Strain Transformation Essays - Solid Mechanics, Tensors,

Strain Transformation California State University, Northridge College of Computer Science and Engineering Department of Civil and Manufacturing Engineering STRAIN TRANSFORMATION Submitted to: Nazaret Dermendjian Submitted for: Applied Mechanics 340 Date requested: April 6, 1999 Date due: April 27, 1999 Date submitted: April 27, 1999 The following report will be on Strain Transformation. Strain transformation is similar to stress transformation, so that many of the techniques and derivations used for stress can be used for strain. We will also discuss methods of measuring strain and material-property relationships. The general state of strain at a point can be represented by the three components of normal strain, ?x, ?y, ?z, and three components of shear strain, gxy, gxz, gyz. For the purpose of this report, we confine our study to plane strain. That is, we will only concentrate on strain in the x-y plane so that the normal strain is represented by ?x and ?y and the shear strain by gxy . The deformation on an element caused by each of the elements is shown graphically below. Before equations for strain-transformation can be developed, a sign convention must be established. As seen below, ?x and ?y are positive if they cause elongation in the the x and y axes and the shear strain is positive if the interior angle becomes smaller than 90?. For relative axes, the angle between the x and x' axes, q, will be counterclockwise positive. If the normal strains ?x and ?y and the shear strain gxy are known, we can find the normal strain and shear strain at any rotated axes x' and y' where the angle between the x axis and x' axis is q. Using geometry and trigonometric identities the following equations can be derived for finding the strain at a rotated axes: ?x' = (?x + ?y)/2 + (?x - ?y)cos 2q + gxy sin 2q (1) gx'y' = [(?x - ?y)/2] sin 2q + (gxy /2) cos 2q (2) The normal strain in the y' direction by substituting (q + 90?) for q in Eq.1. The orientation of an element can be determined such that the element's deformation at a point can be represented by normal strain with no shear strain. These normal strain are referred to as the principal strains, ?1 and ?2 . The angle between the x and y axes and the principal axes at which these strains occur is represented as qp. The equations for these values can be derived from Eq.1 and are as followed: tan 2qp = gxy /(?x - ?y) (3) ?1,2 = (?x -?y)/2 ? {[(?x -?y)/2]2+ (gxy/2)2 }1/2 (4) The axes along which maximum in-plane shear strain occurs are 45? away from those that define the principal strains and is represented as qs and can be found using the following equation: tan 2qs = -(?x - ?y) / 2 (5) When the shear strain is maximum, the normal strains are equal to the average normal strain. These values are determined from the following equations: gmax / 2 = {[(?x - ?y) / 2]2 + (gxy / 2)2}1/2 (6) ?avg = (?x + ?y) / 2 (7) We can also solve strain transformation problem using Mohr's circle. The coordinate system used has the abscissa represent the normal strain ?, with positive to the right and the ordinate represents half of the shear strain g/2 with positive downward. Determine the center of the circle C, which is on the ? axis at a distance of ?avg from the origin. Please note that it is important to follow the sign convention established previously. Plot a reference point A having coordinates (?x , gxy / 2). The line AC is the reference for q = 0. Draw a circle with C as the center and the line AC as the radius. The principal strains ?1 and ?2 are the values where the circle intersects the ? axis and are shown as points B and D on the figure below. The principal angles can be determined from the graph by measuring 2qp1 and 2qp2 from the reference line AC to the ? axis. The element will be elongated in the x' and y' directions as shown below. The average normal strain and the maximum shear strain are shown as points E and F on the figure below. The element will be elongated as shown. To measure the

