scholarly journals A Consistent Theory for Elastic Deformations With Small Strains

1984 ◽  
Vol 51 (4) ◽  
pp. 717-723 ◽  
Author(s):  
R. T. Shield
Keyword(s):  
Classical Theory ◽  
The Body ◽  
Elastic Behavior ◽  
Pure Torsion ◽  
Consistent Theory ◽  
Elastic Deformations ◽  
Linear Elastic ◽  
Small Strains ◽  
Infinitesimal Deformations ◽  
Long Cylinder

A consistent theory is developed for linear elastic behavior in which the strains are small but in which no restriction is placed on the magnitudes of the displacements or the rotations of elements of the body. The theory reduces to the classical theory for infinitesimal deformations when the rotations are small. Pure torsion of a long cylinder and the bending of a beam by a terminal load are treated in order to illustrate the application of the theory. The bending solution agrees with the St. Venant flexure solution when the deflections are small and with the theory of the elastica when the deflections are large.

Elastic Deformations of Strips and Circular Plates Under Uniform Pressure

1986 ◽  
Vol 53 (4) ◽  
pp. 873-880
Author(s):  
S. Im ◽  
R. T. Shield
Keyword(s):  
Rectangular Plate ◽  
Small Strain ◽  
Structural Theory ◽  
Thin Plates ◽  
Elastic Behavior ◽  
Uniform Pressure ◽  
Circular Plates ◽  
Consistent Theory ◽  
Elastic Deformations ◽  
Linear Elastic

A consistent theory for linear elastic behavior in which the strains are small but in which the displacements and rotations can be large is applied to the bending of a long rectangular plate and of a circular plate by uniform pressure. Within the range of small-strain, linear elastic behavior, the theory provides solutions for all slenderness ratios of the plates and magnitudes of the loading. Thus the theory bridges the gap between the classical theory and the nonlinear structural theory of Fo¨ppl and von Ka´rma´n. The results show that the von Ka´rma´n equations provide accurate solutions for thin plates for which deflections are not small.

Estimation of the Crack Propagation Direction of a Crack Touching the Interface between Two Elastic Materials

2007 ◽  
Vol 567-568 ◽  
pp. 225-228 ◽  
Author(s):  
Luboš Náhlík ◽  
Lucie Šestáková ◽  
Pavel Hutař
Keyword(s):  
Crack Propagation ◽  
Protective Coatings ◽  
The Body ◽  
Elastic Behavior ◽  
Layered Composites ◽  
The Finite Element Method ◽  
Elastic Materials ◽  
Linear Elastic ◽  
Composites Materials ◽  
Elastic Fracture

The objective of the paper is to investigate the direction of a further crack propagation from the interface between two elastic materials. The angle of crack propagation changes when the crack passes the interface. The suggested procedure makes it possible to estimate an angle of propagation under which the crack will propagate into the second material. The assumptions of linear elastic fracture mechanics and elastic behavior of the body with interfaces are considered. The finite element method was used for numerical calculations. The results obtained might contribute to a better understanding of the failure of materials with interfaces (e.g. layered composites, materials with protective coatings) and to a more reliable estimation of the service life of such structures.

Development of a New Artificial Knee Joint for an Asian and Middle Eastern Population

2013 ◽  
Author(s):  
Harcharan Singh Ranu
Keyword(s):  
Finite Element ◽  
Body Weight ◽  
Maximum Load ◽  
The Body ◽  
The Other ◽  
Elastic Behavior ◽  
Loading Conditions ◽  
Load Bearing Capacity ◽  
Linear Elastic ◽  
Materials Used

