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.

Ideals, in modern algebra, are subrings of a mathematical ring with certain absorption properties. The concept of an ideal was first defined and developed by German mathematician Richard Dedekind in 1871. In particular, he used ideals to translate ordinary properties of arithmetic into properties of sets.

The origin of the notion of ideals in a ring lies in the idea of “ideal numbers”, numbers which are missing but are really ought to be there. Ernst Kummer invented the concept of ideal numbers to serve as the “missing” factors in number rings in which unique factorization fails; here the word “ideal” is in the sense of existing in imagination only.

In this chapter, the abstraction of ideals is explored through various examples. The study is examined through various problems to enable students to apprehend the notion of the ideals.

Key Concepts

• • Steps involved for developing sustainable organizations

• • Case study on a university campus

• • Integration of green sources of energy

• • Implementation of energy efficiency measures

• • Ensuring participation of stakeholders for energy conservation

Introduction

The achievement of SDGs defined under the Paris Agreement requires concerted efforts at the international, national, state, organization, and individual levels. The organizations which follow the principles of sustainable development can serve as a role model for others to follow.

Colleges for higher education and the universities also have an important role to play in achieving the SDGs in general and in the adoption and promotion of green sources of electricity in particular. Goal 4 of SDGs, although, is specific to the availability of quality education to all, but these institutions can play a much broader role in realizing the wide-ranging SDGs. For example, Goal 9: Industry, infrastructure and innovation; Goal 12: Responsible production and consumption; and Goal 13: Climate Action cannot possibly be achieved without the mindful and positive influence of higher education institutions.

More importantly, these institutes need to work on the creation of awareness about the need for sustainable development and SDGs, a crucial requirement for their achievement. The institutes should also make sustainable development an integral part of their future plans. Green and renewable sources of energy like solar PV should be adopted for existing buildings, and these should be made mandatory for the new buildings. The academic institutes, more importantly, should practice on their campuses what they are preaching in the class.

Key Concepts

• " Working of solar PV power plants and their benefits

• " Different configurations of solar PV systems, such as grid-connected, stand-alone, and hybrid solar PV plants

• " Metering mechanisms, such as net metring and gross metring

• " Working and classification of different types of inverters used in solar energy generation

• " Different performance evaluation parameters for solar PV power plants and effect of environmental conditions

• " Components used in solar PV power plants

• " Challenges related to the large-scale integration of solar PV plants with the power grid

Introduction

Solar energy is a renewable source of energy, and when electricity is produced from solar, it does not lead to any CO2 emissions. Apart from being a green and renewable source of energy, solar is the simplest system of electricity generation. As described by Professor Martin Green, ‘The whole photovoltaic technology itself is a bit magical. Sunlight just falls on this inert material and you get electricity straight out of it.’ This technology has emerged as the most powerful solution for decarbonizing the energy system.

The solar PV plants can be installed in two modes: grid-connected and off-grid system. At present, grid-connected solar PV (GCSPV) plants are the most commonly used systems. Although solar PV cells, were discovered in the year 1953, solar PV plants for generating electricity did not gain widespread acceptance primarily because of the panel cost as well as the issues with the batteries involved. GCSPV technology has removed the weak link, the battery from the system, making it an efficient, economical, and durable system with minimum maintenance requirements. These benefits have made the solar PV the fastest rising system in the world.

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.

Introduction

A current mirror is a transistor-based circuit that the current level is controlled in an adjacent transistor, and the adjacent transistor essentially acts as a current source. Such circuits are now considered a commonly used building block in a number of analog integrated circuits (IC). Operational amplifiers, operational transconductance amplifiers, and biasing networks are examples of such circuits that essentially use current mirrors. Analog IC implementation techniques such as current-mode and switched-current circuits use current mirrors as basic circuit elements.

A significant advantage associated with the current mirrors is that they act as a near-ideal current source while fabricated using transistors and can replace large-value passive resistances in analog circuits, saving large chip area.

The later part of the chapter discusses another important analog circuit, namely, differential amplifier. As the name suggests, differential amplifiers amplify the difference between two signals that are applied to their two inputs. In addition to the differential amplification, it is also required that differential amplifiers suppress unwanted signal, which is present on the two input signals in the form of a common-mode signal. A differential amplifier is a particularly very useful and essential part of operational amplifiers. A differential pair is the basic building block of a differential amplifier that comprises of two transistors in a special form of connection.

