1,721,042 research outputs found
Elasticity for geotechnicians: a modern exposition of Kelvin, Boussinesq, Flamant, Cerruti, Melan, and Mindlin problems
No full textThis book deals in a modern manner with a family of named problems from an old and mature subject, classical elasticity. These problems are formulated over either a half or the whole of a linearly elastic and isotropic two- or three-dimensional space, subject to loads concentrated at points or lines. The discussion of each problem begins with a careful examination of the prevailing symmetries, and proceeds with inverting the canonical order, in that it moves from a search for balanced stress fields to the associated strain and displacement fields. The book, although slim, is fairly well self-contained; the only prerequisite is a reasonable familiarity with linear algebra (in particular, manipulation of vectors and tensors) and with the usual differential operators of mathematical physics (gradient, divergence, curl, and Laplacian); the few nonstandard notions are introduced with care. Support material for all parts of the book is found in the final Appendix
Independence of Poisson's ratio in classical elastostatics with generalized boundary conditions
No full textElastic states solving the general boundary value problem of classical elasticity, and being partially completely indepenedent of Poisson's ratio, are characterized in terms of conditions on the accompanying dilatation field
A justification of the Timoshenko beam model through Γ-convergence
No full textWe validate the Timoshenko beam model as an approximation of the linear-elasticity model of a three-dimensional beam-like body. Our validation is achieved within the framework of Γ-convergence theory, in two steps: firstly, we construct a suitable sequence of energy functionals; secondly, we show that this sequence Γ-converges to a functional representing the energy of a Timoshenko beam
Analytical Thermodynamics
Full text linkThis paper proposes a theory that bridges classical analytical mechanics and
nonequilibrium thermodynamics. Its intent is to derive the evolution equations
of a system from a stationarity principle for a suitably augmented Lagrangian
action. This aim is attained for homogeneous systems, described by a finite
number of state variables depending on time only. In particular, it is shown
that away from equilibrium free energy and entropy are independent constitutive
functions
Scientific Life and Works of Walter Noll
No full textWalter Noll (1925–2017) was an American mathematician of German birth who made lasting contributions to the foundations of continuum physics and the classical non- linear field theory. This essay is an attempt to put in a broader perspective Noll’s methods and achievements in the hope that young generations of researchers may find their inspira- tion in the talent and depth of the old. By no means should this be considered as a historical account on the development of continuum mechanics through the second half of the twenti- eth century. We are content to illuminate Noll’s precious legacy
An asymptotic analysis for a nonstandard Cahn-Hilliard system with viscosity
No full textThis paper is concerned with a diffusion model of phase-field type, consisting of a parabolic system of two partial differential equations, interpreted as balances of microforces and microenergy, for two unknowns: the problem's order parameter and the chemical potential; each equation includes a viscosity term and the field equations are complemented by Neumann homogeneous boundary conditions and suitable initial conditions. In the recent paper "Well-posedness and long-time behavior for a nonstandard viscous Cahn-Hilliard system" the same authors proved that this problem is well posed and investigated the long-time behavior of its solutions. Here we discuss the asymptotic limit of the system as the viscosity coefficient of the order parameter equation tends to 0. We prove convergence of solutions to the corresponding solutions for the limit problem, whose long-time behavior we characterize; in the proofs, we employ compactness and monotonicity arguments
Well-posedness and long-time behavior for a nonstandard viscous Cahn-Hilliard system
No full textThe authors study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a careful development of uniform estimates and the deduction of certain useful boundedness properties, we prove existence and uniqueness of a global-in-time smooth solution to the associated initial/boundary-value problem; moreover, we give a description of the relative omega-limit set
Existence and uniqueness of a global-in-time solution to a phase segregation problem of the Allen-Cahn type
No full textAbstract. We study a model of phase segregation of the Allen-Cahn type, consisting in a system of two differential equations, one partial the other ordinary, respectively interpreted as balances of microforces and microenergy; the two
unknowns are the order parameter entering the standard A-C equation and the chemical potential. We introduce a notion of maximal solution to the o.d.e., parameterized on the order-parameter field; and, by substitution in the p.d.e. of the so-obtained chemical potential field, we give the latter
equation the form of an Allen-Cahn equation for the order parameter, with a memory term. Finally, we prove existence and uniqueness of global-in-time smooth solutions to this modified A-C equation, and we give a description of the relative omega limit set
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