Design of an artificial knee was developed using computer 3-D modeling, the high flexion knee was obtained by using a multi-radii design pattern, The increase of final 20 degrees in flexion was obtained by increasing the condylar radii of curvature. The model of the high flexion knee was developed and one of the models was subjected to finite element modeling and analysis. The compositions of components in the artificial knee were, femoral component and the tibial component were metal, whereas the patellar component and the meniscal insert were made using polyethylene. The metal component used for the analysis in this study was Ti6Al4V and the polyethylene used was UHMWPE. Overall biomaterials chosen were: meniscus (UHMWPE, mass = 0.0183701 kg, volume = 1.97518e-005 m3), tibial component (Ti6Al4V, mass = 0.0584655 kg, volume = 1.32013e-005 m3), femoral component (Ti6Al4V, mass = 0.153122 kg, volume = 3.45742e-005 m3), total artificial assembly (mass = 0.229958 kg, volume = 6.75e-005m3). However, in this design the load had been taken to 10 times the body weight. The weight over single knee is only half the maximum load as the load is shared between the two knee joints. Following were the loading conditions, taking average body weight to be 70Kgs and taking extreme loading conditions of up to 10 times the body weight, i.e. 700Kgs on each of the leg performed the Finite Element Analysis (FEA) over the newly designed knee. The loading was done at an increment of 100 Kgs. The loading conditions and the meshing details for the analysis of the assembly were Jacobian check: 4 points, element size: 0.40735 cm, tolerance: 0.20367 cm, quality: high, number of elements: 80909, number of nodes: 126898. A maximum load of 600 Kgs is optimum for this model. The other components observed linear elastic behavior for the applied loads. Based on these results it was determined that the load bearing capacity of the model were well within the failure levels of the materials used for the analysis. A maximum load of 600 Kgs is optimum for this model. The other components observed linear elastic behavior for the applied loads. Based on these results it was determined that the load bearing capacity of the model were well within the failure levels of the materials used for the analysis. Conclusion drawn from this is that for the first time an innovative new design of an artificial knee joint to suite a segment of some religious population has been developed. This allows them to pray, bend in different positions and squat without too much difficulty.

Dynamics of Nanoparticle Chain Aggregates of Carbon Under Tension

2003 ◽  
Vol 778 ◽  
Author(s):  
Rajdip Bandyopadhyaya ◽  
Weizhi Rong ◽  
Yong J. Suh ◽  
Sheldon K. Friedlander
Keyword(s):  
Mechanical Properties ◽  
Carbon Black ◽  
Polymer Film ◽  
Elastic Behavior ◽  
Small Strains ◽  
Transmission Electron ◽  
Chain Aggregates ◽  
Nanoparticle Chains ◽  
Reinforcing Filler

AbstractCarbon black in the form of nanoparticle chains is used as a reinforcing filler in elastomers. However, the dynamics of the filler particles under tension and their role in the improvement of the mechanical properties of rubber are not well understood. We have studied experimentally the dynamics of isolated nanoparticle chain aggregates (NCAs) of carbon made by laser ablation, and also that of carbon black embedded in a polymer film. In situ studies of stretching and contraction of such chains in the transmission electron microscope (TEM) were conducted under different maximum values of strain. Stretching causes initially folded NCA to reorganize into a straight, taut configuration. Further stretching leads to either plastic deformation and breakage (at 37.4% strain) or to a partial elastic behavior of the chain at small strains (e.g. 2.3% strain). For all cases the chains were very flexible under tension. Similar reorientation and stretching was observed for carbon black chains embedded in a polymer film. Such flexible and elastic nature of NCAs point towards a possible mechanism of reinforcement of rubber by carbon black fillers.

Performance Based Evaluation of Bridge Substructure in North Mississippi Using Nonlinear FEM and Field Vibration Measurement

2000 ◽  
Author(s):  
Chris L. Mullen ◽  
Prabin R. Tuladhar
Keyword(s):  
Finite Element ◽  
Transfer Functions ◽  
Response Spectrum ◽  
Three Dimensional ◽  
Vibration Measurement ◽  
Elastic Behavior ◽  
Evaluation Procedure ◽  
Vibration Measurements ◽  
Linear Elastic ◽  
Performance Based Evaluation