A Pale View of Hills by Kazuo Ishiguro Essays

A Pale View of Hills by Kazuo Ishiguro Essays A Pale View of Hills by Kazuo Ishiguro Paper A Pale View of Hills by Kazuo Ishiguro Paper Essay Topic: Literature The character of Mariko in the novel A Pale View of Hills by Kazuo Ishiguro is that of a young girl who is about ten years old. She is presented by the author as an awkward and often difficult girl who struggles for her mother Sachikos nonexistent love and acceptance. Her character, behaviour, and personality have all been shaped by her experiences of the war and the Nagasaki bombing of 1945. However, despite the childhood traumas Mariko has gone through, she also shows acts of tremendous love, devotion and commitment towards things or aspects of her life she feels strongly for. The first thing that may be immediately noticeable in Marikos personality is that she is quite an awkward child. This is illustrated quite clearly in the scene where Mariko attempts to eat a spider crawling up the wall of Sachikos cottage. Certainly, Etsuko is alarmed when Mariko does this, as she says, I started back, and later, It took a moment for me to recover. Etsuko describes her as having a vaguely disturbing quality, and says that Mariko has a strangely expressionless look. The author uses words to similar effect throughout the novel to describe Mariko. Another obvious trait of Marikos is that she is not loved by her mother. Sachiko implies that Mariko is a great burden to her when she says things were very difficult when Mariko was born. She also does not help Mariko cope with the ordeals she has been through, as she says to Etsuko, So please dont bother too much with her. Sachiko simply does not care about Mariko, and fails to even stand up for her daughter when she is accused of something she did not do. When Sachiko drowns the kittens, the struggling animals are representative of Marikos emotional struggles for her mothers love and attention. Near the end of the novel, when saying, Do you think I imagine for one moment that Im a good mother to her? Sachiko admits that she knows she was never the caring, loving, devoted mother to Mariko she should have been. Mariko is also seen to have a closed mind. Ishiguro uses pathetic fallacy to illustrate this point. Her thoughts are withdrawn and reclusive, and Etsuko says of Mariko, I could see only darkness. A quote in the spider scene, [Mariko] closed her hand on top of it so that [the spider] was imprisoned, is very symbolic in the sense that Mariko is imprisoned inside her own mind. Her relative reticence Mariko remained silent throughout that journey home is also likely a reflection of her withdrawn nature, as she thinks inwardly rather than voice them out like other children her age would. However, Mariko also shows full affection towards things she deeply cares for. Her kittens are the prime example in this novel, and she makes constant and consistent reference to them. She insists on playing at the kujibiki stand until she wins a box which she uses as a home for her kittens We could carry the kittens in there We could take them in the box, couldnt we, Mother? When Yasuko-San tells Mariko, And youre not to worry about your kittens, we get the impression that Mariko has already expressed her concerns for the well-being of her pets to Yasuko-San. Mariko also tries to be protective of her kittens when Sachiko demands to have them by turning to Etsuko for support. She says, Do you want to see [Atsu, one of the kittens], Etsuko-San? once again illustrating her love for the kittens and also her helplessness in front of her mother, Sachiko. Despite Marikos motherly disposition towards the kittens, she can also demonstrate very child-like behaviour. Mariko shouted something and pointed. Then she hurried on excitedly. This phrase, for example, shows the normal, innocent nature of a child she Mariko still has in her in spite of all that has ever happened to her. She shows similar behaviour in another section of the novel, when she ran a little way ahead, then waited for us to catch up. Her naivety is shown also when she is oblivious of a woman staring at her from the train platform. Mariko continued to look out of the window, quite unaware of the woman. Her enthusiasm when looking through her binoculars, Mariko seemed to be testing the effectiveness of her binoculars, holding them to her eyes one moment, taking them away the next is also a good example of when Mariko is still very much a child. For most of the novel A Pale View of Hills, Mariko is presented as a young girl who has a hard time in communicating and socialising. She is often awkward, and clearly does not receive the amount of love she should be receiving from her mother. However, she also does display qualities that prove she would be a much better mother than Sachiko herself, and even hints that she would be an even better child than she is for most of the novel.

The terms 'ethnic minority' hides the diversity between and within Essay

The terms 'ethnic minority' hides the diversity between and within minority ethnic groups. Discuss - Essay Example dress issues of discrimination on racial or ethnic lives have not been able to efficiently iron out details about ethno-religious matters, gender and ethnicity, ethno-politico issues and other such gray areas. Members of these minority groups have had to endure their situation or fight like the black feminists did. This paper aims to discuss an array issues that touch on this issue of differences between and within ethnic minority groups. Looking at self-employement sector in Britain for example the self-employment rate is 14.6 percent for non-whites compared to 12.3 percent for whites. However beneath this statistics are the glaring differences between the groups. The self-employment rate for black Carribeans is 5.8 percent while that for Chinese is 26.6 percent (Kenneth and Drinkwater, 1). Factors that could create these differences would include social support from one’s community to facilitate a self-sustaining economic environment, effects of religion or access to informal sources of capital and manpower from the family ties or members of the ethnic community (Kenneth and Drinkwater, 1). Cultural endowments too determine such kinds of trends since it does determine one’s attitude towards entrepreneurship. It also has a bearing on consumer behaviour and how much of a good is ordered (Rafiq, 46). Some of these consumer behaviours become so pronounced as to qualify some goods being referred to as ethnic goods. When a good number of members of a certain ethnic group live together in one neighbourhood, a protected market scenario arises. The shop owners are able to maintain a monopoly of sorts within the neighbourhood and the members give support by being loyal to these businesses. The shop owners are keener to provide goods and services that meet the memb ers’ preferences. Religious goods are particularly a favourite. So are goods from the ethnic group’s country of origin. Religion is another strong influence. Rafiq, (50-55) argues that in