The ideology of Marxism–Leninism seemingly contradicts competition, yet competition was prevalent in former communist countries to foster productivity and economic growth. The Stakhanovite movement, originating in the Soviet Union, incentivized laborers to excel as an economic propaganda tool, while also honoring them as socialist heroes but also penalizing dissent as a political propaganda tool. Competition extended to managers of state-owned enterprises (SOEs) vying for government resources. Consumer competition arose from pervasive shortages, driving black market economies. Underground enterprises, which were protected from competition, resisted economic reform from a planned economic system to a more market-oriented system to maintain their privileged status. Post-World War II, some SOEs adopted market-based approaches, competing domestically and globally. This chapter argues that such forms of competition emerge when humans struggle for survival amid perceived inequalities in the existing system, prompting them to seek opportunities and thrive.

8.1 INTRODUCTION [LO1]

In simple words, the application of a torque on a prismatic member causes twisting or torsion. This causes shear stress if a torque alone is applied. However, this is rarely true in practical cases. A circular bar, used to transmit torque between a prime mover and a machine, is a typical example of a torsion member. However, in many applications, a torque along with a bending moment and axial loading are applied, and there we need to combine these effects and find the principal stresses. A typical example of such combined stresses is a propeller shaft. Torsional problems are important in many applications both in industry and in our daily life. Therefore, we consider torsion alone in this chapter in some detail.

Torsional problems for circular members are generally solved assuming that plane sections normal to the axis of the bar remain plane even after twisting. This assumption was first made by Coulomb intuitively in 1784, and he came up with a correct usable equation for members with circular sections. However, this assumption does not apply to bars with a noncircular cross-section. Navier attempted to solve torsional problems with noncircular sections using Coulomb's assumption and came up with an erroneous solution. The correct solution was provided by St. Venant in 1853 using a warping function. Much later, in 1903, Prandtl came up with a membrane analogy method that could solve problems with any complicated cross-section. First, we shall consider torsional problems with circular cross-sections.

8.2 TORSION OF MEMBERS WITH CIRCULAR CROSS-SECTION [LO2]

The torsion analysis of members with a circular cross-section starts with simplified assumptions made by Coulomb. In order to establish a relation between the applied torque and shear stress developed and the angle of twist in such cases, the following assumptions are made:

• 1. Material is homogeneous and isotropic.

• 2. Plane sections perpendicular to the axis of a circular member remain plane after twisting. No warping or distortion of the parallel planes occurs.

11.1 INTRODUCTION [LO1]

Stresses developed at the contact between two loaded elastic bodies are generally localized and most machine parts or structures are designed based on the stresses in the main body. However, there are many important machine members where the localized stresses developed at the contact between curved surfaces with initially limited contact area play an important role in their design. Ball or roller bearings, gears, cams, and valve tappets of internal combustion engines are some of the examples of machine parts where contact stresses must be taken into account in order to predict their failure probability.

The localized contact stresses that develop between two curved bodies as they are loaded with small deformations are often referred to as Hertzian stresses, following the work of H. Hertz (1881), who first solved these contact problems elegantly more than a century ago. Since then the topic has received a good deal of attention by the researchers due to its importance in engineering practice and science. Much work has been done on the stress distribution at the Hertzian contact surfaces and sub-surfaces. Ball bearings and gear teeth often fail by pitting. Hertzian stress analysis can precisely locate the depth at which maximum shear stress occurs where cracks may initiate and propagate leading to failure. Thus, a remedy to such failures may be prescribed in terms of limiting stresses. In many rolling contact problems, failure occurs with the initiation of a tiny crack that eventually grows due to repeated contacts. Analysis of crack initiation and growth is often based on Hertzian stress analysis. In this chapter, we shall consider the basics and application of contact stress analysis, beginning with some basic elasticity theory necessary for such analyses.

Through this chapter, I explored life in a competitive arena during socialist mass movements in North Korea. Since liberation from Japanese rule at the end of World War II, North Korea has implemented mass movements to increase labor productivity, known as "Socialist Efforts toward Competition Movements." These movements have permeated various settings, including individuals, workplaces, enterprises, and cooperative farms. The Chollima movement, initiated in December 1956, symbolizes North Korea’s path toward economic development. It has promoted labor competition through mass movements such as "Speed War" and "Learning to Follow Hidden Heroes." Socialist mass movements influenced my daily life, fostering competition in schools and workplaces. Through the lens of my lived experiences, I share stories covering my life journey from North to South Korea, historical backgrounds of North Korea’s competition movements, a comparison analysis before and after the North Korean Famine in the mid-1990s, and characteristics of competition in North Korean society.

2.1 MATHEMATICAL PRELIMINARIES [LO1]

In any scientific or engineering field of study, knowledge of some mathematical techniques and methods are essential. Solid mechanics is no exception. To develop proper formulation methods and solution techniques for elasticity problems, it is necessary to have an appropriate mathematical background. In this chapter, we shall discuss Cartesian tensors, which have a special significance in the discussion of stress, strain, and displacement fields, and their manipulation. Other mathematical details will be discussed as and when they are required in solving different problems.

