An Introduction to Continuum Mechanics
This textbook on continuum mechanics reflects the modern view that scientists and engineers should be trained to think and work in multidisciplinary environments. A course on continuum mechanics introduces the basic principles of mechanics and prepares students for advanced courses in traditional and emerging fields such as biomechanics and nanomechanics. This text introduces the main concepts of continuum mechanics simply with rich supporting examples but does not compromise mathematically in providing the invariant form as well as component form of the basic equations and their applications to problems in elasticity, fluid mechanics, and heat transfer. The book is ideal for advanced undergraduate and beginning graduate students. The book features: derivations of the basic equations of mechanics in invariant (vector and tensor) form and specializations of the governing equations to various coordinate systems; numerous illustrative examples; chapter-end summaries; and exercise problems to test and extend the understanding of concepts presented.
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Airy stress function beam body force boundary conditions Cartesian Cauchy compute Consider constant constitutive equations continuity equation continuum continuum mechanics cylindrical coordinate system deﬁned deﬁnition deﬂection deformation gradient deformation gradient tensor deformation tensor deformed conﬁguration denotes density derivative determine deviatoric differential direction displacement vector eigenvalues eigenvectors equations of motion equilibrium example expressed ﬁrst ﬁxed ﬂow ﬂuid given governing equations heat transfer incompressible inﬁnitesimal integral inverse Laplace transform linear elastic load mass material coordinates matrix mechanics modulus normal obtain particle plane rectangular relations relaxation response rotation satisﬁes scalar second-order tensor shear stress shown in Figure solution speciﬁed spherical coordinate system strain tensor stress ﬁeld stress tensor stress vector surface symmetric temperature theorem tion undeformed velocity viscoelastic viscous volume zero
Page 8 - A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.