An Exploratory Study of Stress Concentrations in Thermal Shock Fields

1962 ◽  
Vol 84 (3) ◽  
pp. 343-348 ◽  
Author(s):  
Herbert Becker
Keyword(s):  
Thermal Shock ◽  
Upper Bound ◽  
Experimental Program ◽  
Radius Of Curvature ◽  
Elastic Plane ◽  
Space Theory ◽  
Stress Concentrations ◽  
Local Boundary ◽  
Plane Space ◽  
Boundary Radius

Exploratory investigations were performed on the effect of stress concentrations upon the stresses generated in a free elastic plane space by thermal shock applied to the boundary. The emphasis was on a search for a general upper bound to the stresses induced in a plane space of arbitrary shape by a temperature change T0 applied to the boundary of the space. Theory indicates that, when a thermal shock penetrates into a plane elastic space a distance less than half the local boundary radius of curvature, then αET0 would be the magnitude of the upper bound and the stress field would be confined to a boundary layer. In order to obtain the reported results it was necessary to obtain temperature and fringe pattern data within 10 sec from initiation of thermal shock. The experimental program to accomplish this result is reported in detail.

A Sequel to Technical Note 13: The Curved Tetrahedronal and Triangular Elements TEC and TRIC for the Matrix Displacement Method

1969 ◽  
Vol 73 (697) ◽  
pp. 55-65 ◽  
Author(s):  
J. H. Argyris ◽  
D. W. Scharpf
Keyword(s):  
Computational Analysis ◽  
Three Dimensional ◽  
Technical Note ◽  
Radius Of Curvature ◽  
Two Dimensional ◽  
Displacement Method ◽  
Stress Concentrations ◽  
The Past ◽  
The Matrix ◽  
Triangular Elements

It is by now well established that the computational analysis of significant problems in structural and continuum mechanics by the matrix displacement method often requires elements of higher sophistication than used in the past. This refers, in particular, to regions of steep stress gradients, which are frequently associated with marked changes in geometry, involving rapid variations of the radius of curvature. The philosophy underlying the idealisation of such configurations into finite elements was discussed in broad terms in ref. 1. It was emphasised that the so successful, constant strain, two-dimensional TRIM 3 and three-dimensional TET 4 elements do not, in general, prove the best choice. For this reason elements with a linear variation of strain like TRIM 6 and TET 10 were originally evolved and followed up with the quadratic strain elements TRIM 15, TRIA 4 (two-dimensional) and TET 20, TEA 8 (three-dimensional) of ref. 2. However, all these elements are characterised by straight edges and necessitate a polygonisation or polyhedrisation in the idealisation process. This may not be critical in many problems, but is sometimes of doubtful validity in the immediate neighbourhood of a curved boundary, where stress concentrations are most pronounced. To overcome this difficulty with a significant (local) increase of elements does not always yield the most economical and technically satisfactory solution. Moreover, there arises another inevitable shortcoming when dealing with TRIM and TET elements with a linear or quadratic variation of strain. Indeed, while TRIM 3 and TET 4 elements permit a very elegant extension into the realm of large displacements, this is not possible for the higher order TRIM and TET elements. This is simply due to the fact that TRIM 3 and TET 4 elements, by virtue of their specification, always remain straight under any magnitude of strain, but this is not so for the triangular and tetrahedron elements of higher sophistication.

A Compact Cantilever Model That Includes Fillets

2012 ◽  
Author(s):  
Aarti Chigullapalli ◽  
Jason V. Clark
Keyword(s):  
Radius Of Curvature ◽  
Model Parameters ◽  
Beam Model ◽  
Stress Concentrations ◽  
Feature Size ◽  
Element Analysis ◽  
Size Limitation ◽  
Reducing Stress ◽  
Analytical Expressions ◽  
Typical Model

In this paper we present analytical expressions for determining the stiffness of cantilevers with fillets and tappers. We consider the unavoidable fillet due to the feature size limitation of lithography that rounds acute vertices, and the intentional tapper that is often used for reducing stress concentrations or can be used to reduce the effect of fillets. Previous compact models have not included the stiffness contributions from fillets. However, although fillets are small, they can measurably affect the performance of MEMS by affecting deflection or resonance frequency by their second most significant digit. We extend the well-known analytical beam model to include fillets. To our knowledge, this is the first analytical model of a filleted cantilever. In addition to the typical model parameters of beams, our model also includes process variation overcut and fillet radius of curvature, which are key parameters for MEMS designers. Our analytical solution is within 0.01% of finite element analysis.