Tensors may be defined in a number of ways. One simple definition is that a tensor is a physical quantity that is governed by certain transformation laws when the coordinate system is changed. A tensor is invariant under any change of coordinate system, but its components along the coordinate axes change with the changed coordinate system. Tensors of order zero are called scalars. Common examples of scalars are temperature, density, Young's modulus, or Poisson's ratio. They have a single magnitude at each point in space, and they are invariant with coordinate transformations. A typical example of scalars is often taken as temperature T at a point in space with coordinates (x, y, z) represented as T(x, y, z). Temperature at the same point does not change if we choose a different coordinate system (x′, y′, z′) represented as T′(x′, y′, z′) and we may say

T=T′. (2.1.1)

Tensors of first order are vectors, and we know that a vector has a magnitude and a direction. A typical example of a vector is a velocity vector V. It is sometimes taken as a convention to represent a vector by a bold letter. Consider the velocity vector V in (x, y, z) coordinate system.

Little attention has been paid to competitive dynamics from a political perspective, despite numerous instances of political competition across cultures and systems. In liberal democratic societies, political competition is legalized, allowing citizens to elect leaders who represent their ideas. Conversely, in totalitarian societies, citizens lack voting rights, and political authority is not challenged through democratic means. However, political competitions still occur among ruling elites, often through purges to seize power. This chapter explores political competition, particularly in totalitarian regimes, where purges eliminate rivals among ruling elites. The collapse of such regimes has marked an evolution toward freedom and equal opportunities for all individuals, regardless of background, which aligns with Darwin’s theory of evolution. Highlighting the lack of research on political competitions from an evolutionary psychology perspective, this chapter underscores the need for future research on human emotions and competitive behaviors in the political arena.

Solid mechanics, compared to mechanics of materials or strength of materials, is generally considered to be a higher level course. It is usually offered in higher semester to senior students. There are many textbooks available on solid mechanics, but they generally include a large part of theory of elasticity with in depth mathematical formulations. The usual prerequisites are one or two semester course on elementary strength of materials and a thorough mathematical background, including scalar, vector, and tensor field theory and cartesian and curvilinear index notation. The difference in levels between these books and elementary texts on strength of materials is generally formidable. However, in our experience of teaching this course for many years at premier institutes like IIT Kharagpur and Jadavpur University, despite its complexity, senior students generally cope well with the course using the readily available textbooks.

However, there is a vast student population pursuing mechanical, civil, or allied engineering disciplines across the country in colleges where AICTE curriculum is followed. Through several years of interaction with this group of students, we have found that there is no suitable textbook that suits their requirements. The book is primarily aimed at this group of students, attempting to bridge the gap between complex formulations in the theory of elasticity and elementary strength of materials in a simplified manner for better understanding. Index notations have been avoided, and the mathematical derivations are restricted to second-order differential equations, their solution methodologies, and only a few special functions, such as stress function and Laplacian operators.

The text follows more or less the AICTE guidelines and consists of twelve chapters. The first five chapters introduce the engineering aspects of solid mechanics and establish the basic theorems of elasticity, governing equations, and their solution methodologies. The next four chapters discuss thick cylinders, rotating disks, torsion of members with both circular and noncircular cross-sections, and stress concentration in some depth using the elasticity approaches. Thermoelasticity is an important issue in the design of high-speed machinery and many other engineering applications. This is dealt with in some detail in the tenth chapter. Problems on contact between curved bodies in two-dimensional and three-dimensional situations can be challenging, and they have wide applications in mechanical engineering such as in bearing and gear technology.

From the 1960s onwards, New Household economists like Theodore Schultz and Gary Becker shifted focus onto the poverty-alleviating impacts of family investment in human capital. This move was informed, first, by increased cultural and political awareness of what Becker referred to as an impoverished ‘underclass’ (1964/1993); second, by the social movements, including civil rights challenges to racial discrimination in schools and labour markets; and third, by government debates during the War on Poverty about the causes of Black family instability. Becker explained family instability as a rational response to price changes in the goods – including children – that families wanted. Given a set of preferences for basic commodities, and facing a defined range of choices, families were conceptualised as maximising utility, subject to constraints of income and time. This permitted hypotheses about how wages and human capital investment affected the cost of children, with effects on family formation and dissolution, fertility, and care-provision by women. As for poverty-alleviation, Becker favoured low-interest education loans. He rejected progressive income taxation and family welfare for incentivising underinvestment in education. Compensatory education programmes would fail by being offset. These policy positions were described by Nancy Folbre and Randy Albelda as a War on the Poor.

3.1 STATE OF STRESS AT A POINT [LO1]

When a body is subjected to external forces, its behavior depends on the magnitude and distribution of forces and properties of the body material. Depending on these factors, the body may deform elastically or plastically, or it may fracture. The body may also fail by fatigue when subjected to repetitive loading. Here we are primarily interested in elastic deformation of materials.

In order to establish the concept of stress and stress at a point, let us consider a straight bar of uniform cross-section of area A and subjected to uniaxial force F as shown in Figure 3.1. Stress at a typical section A - A′ is normally given as σ = F/A. This is true only if the force is uniformly distributed over the area A, but this is rarely true. Therefore, definition of stress must be considered by progressively reducing the area until it is small enough such that the force may be considered to be uniformly distributed.

To understand this, consider a body subjected to external forces P1, P2, P3, and P4 as shown in Figure 3.2. If we now cut the body in two pieces,

Internal forces f1, f2, f3, etc. are developed to keep the pieces in equilibrium. Now consider an infinitesimal element of area ΔA Dat the cut section and let the resultant force on the element be Δf.

Chapter 1 introduces common rock-forming minerals for igneous and metamorphic rocks. These are presented by mineral group, the optical properties used to recognize each mineral in thin-section are described, and each mineral’s distinctive characteristics and paragenesis is summarized. Color images show typical occurrence and textures with scale. Additional information on solid-solution and polymorphism is provided, as are mineral applications using imaging techniques, barometry, thermometry, and geochronology.