56 research outputs found
Marginal material stability
No full text1 online resource (PDF, 62 pages, includes illustrations)Grabovsky, Yury; Truskinovsky, Lev. (2012). Marginal material stability. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/181209
Exact Relations Satisfied by the Effective Tensors of Two-Dimensional Two-Phase Thermoelectric Composites
No full textThermoelectric materials have been used for cooling and heating systems for
over a hundred years. Today practical applications of thermoelectric devices
include cooling car seats, power generation, and
refrigeration. Thermoelectric materials are special for their ability to
convert temperature imbalances into electricity. Their applications can
inform the discourse about the transition to renewable energy
sources---something that our Earth most desperately needs. The goal of this
dissertation is to describe how the effective tensors of two-dimensional
thermoelectric composites made from two isotropic materials depend on
thermoelectric parameters of the constituents. Using the theory of exact
relations and links developed by Grabovsky and his collaborators, we
describe all equations satisfied by the thermoelectric effective tensor of a
composite without the explicit knowledge of its microstructure. In some
special cases, the effective tensor can be determined completely. Even in
the general case, four out of 10 components of the two-dimensional
thermoelectric tensor can be expressed in terms of the remaining 6,
regardless of the microstructure. We started with special cases and worked
our way up to the more general ones.Mathematic
Explicit Solution of an Optimal Design Problem With Non-Affine Displacement Boundary Conditions.
No full textStructural optimization problems with non-affine boundary conditions must usually be solved numerically. Here we present an example of such a problem which can be solved analytically. Our method utilizes extremal composites as structural components, and makes use of the explicit form of a certain optimal energy bound. 1 Introduction. A typical problem of optimal design seeks to arrange fixed quantities of given materials within a set\Omega 2 R n , so that the resulting structure has an "optimal" response to a particular load. The performance of the design may be measured by some functional of the elastic fields in the structure. Then the goal is to minimize or maximize this functional over all possible geometric arrangements of materials (microstructures). In this article we consider an optimal material distribution problem, with the objective functional being the strain-energy -- Z \Omega (C(x)e(u); e(u))dx. Here C(x) is the local Hooke's law which may take only two values corr..
Algebra, Geometry, and Computations of Exact Relations for Effective Moduli of Composites
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