Mechanics of materials (also called strength of materials) is an area of engineering that describes the deformation of bodies and the distribution of forces within those bodies. Introductory courses in this discipline normally consider three types of simple deformations – the stretching or compression of axially loaded bars, the bending (flexure) of laterally loaded beams, and the torsion (twisting) of circular shafts. Many complex structures are composed of members that have these simple types of behavior. This chapter will outline the analysis of these three types of problems and review the basic assumptions made so that those assumptions can be later examined and, in some cases, relaxed.

The bending of unsymmetrical beams was considered in Chapter 10, where we showed that, for thin sections, we could obtain explicit expressions for both the flexure stresses and the shear flows (shear stresses). In Chapter 11 similar explicit expressions were found for the shear stresses or shear flows for the torsion of thin, open and closed cross-sections. In this chapter we will examine cases where a thin member is in a combination of bending and torsion. We will also consider the case where axial loads acting on a thin section can induce torsional deformations. A new quantity called a bimoment will be shown to be a resultant of the axial stress distribution that produces torsion.

This chapter examines the process of introspection and examining our own minds. It looks at different types of introspection. it examines the philosophical process and discipline of phenomenology, particularly the work of Husserl. We look at psychological methods of examining the contents of our thoughts, particularly using experience sampling. We then look at the reliability of our own beliefs, and how we can be misled by illusions and delusions. The chapter looks at examples such as schizophrenia, mass hysteria, confabulation and the neurological disorder denial, all of which make us question the reliability of our beliefs. We ask to what extent we could be wrong about the nature of our experience. The chapter moves on to consider what is outside consciousness, and the Freudian concept of the unconscious, and the Jungian concept of the collective unconscious and its contents. The chapter concludes by examining subliminal processing.

This chapter looks at meditation and mindfulness and other forms of heightened awareness. It first looks at the evidence that meditation leads to both temporary and permanent changes in the brain, and has both short- and long-term benefits for physical and mental health. It asks: what then is the relation between mind and brain, and what is the direction of flow of causality? The chapter then looks at transcendental consciousness, and ‘better than normal states’. We focus in particular on religious experiences, and the involvement of the temporal lobes and other structures, as well as evaluating the evidence for the efficacy of Persinger’s ‘god helmet’. It mentions again entheogens, drugs that give religious-like experiences. The chapter concludes with a discussion of Buddhism, particularly Zen.

Most problems involving complex-shaped deformable bodies require a numerical solution of the governing equations and boundary conditions. However, there are some important simple problems that can be solved analytically and that reveal the nature of the stresses and deformations in geometries of practical significance. In this chapter we will examine a number of such problems, including thick-wall pressure vessels, shrink-fits, the stress concentration at a hole in a plate, the bending of a curved beam, and a concentrated force acting on a wedge. Both displacement-based approaches as well as stress-based approaches using the Airy stress function will be considered.

Just as the concept of stress gives us a measure of force distributions in a deformable body, the concept of strain describes the distribution of deformations locally at every point within the body. In this chapter we will define strains and describe how strains change with directions and with the choice of coordinates, as was done with stresses. Strains will also be related to the displacements of the deformable body. It will be shown that strains must satisfy a set of compatibility equations at every point in a body to ensure that they represent a well-behaved deformation. Since the strains often found in practice are quite small, this book will only consider problems for small strains.

This chapter looks at the state of sleep and its biology. it begins by looking at what comprises the state of sleep, and examines comparatively which, and how, other animals sleep. It looks at circadian rhythms, and how the sleep--wake cycle is controlled, with melatonin manufactured by the pineal gland. There is emphasis on the electrophysiology of sleep (sleep EEG), and a description of the stages of sleep and how they are characterised by different EEG profiles, particularly the distinction between REM and non-REM sleep. The neurology of sleep looks at the role of structures such as the brainstem and reticular activating system, and the effect of damage at different levels of the brain on sleeping behaviour. The psychopharmacology of sleep looks at the changing role of neurotransmitters throughout the day and night, and in dreaming and dreamless sleep. The chapter then examines the range of sleep disorders, including problems getting to sleep, as well as sleep walking and sleep talking. It then looks at the effects of sleep deprivation. The chapter concludes with a discussion of why we sleep, covering the possible evolutionary functions of sleep, with focus on the role of sleep in learning and memory consolidation.

