, the crack suddenly stops, then kinks and propagates with constant speed vc, making an angle δ with the original crack. The exact full field solution of the propagating crack is constructed by using a superposition of fundamental solutions for a particular class of problems. When the crack suddenly stops, the stress field for a stationary crack with the new crack length is radiated out from the stopped crack tip. The dynamic stress intensity factor at the kinked crack tip can then be obtained by using a perturbation method.

scholarly journals Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows

1975 ◽  
Vol 67 (4) ◽  
pp. 787-815 ◽  
Author(s):  
Allen T. Chwang ◽  
T. Yao-Tsu Wu
Keyword(s):  
Exact Solutions ◽  
Stokes Flow ◽  
Fundamental Solutions ◽  
The Body ◽  
Circular Cylinders ◽  
Geometrical Parameters ◽  
Flow Problems ◽  
Singularity Method ◽  
Wide Range ◽  
Body Shapes

The present study further explores the fundamental singular solutions for Stokes flow that can be useful for constructing solutions over a wide range of free-stream profiles and body shapes. The primary singularity is the Stokeslet, which is associated with a singular point force embedded in a Stokes flow. From its derivatives other fundamental singularities can be obtained, including rotlets, stresslets, potential doublets and higher-order poles derived from them. For treating interior Stokes-flow problems new fundamental solutions are introduced; they include the Stokeson and its derivatives, called the roton and stresson.These fundamental singularities are employed here to construct exact solutions to a number of exterior and interior Stokes-flow problems for several specific body shapes translating and rotating in a viscous fluid which may itself be providing a primary flow. The different primary flows considered here include the uniform stream, shear flows, parabolic profiles and extensional flows (hyper-bolic profiles), while the body shapes cover prolate spheroids, spheres and circular cylinders. The salient features of these exact solutions (all obtained in closed form) regarding the types of singularities required for the construction of a solution in each specific case, their distribution densities and the range of validity of the solution, which may depend on the characteristic Reynolds numbers and governing geometrical parameters, are discussed.

scholarly journals Computational Modeling of Vortex Generators for Turbomachinery

2002 ◽  
Author(s):  
R. V. Chima
Keyword(s):  
Computational Models ◽  
Body Force ◽  
Secondary Flows ◽  
The Body ◽  
Vortex Generators ◽  
Force Model ◽  
Suction Surface ◽  
Near Surface ◽  
Compressor Rotor ◽  
Surface Particle

In this work computational models were developed and used to investigate applications of vortex generators (VGs) to turbomachinery. The work was aimed at increasing the efficiency of compressor components designed for the NASA Ultra Efficient Engine Technology (UEET) program. Initial calculations were used to investigate the physical behavior of VGs. A parametric study of the effects of VG height was done using 3-D calculations of isolated VGs. A body force model was developed to simulate the effects of VGs without requiring complicated grids. The model was calibrated using 2-D calculations of the VG vanes and was validated using the 3-D results. Then three applications of VGs to a compressor rotor and stator were investigated: 1. The results of the 3-D calculations were used to simulate the use of small casing VGs used to generate rotor preswirl or counterswirl. Computed performance maps were used to evaluate the effects of VGs. 2. The body force model was used to simulate large partspan splitters on the casing ahead of the stator. Computed loss buckets showed the effects of the VGs. 3. The body force model was also used to investigate the use of tiny VGs on the stator suction surface for controlling secondary flows. Near-surface particle traces and exit loss profiles were used to evaluate the effects of the VGs.

Stresses and Displacements in a Rotating Conical Shell

1943 ◽  
Vol 10 (2) ◽  
pp. A53-A61
Author(s):  
J. L. Meriam
Keyword(s):  
Conical Shell ◽  
Body Force ◽  
Theory Of Elasticity ◽  
Common Type ◽  
The Body ◽  
Surface Loading ◽  
Thin Walled Structures ◽  
Special Cases ◽  
Engineering Problems ◽  
Rotating Conical Shell

Abstract The analysis of shells is an important subdivision of the general theory of elasticity, and its application is useful in the solution of engineering problems involving thin-walled structures. A common type of shell is one which possesses symmetry with respect to an axis of revolution. A theory for such shells has been developed by various investigators (1, 2, 3, 6) and applied to a few simple cases such as the cylindrical, spherical, and conical shapes. Boundary conditions, for the most part, have been simple static ones, and conditions of surface loading have been included in certain special cases. This paper extends the theory of axially symmetrical shells by including the body force of rotation about the axis and applies the results to the rotating conical shell. The analysis follows a pattern established by several investigators (1, 2, 3, 6) and for this reason is abbreviated to a considerable extent. Only where the inclusion of the body force makes elucidation advisable or where a slightly different method of approach is used are the steps presented in more detail.