Generalized Equations for Estimating Stress Concentration Factors of Various Notch Flexure Hinges

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Jialu Wang ◽  
Xiaoyuan Liu
Keyword(s):  
Stress Concentration ◽  
Radius Of Curvature ◽  
Tension Stress ◽  
Generalized Equations ◽  
Stress Concentrations ◽  
Minimum Thickness ◽  
Flexure Hinges ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Maximum Stresses

The flexure hinges are the most vulnerable parts in a flexure-based mechanism due to their smaller dimensions and stress concentration characteristics, therefore evaluating the maximum stresses generated in them is crucial for assessing the workspace and the fatigue life of the mechanism. Stress concentration factors characterize the stress concentrations in flexure hinges, providing an analytical and efficient way to evaluate the maximum stress. In this work, by using the ratio of the radius of curvature of the stress-concentrating feature to the minimum thickness as the only fitting variable, generalized equations for both the bending and tension stress concentration factors were obtained for two generalized models, the conic model and the elliptic-arc-fillet model, through fitting the finite element results. The equations are applicable to commonly used flexure hinges including circular, elliptic, parabolic, hyperbolic, and various corner-fillet flexure hinges, with acceptable errors. The empirical equations are tractable and easy to be employed in the design and optimization of flexure-based mechanisms. The case studies of the bridge-type displacement amplifiers demonstrated the effectiveness of the generalized equations for predicting the maximum stresses in flexure-based mechanisms.

scholarly journals How does tooth cusp radius of curvature affect brittle food item processing?

2013 ◽  
Vol 10 (84) ◽  
pp. 20130240 ◽  
Author(s):  
Michael A. Berthaume ◽  
Elizabeth R. Dumont ◽  
Laurie R. Godfrey ◽  
Ian R. Grosse
Keyword(s):  
Finite Element ◽  
Food Item ◽  
Sampling Method ◽  
High Stress ◽  
Radius Of Curvature ◽  
Finite Element Models ◽  
Partial Support ◽  
Stress Concentrations ◽  
Food Items ◽  
Better Than

Tooth cusp sharpness, measured by radius of curvature (RoC), has been predicted to play a significant role in brittle/hard food item fracture. Here, we set out to test three existing hypotheses about this relationship: namely, the Blunt and Strong Cusp hypotheses, which predict that dull cusps will be most efficient at brittle food item fracture, and the Pointed Cusp hypothesis, which predicts that sharp cusps will be most efficient at brittle food item fracture using a four cusp bunodont molar. We also put forth and test the newly constructed Complex Cusp hypothesis, which predicts that a mixture of dull and sharp cusps will be most efficient at brittle food item fracture. We tested the four hypotheses using finite-element models of four cusped, bunodont molars. When testing the three existing hypotheses, we assumed all cusps had the same level of sharpness (RoC), and gained partial support for the Blunt Cusp hypotheses. We found no support for the Pointed Cusp or Strong Cusp hypotheses. We used the Taguchi sampling method to test the Complex Cusps hypothesis with a morphospace created by independently varying the radii of curvature of the four cusps in the buccolingual and mesiodistal directions. The optimal occlusal morphology for fracturing brittle food items consists of a combination of sharp and dull cusps, which creates high stress concentrations in the food item while stabilizing the food item and keeping the stress concentrations in the enamel low. This model performed better than the Blunt Cusp hypothesis, suggesting a role for optimality in the evolution of cusp form.

The Stresses Around Square Holes with Rounded Corners

1958 ◽  
Vol 2 (03) ◽  
pp. 37-41
Author(s):  
Joseph S. Brock
Keyword(s):  
Stress Distribution ◽  
Analytical Solution ◽  
Infinite Plate ◽  
Mapping Function ◽  
Mapping Technique ◽  
Radius Of Curvature ◽  
Stress Concentrations ◽  
Method Of Solution ◽  
Christoffel Transformation ◽  
Square Hole

This paper presents an analytical solution for the stress distribution around a square hole with rounded corners in an infinite plate subjected to pure tension. The method of solution is a combination of a conformal mapping technique and the complexvariable method of Muskhelishvili. The form of the mapping function is obtained from the Schwarz-Christoffel transformation. The mapping function is general and gives a good approximation to square holes with rounded corners of arbitrary radius of curvature. The ratios of the corner radius to the width of the opening considered cover the range from 0.03 to 0.5. This is considered 1o be the interesting range for ship structures. The results are given in terms of stress concentrations around the boundary of the opening.