Abstract Discussion of a Performance - Based Engineering evaluation procedure for an existing interstate highway bridge in north Mississippi. The bridge is in a highly trafficked location near the Memphis Metropolitan area and is reflective of modern design practices in Mississippi. Results are presented of nonlinear damage response and displacement ductility performance of the reinforced concrete bents and their foundations predicted using static finite element (FE) computations. The model considers the composite action of the concrete and the reinforcing steel materials under axial force, shear, torsion and flexure. The performance-based evaluation includes three-dimensional computational simulations of the nonlinear bridge system, including substructures and superstructure. The response spectrum dynamic analysis method will also be carried out on the linear elastic three-dimensional model to predict the linear elastic behavior. Field vibration measurements, including ambient and hammer-impact, were performed to calibrate the models. The computed transfer functions are currently being evaluated to correlate vibration measurements and the Finite element models.

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.

MULTIBODY DYNAMIC MODELING AND FLUTTER ANALYSIS OF A FLEXIBLE SLENDER VEHICLE

2012 ◽  
Vol 12 (06) ◽  
pp. 1250049 ◽  
Author(s):  
A. RASTI ◽  
S. A. FAZELZADEH
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Dynamic Modeling ◽  
Equations Of Motion ◽  
The Body ◽  
Elastic Deformations ◽  
Strip Theory ◽  
Multibody Dynamic ◽  
Flutter Analysis ◽  
Rigid Body Motions

In this paper, multibody dynamic modeling and flutter analysis of a flexible slender vehicle are investigated. The method is a comprehensive procedure based on the hybrid equations of motion in terms of quasi-coordinates. The equations consist of ordinary differential equations for the rigid body motions of the vehicle and partial differential equations for the elastic deformations of the flexible components of the vehicle. These equations are naturally nonlinear, but to avoid high nonlinearity of equations the elastic displacements are assumed to be small so that the equations of motion can be linearized. For the aeroelastic analysis a perturbation approach is used, by which the problem is divided into a nonlinear flight dynamics problem for quasi-rigid flight vehicle and a linear extended aeroelasticity problem for the elastic deformations and perturbations in the rigid body motions. In this manner, the trim values that are obtained from the first problem are used as an input to the second problem. The body of the vehicle is modeled with a uniform free–free beam and the aeroelastic forces are derived from the strip theory. The effect of some crucial geometric and physical parameters and the acting forces on the flutter speed and frequency of the vehicle are investigated.

scholarly journals Large elastic deformations of isotropic materials. I. Fundamental concepts

1948 ◽  
Vol 240 (822) ◽  
pp. 459-490 ◽  
Keyword(s):  
The Body ◽  
Elastic Behaviour ◽  
Stress And Strain ◽  
Elastic Deformations ◽  
Hooke’S Law ◽  
Widespread Agreement ◽  
Wide Range ◽  
Hooke's Law ◽  
High Degree

The mathematical theory of small elastic deformations has been developed to a high degree of sophistication on certain fundamental assumptions regarding the stress-strain relationships which are obeyed by the materials considered. The relationships taken are, in effect, a generalization of Hooke’s law— ut tensio, sic vis . The justification for these assumptions lies in the widespread agreement of experiment with the predictions of the theory and in the interpretation of the elastic behaviour of the materials in terms of their known structure. The same factors have contributed to our appreciation of the limitations of these assumptions. The principal problems, which the theory seeks to solve, are the determination of the deformation which a body undergoes and the distribution of stresses in it, when certain forces are applied to it, and when certain points of the body are subjected to specified displacements. These problems are always dealt with on the assumption that the generalization of Hooke’s law is obeyed by the material of the body and that the deformation is small, i.e. the change of length, in any linear element in the material, is small compared with the length of the element in the undeformed state. Apart from the fact that the generalization of Hooke’s law is obeyed accurately by a very wide range of materials, under a considerable variety of stress and strain conditions, it has the further advantage that it leads to a mathematically tractable theory.

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.

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