MARKOV CHAINS WERE first formulated as a stochastic model1 by Russian mathematician Andrei Andreevich Markov. Markov spent most of his professional career at St. Petersburg University and the Imperial Academy of Science. During this time, he specialized in the theory of numbers, mathematical analysis, and probability theory. His work on Markov chains utilized finite square matrices (stochastic matrices) to show that the two classical results of probability theory, namely, the weak law of large numbers and the central limit theorem, can be extended to the case of sums of dependent random variables. Markov chains have wide scientific and engineering applications in statistical mechanics, financial engineering, weather modeling, artificial intelligence, and so on. In this chapter, we will look at a few applications as we build the concepts of Markov chains. Additionally, we will also implement a technique (using Markov chains) to solve a simple and practical engineering problem related to aircraft control and automation.

3.1 Chapter objectives

The chapter objectives are listed as follows.

• 1. Students will learn the definition and applications of Markov processes.

• 2. Students will learn the definition of the stochastic matrix (also known as the probability transition matrix) and perform simple matrix calculations to compute conditional probabilities.

• 3. Students will learn to solve engineering and scientific problems based on discrete time Markov chains (DTMCs) using multi-step transition probabilities.

• 4. Students will learn to compute return times and hitting times to Markov states.

• 5. Students will learn to classify different Markov states.

• 6. Students will learn to use the techniques of DTMCs introduced in this chapter to solve a complex engineering problem related to flight control operations.

Chapter 1 introduces the key concepts of the book, lays out the main argument, and discusses the empirical approach and data used in later chapters. It emphasizes that variation in governance outcomes cannot be understood without examining the incentives and interactions of politicians, bureaucrats, and voters. Ultimately, I argue that politicians in developing democracies have incentives to hire competent bureaucrats but will simultaneously retain tools to influence their career progression. Using tools of career control – interference in bureaucrats’ promotions, work locations, and day-to-day work tasks – politicians can extract bureaucratic loyalty. The introduction also situates the book within existing scholarship. The empirical strategy combines qualitative interviews, survey experiments, and observational data, largely drawn from Ghana but supplemented with comparative insights. Ultimately, the chapter frames the book as an inquiry into how the competing incentives of politicians and bureaucrats shape governance.

Chapter 6 shifts from procurement to the spatial allocation of local public goods, examining how partisan considerations shape the placement of infrastructure in communities. It begins by outlining the formal planning processes, in which bureaucrats are expected to design allocations based on community needs. However, interviews and prior research reveal frequent deviations from these plans, often driven by political pressure. Using data from Ghana’s Central Region, the chapter shows a strong correlation between the ruling party’s prior vote share and the number of projects a community receives. At the same time, the analysis highlights the role of need: poorer communities are more likely to secure projects than wealthier ones. These patterns suggest a dual influence – politicians seek to reward co-partisan communities, while bureaucrats attempt to prioritize developmental considerations. To probe this further, the chapter employs a survey experiment across eighty local governments. Results confirm that bureaucrats perceive both partisanship and need as influential, but partisan alignment often outweighs need in determining outcomes. The evidence thus reveals a tug-of-war between politicians and bureaucrats, with distributive outcomes shaped by the balance of partisan incentives and bureaucratic resistance. This politicization of allocation ultimately undermines equitable and efficient public service delivery.

Chapter 4 examines how politicians’ ability to influence bureaucrats’ careers creates opportunities for corruption in public procurement. Drawing on surveys and interviews with bureaucrats across local governments in Ghana, it finds that nearly half of bureaucrats believe procurement contracts are awarded uncompetitively, often in exchange for party financing. These perceptions highlight the vulnerability of procurement processes to partisan manipulation. A key mechanism through which politicians secure bureaucratic compliance is career control, particularly the threat of geographic transfers. Bureaucrats who resist corrupt demands risk reassignment to less desirable locations, a sanction that can disrupt both professional advancement and personal lives. Evidence from a survey experiment underscores this fear: bureaucrats anticipate that opposing corruption would trigger punitive transfers. By focusing on career management as a channel of influence, the chapter contributes to broader debates on bureaucratic autonomy and political interference. It also demonstrates that corruption is not merely the result of bureaucrats’ individual incentives but of institutionalized practices that bind bureaucrats’ careers to politicians’ partisan strategies.

Chapter 3 introduces Ghana as the central case study. Ghana is a lower-middle-income country in West Africa that transitioned to a multi-party democracy in 1992. Since then, two dominant parties – the New Patriotic Party and the National Democratic Congress – have alternated peacefully in power. The chapter outlines the institutional structure of local governance. The country is divided into districts, each led by a mayor-like political head appointed by the president, and administered by a District Coordinating Director, the top local bureaucrat. Local governments are responsible for development planning and receive central transfers to construct infrastructure such as schools, roads, and markets. Using a combination of qualitative interviews and quantitative data, the chapter shows that bureaucrats working in local governments are largely recruited based on merit rather than partisan loyalty. Despite this meritocratic entry point, bureaucrats remain vulnerable to political influence once in position. The chapter establishes the institutional and political backdrop necessary for understanding the dynamics of bureaucratic control explored in later chapters.