Conceptual Design of Structures Using an Upper Bound of von Mises Stress

2018 ◽  
Vol 19 (1) ◽  
Author(s):  
Ashok V. Kumar
Keyword(s):  
Topology Optimization ◽  
Stress Concentration ◽  
Upper Bound ◽  
Von Mises Stress ◽  
Optimization Approach ◽  
Objective Functions ◽  
Stress Concentrations ◽  
Handling Stress ◽  
Design Concepts ◽  
Von Mises

Optimal layouts for structural design have been generated using topology optimization approach with a wide variety of objectives and constraints. Minimization of compliance is the most common objective but the resultant structures often have stress concentrations. Two new objective functions, constructed using an upper bound of von Mises stress, are presented here for computing design concepts that avoid stress concentration. The first objective function can be used to minimize mass while ensuring that the design is conservative and avoids stress concentrations. The second objective can be used to tradeoff between maximizing stiffness versus minimizing the maximum stress to avoid stress concentration. The use of the upper bound of von Mises stress is shown to avoid singularity problems associated with stress-based topology optimization. A penalty approach is used for eliminating stress concentration and stress limit violations which ensures conservative designs while avoiding the need for special algorithms for handling stress localization. In this work, shape and topology are represented using a density function with the density interpolated piecewise over the elements to obtain a continuous density field. A few widely used examples are utilized to study these objective functions.

scholarly journals On the scaling of three dimensional shock induced separated flow due to protuberances

2021 ◽  
Author(s):  
Sourabh Bhardwaj ◽  
Sriram Rengaran ◽  
Kakumani Hemanth Chandra Vamsi
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Scaling Law ◽  
Horseshoe Vortex ◽  
Radius Of Curvature ◽  
Geometrical Parameters ◽  
Incoming Flow ◽  
Recirculation Bubble ◽  
Local Boundary ◽  
3 Dimensional

Supersonic flow over 3-dimensional bodies protruding out of the turbulent boundary layer was investigated by performing experiments and numerical computations. A parametric study was undertaken varying shapes, heights, and diameters of the protuberance. To study the Mach number effects on the shock boundary layer interactions due to protuberances flows with varying Mach numbers (1.5, 2, 2.5, 3, 3.5) were also examined. Surface oil flow technique, surface pressure measurements and schlieren flow visualization using a high-speed camera were employed along with 3-dimensional RANS computations to elicit flow features such as core of the horseshoe vortex, which greatly influences the flow in recirculation bubble. Though some of the parameters involved in such interactions are individually investigated in the literature, a comprehensive study is still lacking. It was observed that the viscous interaction was strongly related to the inviscid phenomenon happening close to the surface of the protuberance. Radius of curvature of the inviscid shock at the nose was found to be a determining parameter incorporating information on adverse pressure gradient experienced by local boundary layer, geometrical parameters of the protuberances, and Mach number of the incoming flow. Based on this, a scaling law is presented to relate the separation length involved in such interaction with various geometrical and incoming flow parameters. The scaled separation length was predicted remarkably well by the proposed correlation. As a comprehensive correlation, it was also tested with data from a 2-dimensional forward facing step study in the literature, and a good agreement was found. It was also observed that the location of the horseshoe vortex core was also dependent on the inviscid shock in the same way as is separation length.

Evaluation of stored energy after accumulative roll bonding of an interstitial-free steel by means of orientation microscopy data

2005 ◽  
Vol 38 (4) ◽  
pp. 668-674 ◽  
Author(s):  
K. Lee ◽  
A. C. C. Reis ◽  
G. Kim ◽  
L. Kestens
Keyword(s):  
Accumulative Roll Bonding ◽  
Cellular Network ◽  
Boundary Energy ◽  
Orientation Imaging Microscopy ◽  
Radius Of Curvature ◽  
Interstitial Free ◽  
Stored Energy ◽  
Roll Bonding ◽  
Local Boundary ◽  
Von Mises

The stored energy of warm-rolled interstitial-free steels, produced in an accumulative roll bonding process, is evaluated by using the textural and microstructural information contained in orientation imaging microscopy (OIM) scans which were measured after accumulated von Mises strains (∊vM) of 0.8, 1.6, 2.4 and 4.0, respectively. It is assumed that the plastic strain energy is stored in a cellular network of local boundaries of low and high misorientations. The presence of intracellular dislocations which do not contribute to a local crystal orientation gradient is ignored in the present analysis. On the basis of the Read–Shockley equation, the local misorientation can be associated with a local boundary energy which can be expressed as a local stored energy by taking into account the radius of curvature of the cellular network. The validity of this procedure was verified by comparing the integrated average stored energy of the sample with the Vickers hardness data, which produced a reasonable correspondence. The present analysis also allowed the calculation of the stored energy distribution in the areas of the orientation representation space which were sufficiently populated by sample crystal orientations,i.e.the γ fibre (〈111〉||ND) of the present deformation texture. The distribution of stored energy along this fibre displayed a maximum on the {111}〈211〉 texture component, particularly after a von Mises strain of 1.6, whereas the {111}〈110〉 component displayed a local minimum of stored energy after ∊vM= 2.4 and 4.0.

Sign in / Sign up

Export Citation Format

Share Document