scholarly journals Multiscale modelling and homogenisation of fibre-reinforced hydrogels for tissue engineering

2018 ◽  
Vol 31 (1) ◽  
pp. 143-171 ◽  
Author(s):  
M. J. CHEN ◽  
L. S. KIMPTON ◽  
J. P. WHITELEY ◽  
M. CASTILHO ◽  
J. MALDA ◽  
...  
Keyword(s):  
Tissue Engineering ◽  
Applied Load ◽  
The Body ◽  
Unconfined Compression ◽  
Linear Elastic ◽  
Recent Approach ◽  
Poroelastic Material ◽  
3D Printed ◽  
Construct Dimensions

Tissue engineering aims to grow artificial tissues in vitro to replace those in the body that have been damaged through age, trauma or disease. A recent approach to engineer artificial cartilage involves seeding cells within a scaffold consisting of an interconnected 3D-printed lattice of polymer fibres combined with a cast or printed hydrogel, and subjecting the construct (cell-seeded scaffold) to an applied load in a bioreactor. A key question is to understand how the applied load is distributed throughout the construct. To address this, we employ homogenisation theory to derive equations governing the effective macroscale material properties of a periodic, elastic–poroelastic composite. We treat the fibres as a linear elastic material and the hydrogel as a poroelastic material, and exploit the disparate length scales (small inter-fibre spacing compared with construct dimensions) to derive macroscale equations governing the response of the composite to an applied load. This homogenised description reflects the orthotropic nature of the composite. To validate the model, solutions from finite element simulations of the macroscale, homogenised equations are compared to experimental data describing the unconfined compression of the fibre-reinforced hydrogels. The model is used to derive the bulk mechanical properties of a cylindrical construct of the composite material for a range of fibre spacings and to determine the local mechanical environment experienced by cells embedded within the construct.

A Review of Inlet-Fan Coupling Methodologies

2017 ◽  
Author(s):  
Benjamin Godard ◽  
Edouard De Jaeghere ◽  
Nabil Ben Nasr ◽  
Julien Marty ◽  
Raphael Barrier ◽  
...  
Keyword(s):  
Experimental Data ◽  
Industrial Design ◽  
Body Force ◽  
The Body ◽  
Source Terms ◽  
Force Modeling ◽  
Actuator Disc ◽  
Flow Deviation ◽  
New Challenges ◽  
Bypass Ratio

With the rise of ultra high bypass ratio turbofan and shorter and slimmer inlet geometries compared to classical architectures, designers face new challenges as nacelle and fan design cannot anymore be addressed independently. This paper reviews CFD methods developed to simulate inlet-fan interactions and suitable for industrial design cycles. In addition to the reference isolated fan and nacelle models, the methodologies evaluated in this study consist of two fan modeling approaches, an actuator disc and body-force source terms. The configuration is a modern turbofan with a high bypass ratio under cross-wind. Results are compared to experimental data. As to be predicted, the body-force modeling approach enables early inlet reattachment. In addition, it provides a representative flow deviation across the fan zone which enables performance and stability assessments.

Rack Level Modeling of Air Flow Through Perforated Tile in a Data Center

2012 ◽  
Author(s):  
Vaibhav K. Arghode ◽  
Pramod Kumar ◽  
Yogendra Joshi ◽  
Thomas S. Weiss ◽  
Gary Meyer
Keyword(s):  
Data Center ◽  
Body Force ◽  
Air Flow ◽  
The Body ◽  
Physical Models ◽  
Cfd Modeling ◽  
Computational Time ◽  
Force Model ◽  
Flow Through ◽  
Tile Surface

Effective air flow distribution through perforated tiles is required to efficiently cool servers in a raised floor data center. We present detailed computational fluid dynamics (CFD) modeling of air flow through a perforated tile and its entrance to the adjacent server rack. The realistic geometrical details of the perforated tile, as well as of the rack are included in the model. Generally models for air flow through perforated tiles specify a step pressure loss across the tile surface, or porous jump model based on the tile porosity. An improvement to this includes a momentum source specification above the tile to simulate the acceleration of the air flow through the pores, or body force model. In both of these models geometrical details of tile such as pore locations and shapes are not included. More details increase the grid size as well as the computational time. However, the grid refinement can be controlled to achieve balance between the accuracy and computational time. We compared the results from CFD using geometrical resolution with the porous jump and body force model solution as well as with the measured flow field using Particle Image Velocimetry (PIV) experiments. We observe that including tile geometrical details gives better results as compared to elimination of tile geometrical details and specifying physical models across and above the tile surface. A modification to the body force model is also suggested and improved results were achieved.

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