Cosserat Theories: Shells, Rods and Points
Springer Science & Business Media, 9 de març 2013 - 488 pàgines
Continuum Continuum mechanics mechanics provides provides a a theoretical theoretical structure structure for for analyzing analyzing the the response response of of materials materials to to mechanical mechanical and and thermal thermal loads. loads. One One of of the the beauties beauties of of continuum continuum mechanics mechanics is is that that the the fundamental fundamental balance balance laws laws (conservation (conservation of of mass mass and and balances balances of of linear linear momentum, momentum, angular angular momentum, momentum, energy energy and and entropy) entropy) are are valid valid for for all all simple simple materials. materials. Most Most of of the the modern modern research research in in continuum continuum mechanics mechanics focuses focuses on on the the development development of of constitutive constitutive equations equations which which are are used used to to characterize characterize the the response response of of a a particular particular class class of of materials materials (e.g. (e.g. invisicid invisicid fluids, fluids, viscous viscous fluids, fluids, elastic elastic solids, solids, viscoelastic viscoelastic solids, solids, elastic elastic plastic solids, elastic-viscoplastic solids, etc.). plastic solids, elastic-viscoplastic solids, etc.).
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angular momentum arbitrary assigned fields associated balance laws balance of angular balance of linear balances of director base vectors beam body force boundary conditions characterized components conservation of mass constant constitutive equations constraint responses continuum mechanics Cosserat point Cosserat solution Cosserat theory definitions denoted derivative determined developed director couples director inertia coefficients displacements dot product elastic materials equations of motion exact solution follows homogeneous deformations independent invariant under SRBM ISBN isotropic IUTAM Symposium kinematic assumption kinetic quantities Lagrangian coordinates lateral surface linear momentum material point mechanical power Moreover Naghdi nonlinear elastic orthotropic plate point-like structure position vector present configuration Prove the validity rectangular reference configuration region Rubin satisfy the restrictions second order tensor shear deformation shown sin(o"t sinée specified strain energy function stress string symmetric tensor thickness three-dimensional theory values vanishes velocity vibrations yields