A One-dimensional Introduction to Continuum Mechanics
Many textbooks on continuum mechanics plunge students in at the ?deep end? of three-dimensional analysis and applications. However a striking number of commonplace models of our physical environment are based entirely within the dynamics of a one-dimensional continuum. This introductory text therefore approaches the subject entirely within such a one-dimensional framework.The principles of the mathematical modeling of one-dimensional media constitute the book's backbone. These concepts are elucidated with a diverse selection of applications, ranging from tidal dynamics and dispersion in channels to beam bending, algal blooms, blood flow, and the greenhouse effect.The book is ideally suited to elementary undergraduate courses as it makes no use of multivariable calculus. A number of graded problems are included at the end of each section.
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Describing the motion of a continuum
Conservation of material
Balance of momentum
Stress and strain
Applications of 1D continuum mechanics
amoebae applied approximation artery atmosphere average beam behaviour body force boundary conditions car density car traffic characteristic diagram characteristic solution coefficient components conservation Consider constant continuity equation continuum mechanics creep cross-section D'Alembert's solution dashpot deformation dendrites denote dependence derive described differential equation diffusion downstream dynamics elastic equa equation 2.4 Eulerian description exact solution example exponential decay fluid flux function gives governing equation Hence Hooke's law Hookean ideal gas infrared initial integration John Scott Russell km/hr Lagrangian length linear linearised liquid material method of characteristics microscopic model of visco-elasticity molecules momentum equation muscle N-wave nonlinear one-dimensional continuum partial differential equations particle physical pressure propagation pulse quantities radiation region Section shock shown in Figure simply slice solid solitary wave strain stress Substituting temperature tion tracer traffic light travelling typical velocity vertical visco-elasticity vortex tube water waves wave equation wave speed wavenumber