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.

Ritual and its linkage to meaning permeates human relations from households through complex state and inter-state organizations. As globally understood, religions and associate ritual creates common and opposing relationships of identify and meaning that motivate group formations from regional forager groups to imperial conquests. Religion, however, is not abstract and held only in human heads; it is manifest in ritual activities, objects, and labor contributions that link to an economic sector supporting religious activities, monumental construction, and personal engagement.

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.

This chapter focuses on the expressive functions of tears, the face and the body on the early modern stage, to probe the deep relation between drama and the law, including their entwined but distinct investments in natural self-evidence and the rhetoric of presence. Through an interdiscursive approach, it shows how drama mines the complexities of hypokrisis through an engagement with the radical performativity at the core of law, and offers the provocation that law’s disknowledges are turned into a poetic condition of theatrical knowledge, and a forging of subjecthood and inwardness that complicates the distinction between the fiction of theatre and the reality of the law court. It ends with the suggestion that the theatre looks at, as well as beyond, the vivid invisibilities of judicial encounters to unpack the epistemic, affective and ethical impulses structuring the ‘scene’ of law.

Introduction

Data convey information about greenhouse gas emissions, financial flows, and climate impacts. Such information is used to give meaning to the unfolding climate crisis and global efforts to respond to it. Moreover, data are assumed to increase transparency and accountability (see Gupta and van Asselt 2019), and related reporting and disclosure mechanisms work to facilitate continuous engagement with relevant governance fora and processes (Heyvaert 2018, 110–111). Importantly, in addition to supporting meaningmaking, transparency, accountability, and engagement, data themselves have emerged as a central means of climate change governance. They have become operational elements of institutionalized mobilization, organizing, and steering. At the global level, the United Nations (UN) Climate Change Secretariat, for example, relies on data to strategically structure governance processes, animate implementation activity, and coordinate between actor groups (Mai and Elsässer 2022), and at the transnational level, cross-border climate governance initiatives have begun to collect local climate data to position cities as central players in climate change governance (Mai 2024). Thus, rather than merely supporting or being the outputs of governance processes, data, in a very real sense, do governing work. They constitute and restructure relations between actors, create and sustain novel forms of power and authority, and disrupt existing modes of claiming legitimacy (see Johns 2021). This chapter refers to such governing work as the ‘datafication’ of climate change governance. As data transform ‘what counts as known, probable, certain, and in the process’ (Hong 2020, 1), they powerfully reconfigure existing and give rise to alternative modalities for governing.

The fifth chapter details an especially elite investment in the Subura’s residential fabric and the emergence of Christian communities in the fourth century CE, after Constantine passed the Edict of Milan in 313. Several churches are evident in the upper Subura on the Cispian hill, most notably a basilica built by the bishop Liberius. The general orientation of the Subura valley thus began to shift away from the lower portion closer to the Forum and toward its upper extents.

In Africa, heads of government and civil society representatives have linked climate resilience to the urgent need to address the continent's debt crisis. The African Leaders Nairobi Declaration on Climate Change has called for a restructuring and relief from the debt as being essential to achieving climate goals, along with access to health and education (African Union 2023). A 2023 statement clarifies that Africa is bearing the social and economic brunt of global warming despite not being responsible for it. Dealing with the catastrophic effects of climate change on lives, livelihoods, and economies through loans is further exacerbating the ‘great financial divide’ between wealthy nations and African countries. This is neither sustainable nor just.

These negotiations reflect historical processes of social exclusion, economic dominance, and political control that have marginalized not just specific communities but also entire geographies. The climate discourse is not spared from this and remains vulnerable to reproducing inequities. The most recent reflection of this is Papua New Guinea's decision to withdraw from the 29th Climate Conference of Parties (COP29) calling it a ‘total waste of time’ (Bush 2024), as there remains inaction on the part of big emitters to reform the economic models to reduce emissions and rich nations to ensure _nancing.

Climate Justice seeks that the climate discourse reject exclusion and recognize marginalization of people and places. In doing so, it creates a complex process of embedding questions of power, hierarchy, fairness, and relief as necessary to understand climate change.

Introduction

India ranks seventh in the 2021 Global Climate Risk Index (Germanwatch 2021), and in 2017, it was the second most-affected country in terms of casualties related to extreme weather (Germanwatch 2017). Water pollution, food and water shortages (Niti Aayog 2019), waste management, and biodiversity loss (Kumari, Wate, and Anil 2014, 107) are just some of India's problems. Its large population coupled with a severe economic dependency on agriculture (FAO 2023) exposes it to severe vulnerabilities. Owing to its geography and high economic dependence on climate-sensitive sectors, India is one of countries most vulnerable to climate change (Harjeet Singh 2015). ‘Food security of India may be at risk in the future due to the threat of climate change leading to an increase in the frequency and intensity of droughts and floods, thereby affecting production of small and marginal farms.’ (Ministry of Environment and Forest 2009, 78). As a protector of people's rights, Indian courts are legally bound to protect the environment.

The chapter's research method involves an analysis of the literature and review of the judicial precedent. The chapter aims to compare the judicial precedents of the Supreme Court of India and the National Green Tribunal (NGT) to understand the evolution of their response to environmental litigation.

Article 48A in the Constitution of India obliges the government to protect the environment and conserve the natural resources of the country.

A wealth of primary sources documents Vasari’s meticulous planning for his posthumous commemoration, his death, and his heirs’ execution of his final wishes. This final chapter explores Vasari’s death and the fate of his earthly remains, as well as the unique place his high altar for the Pieve occupies within the tradition of funerary monuments and chapels made by and for early modern Italian artists and architects. As the largest and principal altar of one of Arezzo’s most prestigious churches and the site of Vasari’s burial, it is nothing less than the most personal work of his long and prolific artistic career. Its alienation in the nineteenth century from the church for which it was made and nearly all of the other works with which Vasari intended it to be seen, however, has long obscured its significance.

The sixth chapter details the sudden appearance of Mary in the Subura’s landscape during the fifth century with Sixtus III’s construction of S. Maria. It argues that Sixtus used the basilica to proclaim his support for the new orthodox belief in Mary as theotokos, to condemn the heretical beliefs against her, and to invalidate Jews and Judaism, which would have been present in the Subura itself, among other areas of the city. After its construction, the basilica of S. Maria sparked the emergence of a new local significance based on the ideal Christian woman.