Technology & Engineering
Solid Mechanics
Solid mechanics is a branch of mechanics that focuses on studying the behavior of solid materials under various conditions, such as stress, strain, and deformation. It encompasses the principles of statics, dynamics, and elasticity to analyze and predict the mechanical response of solids. This field is crucial for designing and analyzing structures, machines, and materials in engineering and technology.
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9 Key excerpts on "Solid Mechanics"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 11 Solid Mechanics Solid Mechanics is the branch of mechanics, physics, and mathematics that concerns the behavior of solid matter under external actions (e.g., external forces, temperature changes, applied displacements, etc.). It is part of a broader study known as continuum mechanics. One of the most common practical applications of Solid Mechanics is the Euler-Bernoulli beam equation. Solid Mechanics extensively uses tensors to describe stresses, strains, and the relationship between them. Relationship to continuum mechanics As shown in the following table, Solid Mechanics inhabits a central place within continuum mechanics. The field of rheology presents an overlap between solid and fluid mechanics. Continuum mechanics The study of the physics of continuous materials Solid Mechanics The study of the physics of continuous materials with a defined rest shape. Elasticity Describes materials that return to their rest shape after an applied stress. Plasticity Describes materials that permanently deform after a sufficient applied stress. Rheology The study of materials with both solid and fluid characteristics. Fluid mechanics The study of the physics of continuous materials which take the shape of t heir container. Non-Newtonian fluids Newtonian fluids Response models A material has a rest shape and its shape departs away from the rest shape due to stress. The amount of departure from rest shape is called deformation, the proportion of deformation to original size is called strain. If the applied stress is sufficiently low (or the imposed strain is small enough), almost all solid materials behave in such a way that the strain is directly proportional to the stress; the coefficient of the proportion is called the modulus of elasticity or Young's modulus. This region of deformation is known as the linearly elastic region.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 4 Solid Mechanics Solid Mechanics is the branch of mechanics, physics, and mathematics that concerns the behavior of solid matter under external actions (e.g., external forces, temperature changes, applied displacements, etc.). It is part of a broader study known as continuum mechanics. One of the most common practical applications of Solid Mechanics is the Euler-Bernoulli beam equation. Solid Mechanics extensively uses tensors to describe stresses, strains, and the relationship between them. Relationship to continuum mechanics As shown in the following table, Solid Mechanics inhabits a central place within continuum mechanics. The field of rheology presents an overlap between solid and fluid mechanics. Continuum mechanics The study of the physics of continuous materials Solid Mechanics The study of the physics of continuous materials with a defined rest shape. Elasticity Describes materials that return to their rest shape after an applied stress. Plasticity Describes materials that permanently deform after a sufficient applied stress. Rheology The study of materials with both solid and fluid characteristics. Fluid mechanics The study of the physics of continuous materials which take the shape of the ir container. Non-Newtonian fluids Newtonian fluids Response models A material has a rest shape and its shape departs away from the rest shape due to stress. The amount of departure from rest shape is called deformation, the proportion of deformation to original size is called strain. If the applied stress is sufficiently low (or the imposed strain is small enough), almost all solid materials behave in such a way that the strain is directly proportional to the stress; the coefficient of the proportion is called the modulus of elasticity or Young's modulus. This region of deformation is known as the linearly elastic region.
eBook - PDF- Allan F. Bower(Author)
- 2009(Publication Date)
- CRC Press(Publisher)
1 1 Overview of Solid Mechanics Solid Mechanics is a collection of physical laws, mathematical techniques, and computer algorithms that can be used to predict the behavior of a solid material that is subjected to mechanical or thermal loading. The field has a wide range of applications, including the following: 1. Geomechanics: Modeling the shape of planets, tectonics, and earthquake prediction 2. Civil engineering: Designing structures or soil foundations 3. Mechanical engineering: Designing load-bearing components for vehicles, engines, or turbines for power generation and transmission, as well as appliances 4. Manufacturing engineering: Designing processes (such as machining) for forming metals and polymers 5. Biomechanics: Designing implants and medical devices, as well as modeling stress driven phenomena controlling cellular and molecular processes 6. Materials science: Designing composites, alloy microstructures, thin films, and developing techniques for processing materials 7. Microelectronics: Designing failure-resistant packaging and interconnects for micro-electronic circuits 8. Nanotechnology: Modeling stress-driven self-assembly on surfaces, manufacturing processes such as nano-imprinting, and modeling atomic-force microscope/sample interactions This chapter describes how Solid Mechanics can be used to solve practical problems. The remainder of the book contains a more detailed description of the physical laws that 2 ◾ Applied Mechanics of Solids govern deformation and failure in solids, as well as the mathematical and computational methods that are used to solve problems involving deformable solids: Chapter 2 covers the mathematical description of shape changes and internal forces in solids. Chapter 3 discusses constitutive laws that are used to relate shape changes to internal forces. Chapter 4 contains analytical solutions to a series of simple problems involving deformable solids.
