Linear Theories Of Elasticity And Thermoelasticity

Reissue of Encyclopedia of Physics / Handbuch der Physik, Volume VIa The mechanical response of solids was first reduced to an organized science of fairly general scope in the nineteenth century. The theory of small elastic deformations is in the main the creation of CAUCHY, who, correcting and simplifying the work of NAVIER and POISSON, through an astounding application of conjoined scholarship, originality, and labor greatly extended in breadth the shallowest aspects of the treatments of par ticular kinds of bodies by GALILEO, LEIBNIZ, JAMES BERNOULLI, PARENT, DANIEL BER NOULLI, EULER, and COULOMB. Linear elasticity became a branch of mathematics, culti vated wherever there were mathematicians. The magisterial treatise of LOVE in its second edition, 1906 - clear, compact, exhaustive, and learned - stands as the summary of the classical theory. It is one of the great "gaslight works" that in BOCHNER'S words! "either do not have any adequate successor[ s] . . . or, at least, refuse to be super seded . . . ; and so they have to be reprinted, in ever increasing numbers, for active research and reference", as long as State and Society shall permit men to learn mathe matics by, for, and of men's minds. Abundant experimentation on solids was done during the same century. Usually the materials arising in nature, with which experiment most justly concerns itself, do not stoop easily to the limitations classical elasticity posits.

J-B. J. FOURIER'S immensely influential treatise Theorie Analytique de la Chaleur [21J, and the subsequent developments and refinements of FOURIER's ideas and methods at the hands of many authors, provide a highly successful theory of heat conduction. According to that theory, the growth or decay of the temperature e in a conducting body is governed by the heat equation, that is, by the parabolic partial differential equation Such has been the influence of FOURIER'S theory, which must forever remain the classical theory in that it sets the standard against which all other theories are to be measured, that the mathematical investigation of heat conduction has come to be regarded as being almost identicalt with the study of the heat equation, and the reader will not need to be reminded that intensive analytical study has t But not entirely; witness, for example, those theories which would replace the heat equation by an equation which implies a finite speed of propagation for the temperature. The reader is referred to the article [9] of COLEMAN, FABRIZIO, and OWEN for the derivation of such an equation from modern Continuum Thermody namics and for references to earlier work in this direction. viii Introduction amply demonstrated that the heat equation enjoys many properties of great interest and elegance.

Reissue of Encyclopedia of Physics / Handbuch der Physik, Volume VIa The mechanical response of solids was first reduced to an organized science of fairly general scope in the nineteenth century. The theory of small elastic deformations is in the main the creation of CAUCHY, who, correcting and simplifying the work of NAVIER and POISSON, through an astounding application of conjoined scholarship, originality, and labor greatly extended in breadth the shallowest aspects of the treatments of par ticular kinds of bodies by GALILEO, LEIBNIZ, JAMES BERNOULLI, PARENT, DANIEL BER NOULLI, EULER, and COULOMB. Linear elasticity became a branch of mathematics, culti vated wherever there were mathematicians. The magisterial treatise of LOVE in its second edition, 1906 - clear, compact, exhaustive, and learned - stands as the summary of the classical theory. It is one of the great "gaslight works" that in BOCHNER'S words! "either do not have any adequate successor[ s] . . . or, at least, refuse to be super seded . . . ; and so they have to be reprinted, in ever increasing numbers, for active research and reference", as long as State and Society shall permit men to learn mathe matics by, for, and of men's minds. Abundant experimentation on solids was done during the same century. Usually the materials arising in nature, with which experiment most justly concerns itself, do not stoop easily to the limitations classical elasticity posits.