This chapter looks at the cognitive correlates of consciousness, and how consciousness is related to the ideas of selection and limitation. It begins by looking at how cognitive processes such as attention, particularly visual attention, language, thought, mental imagery and inner speech involve consciousness. It looks at cross-cultural differences in cognition. We then look at the neuroscience of the default-mode network. The chapter then looks at a number of models of consciousness based in cognition, including the global workspace theory of Baars, and the multiple drafts model of Dennett. We consider the underlying neuroscience. The chapter then considers how cognition enables us to construct a model or representation of the world, and the way in which consciousness might emerge from that representation. We consider again emergence and complexity. Finally the chapter examines the possible role of quantum mechanics as a basis for understanding consciousness.

Work–energy concepts are important for two reasons. First, they provide an alternative way to guarantee equilibrium and compatibility, which are two key elements in all stress analyses. Second, energy methods have become the basis of formulating numerical methods so they are at the heart of the field of computational mechanics, which will be discussed in the next chapter.In this chapter we will discuss two types of internal energy in deformable bodies – strain energy and complementary strain energy. Although we will show that these internal energies are equal for linear elastic bodies, we will see that they play distinct roles in terms of work–energy relations. A number of important general principles and theorems will be described including the principle of virtual work, the principle of complementary virtual work, the principle of minimum potential energy, the theorem of minimum complementary potential energy, and the reciprocity theorem.The classical theorems of Castigliano and Engesser and the principle of least work will be used to solve problems with discrete forces and moments.

Structures can fail in different ways so that one needs to examine a variety of failure modes. In this chapter we will consider (1) a number of the commonly used static failure theories, (2) fatigue failure under alternating loads, and (3) fracture theory. We will also briefly discuss how nondestructive inspections can be used in conjunction with crack growth laws to keep structures safe while in use. Another way that structures can fail is through a loss of stability. The sudden buckling of columns, also called a bifurcation type of instability, will be described as well as other types of instabilities such as limit-load instabilities and snap-through buckling instabilities.

This chapter examines altered states of consciousness (ASCs) and how the the phenomenology of the experience is linked to the changes that give rise to the altered state. The chapter begins by asking what an ASC is, and what is altered in it. I’m It introduces the psychonaut, who tries to explore human experience in part with conscious states. The chapter describes several altered states, including sensory deprivation (and mentions its use as torture), sensory habituation and out-of-body experiences (OBEs). It emphasises that OBEs arise from brain-related changes and do not need to be explained in terms of a soul or astral travel. The chapter similarly examines near-death experiences (NDEs) and how they can be explained in physical terms, without recourse to an afterlife. The chapter also examines migraine prodrome and aura, epilepsy and the sleeping sickness Encephalitis lethargica, as portrayed in Oliver Sacks’s book Awakenings, and the film of the same name.

This chapter looks at dreams. We first examine the definition of a dream and ask how we can be sure that they are real experiences, rather than constructed on awakening, and we ask how reliable is our memory for them. It then looks at lucid dreaming - dreams in which we know we are dreaming - and methods of inducing lucid dreams. The chapter then looks at dream content, including different types of dream, such as nightmares and recurring dreams. It then moves on to the question of why we dream, and whether dreams have any meaning. We examine the biology of dreaming in terms of the default-mode network and the activation--synthesis model. The chapter concludes by looking at why we dream, including accounts such as dealing with threats, and the relationship between dreaming and learning. In particular, we look at psychoanalytic theories, particularly those of Freud, Jung and Adler, and the idea that dreams are a result of a struggle between the ego and the repressed unconscious, and the use of mechanisms such as dream symbols.