eBook - PDF- Roger T. Fenner, J.N. Reddy(Authors)
- 2012(Publication Date)
- CRC Press(Publisher)
1 1 Introduction As engineers we are concerned with solving problems, which may involve not only the engineering sciences but also related subjects such as economics and manage-ment science. The ability to solve problems can be gained through a combination of practical experience of particular problems and the systematic study of underlying principles. Although both are necessary for the practising engineer, the study of principles leads more rapidly to a genuine understanding, and makes it possible to tackle new problems not previously met. For convenience, the total subject matter of engineering science is usually subdivided into a number of topics, such as solid me-chanics, fluid mechanics, heat transfer, properties of materials, and so on, although there are close links between them in terms of the physical principles involved, the methods of analysis employed, and the objective of the study. Solid Mechanics as a subject is usually further subdivided into the mechanics of rigid bodies and the mechanics of ( deformable ) solids , also known as mechanics of materials and strength of materials . The precise meaning of the word “deformable” will be made clear in the coming pages, but at the moment it should be understood as change in the geometry. While the mechanics of rigid bodies is concerned with the static and dynamic behavior under external forces of engineering components and systems which are treated as infinitely strong and undeformable, the mechanics of deformable solids is concerned with the internal forces and associated changes in geometry of the components involved. Of particular importance are the properties of the materials used, the strength of which will determine whether the components fail by breaking in service, and the stiffness of which will determine whether the amount of deformation they suffer is acceptable. While strength is purely a material property, stiffness is a combination of material properties and geometry.
eBook - PDF- Eliahu Zahavi, David M. Barlam(Authors)
- 2000(Publication Date)
- CRC Press(Publisher)
1 1 Basics of Solid Mechanics Solid Mechanics is a part of a continuum mechanics. This chapter forms the foundation in machine design for problem solving within the linear theory of elasticity, 1,2 discussing stresses, displacements, and strains. To stay within the linear theory, the discussion is limited to small displacements. The topic of nonlinearity, including large displacements, plastic materials, and contact, will follow in Chap-ters 3 through 6. Throughout the presentation, to facilitate infinitesimal analysis, bodies are assumed to be ideal, having such properties as flexibility, continuity, and isotropy. We disregard the microstructure of the material. 1.1 STRESS Stress is defined as an internal force per unit area of a section of a body under loading. One of the objectives of Solid Mechanics is to assess the internal state of a flexible body under load and define it in terms of stresses, a discussion of which follows. 1.1.1 D EFINITION OF S TRESSES The stresses in a body in state of equilibrium are analytically derived, using the method of sectioning . This method assumes the body is split into parts that are interconnected by internal forces to preserve it as one entity. Assume the body to be divided into two parts, I and II, with the internal forces acting on the cut surfaces (see Figure 1.1). Limiting the examination to section I, Figure 1.1b, consider an arbitrary infinitesimal area ∆ Α on this cut surface of the section, with an outward normal vector n (Figure 1.2). It is assumed that forces acting upon ∆ Α are reduced to concentrated force ∆ P n , applied at point Q . Note that the direction of ∆ P n does not necessarily coincide with a normal n . The average intensity of internal forces acting upon ∆ A equals (1.1) p n ∆ P n ∆ A ---------= 2 Nonlinear Problems in Machine Design Following the above pattern, the vector of traction at point Q is defined as (1.2) Area ∆ Α , the direction of which is defined by normal n, has a vector of traction p n .
eBook - PDFNonlinear Solid Mechanics
Bifurcation Theory and Material Instability
- Davide Bigoni(Author)
- 2012(Publication Date)
- Cambridge University Press(Publisher)
3 Solid Mechanics at finite strains Kinematics and motion of a solid body are introduced. Mass balance and the concept of force and stress are provided, with emphasis on the notion of work-conjugated stress and strain measures, fundamental in the constitutive description of materials. Rules governing the changes of field quantities for rigid-body rotations of the refer- ence and current configurations are given evidence to clarify the concept of spatial and material fields. The description of the motion, deformation and stress of a solid body subject to external actions is the focus of Solid Mechanics, a science that was initiated more than four centuries ago by G. Galilei (1564–1642). Solid Mechanics is articulated into five main parts: (1) kinematics and the concept of deformation, (2) mass conservation, (3) forces and stress, (4) the constitutive equations and (5) the setting of the boundary value problem. We will be concerned in this chapter with the preceding points (1) through (3), whereas constitutive equations and the setting of the boundary value problem will be deferred to chapters 4 and 6 through 9. As a complement to the material that will be presented in this chapter, we suggest the exhaustive treatments by Truesdell and Noll (1965), Truesdell (1966), Chadwick (1976), Gurtin (1981), Ogden (1984), and Podio Guidugli (2000). 3.1 Kinematics Bodies occupy configurations, which are regions of the three-dimensional Euclidean point space. Obviously, a body should not be confused with its configuration, for the same reason that the center-line of a cantilever beam should not be confused with the points occupied by the elastica. However, a one-to-one correspondence can be set between points of a body and the points they occupy in the Euclidean space. Thus, we will treat a body as a closed set of points occupying a regular 1 region B, called the ‘current’ configuration, of the three-dimensional Euclidean point space.
