By Aaron Marcus
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Extra info for An Introduction to Homological Algebra
The proof that the equations of the linear theory of elasticity have a unique solution (if it exists at all) was ﬁrst given by Kirchhoff . This conclusion is based on the principle of force superposition and the assumption that the displacements do not affect on the external forces. In cases where this principle is not applicable, several different equilibrium forms may correspond to the same loading system. These questions relate to the stability of different equilibrium shapes for elastic bodies.
1 [ 2 [ 3 ¤ ;. 4, to elastic motions of a body occupying a domain with a piecewise smooth boundary . x/, i D 1; 2; 3, are ﬁxed at every point x 2 where the normal n exists.
The constitutive relations are consistent with the thermodynamic laws. Solid mechanics focuses, ﬁrst of all, on the equations which relate stresses with kinematic variables (strains and strain rates). Other physical phenomena, such as heat and mass transfer, electrical conductivity, are usually neglected. It is also supposed that all deformation processes are performed under rather slow changing of loads, so that the body temperature remains constant due to the heat transfer with the environment (isothermal process).
An Introduction to Homological Algebra by Aaron Marcus