- Nam H. Kim, Bhavani V. Sankar, Ashok V. Kumar, Nam-Ho Kim(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
Chapter 5 Review of Solid Mechanics 5.1 INTRODUCTION The finite element method is a powerful numerical method for solving partial differential equations. It has been applied to solve many physical problems whose governing equations are partial differential equations. The method has been implemented and is available as commercial software that can perform a variety of analysis including solids, structures, and thermal systems to mention a few. However, to use these programs effectively, one must understand the underlying physics of the problem being solved. This is important not only to be able to construct the right models for analysis but also to interpret the results and verify its accuracy. In this chapter, we review the main principles and the governing equations of Solid Mechanics. We explain the physical meaning behind the stress and strain tensors and the relation between them. Stress analysis is a major step, and in fact, it can be considered the most important one in the mechanical design process. There are many design considerations that influence the design of a machine element or structure. The most important design considerations are the following 1 : (i) the stress at every point should be below a certain limit for the material; (ii) the deflection should not exceed the maximum allowable for proper functioning of the system; (iii) the structure should be stable; and (iv) the structure or machine element should not fail due to fatigue. The failure mode corresponding to instability is also referred to as buckling. The failure due to excessive stress can take different forms such as brittle fracture, yielding of the material causing inelastic deformations, and fatigue failure. Stress analysis of structures plays a crucial role in predicting failure types (i), (ii), and (iv) above. The analysis of stability of a structure requires a slightly different approach but in general, uses most of the methods of stress analysis
eBook - PDF- Jiro Nagatomi(Author)
- 2011(Publication Date)
- CRC Press(Publisher)
3 1 An Introductory Guide to Solid Mechanics Sarah C. Baxter 1.1 INTRODUCTION The.goal.of.this.chapter.is.to.present.an.overview.of.solid.mechanics.to.an.audience.that.is.expert.in. another.field,.primarily.biology . .In.the.formation.of.interdisciplinary.research.teams,.it.is.important. that.everyone.learn.some.of.the.“other”.field—but.the.tendency.is.to.try.to.prescribe.a.complete. education. .For.mechanics,.this.would.be.to.suggest.that.other.team.members.complete.the.statics,. solids,.dynamics,.continuum.sequence,.as.well.as.the.prerequisite.math.courses.for.each . .This.is. not.a.realistic.solution,.and.takes.no.advantage.of.the.fact.that.the.“students”.are.experts.in.their. own.field;.they.are.independently.good.at.seeing.parallels,.asking.good.questions,.and.analyzing. new.and.unexpected.results . .With.respect.to.mechanics,.what.a.nonmechanician.needs.to.know.is. CONTENTS 1.1 . Introduction. .............................................................................................................................. 3 1.2 . Mechanics:.A.Broad.Definition. ................................................................................................ 4 1.2.1 . Mechanics.of.Materials:.Fundamental.Terms. .............................................................. 4 1.2.1.1 . Concepts.and.Descriptors. .............................................................................. 4 1.2.1.2 . Deformations .................................................................................................. 8 1.2.1.3 . Mechanisms. ................................................................................................... 9 1.3 . Modeling. ................................................................................................................................. 13 1.3.1 . Fundamental.Equations. ..............................................................................................
eBook - PDF- Marko V. Lubarda, Vlado A. Lubarda(Authors)
- 2020(Publication Date)
- Cambridge University Press(Publisher)
Part I Fundamentals of Solid Mechanics 1 Analysis of Stress The concept of stress is the most fundamental concept in the mechanics of solids. The discrete atomistic structure of a material is ignored and the model of a continuum is adopted, according to which the entire space between the boundaries of a considered body is filled with the material. If, at a considered point of a solid body, an infinitesimal surface element dS , with a unit outward normal vector n, transmits a force dF n , the traction vector at that point with respect to the considered surface element is defined by the ratio t n = dF n /dS . The projection of the traction vector in the direction of the vector orthogonal to the surface element is the normal stress over that surface element, σ nn = t n · n. The remaining component, tangential to the surface element, is the shear stress σ nm m = t n − σ nn n, where m is a unit vector tangential to dS . The first index (n) in the stress component σ nm specifies the orientation of the surface element over which σ nm acts, i.e., the direction of the unit vector orthogonal to dS , while the second index (m) specifies the direction tangential to dS along which the stress component σ nm physically acts. This chapter is devoted to the analysis of the normal and shear stresses over differently oriented surface elements through a considered material point of a loaded body. The analysis leads to the notion of a stress tensor, originally intro- duced by the French mathematician, physicist, and engineer Augustin-Louis Cauchy in the nineteenth century. We present the analysis of one-, two-, and three-dimensional states of stress, determine the corresponding principal stresses (maximum and minimum normal stresses) and the maximum shear stress, define the deviatoric and spherical parts of the stress tensor, derive the equations of equilibrium which must be satisfied by the stress field within a loaded body at rest, and formulate the corresponding boundary conditions.
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