Optimal shape design of structural elements based on boundary variations results in final designs that are topologically equivalent to the initial choice of design, and general, stable computational schemes for this approach often require some kind of remeshing of the finite element approximation of the analysis problem. This paper presents a methodology for optimal shape design where both these drawbacks can be avoided. The method is related to modern production techniques and consists of computing the optimal distribution in space of an anisotropic material that is constructed by introducing an infimum of periodically distributed small holes in a given homogeneous, i~otropic material, with the requirement that the resulting structure can carry the given loads as well as satisfy other design requirements. The computation of effective material properties for the anisotropic material is carried out using the method of homogenization. Computational results are presented and compared with results obtained by boundary variations.

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Generating optimal topologies in structural design using a homogenization method

Micro-structure in linear elasticity

The Classical Field Theories

Matter is commonly found in the form of materials. Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in which matter manifests itself only through its inertia, independent of its constitution; “modern” physics likewise turns its back, since it concerns solely the small particles of matter, declining to face the problem of how a specimen made up of such particles will behave in the typical circumstances in which we meet it. Materials, however, continue to furnish the masses of matter we see and use from day to day: air, water, earth, flesh, wood, stone, steel, concrete, glass, rubber, ... All are deformable. A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys.

The non-linear field theories of mechanics

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Elastic materials with couple-stresses R. Toupin

https://hal.archives-ouvertes.fr/hal-00852443/document

Elastic materials with couple-stresses

Wave propagation in thin elastic shells

Simpler static problems in nonlinear theories of rods

In the literature on crystals, “twinning” is a word used to describe a variety of phenomena involving different but symmetry-related configurations which coexist in crystals, meeting to form surfaces of discontinuity. As is discussed by Pitteri [1], there have been various attempts to formulate a more precise general definition of the word, as it applies to crystals. His discussion makes clear that some types of twinning are outside the scope of thermoelasticity theory. His definition excludes some phenomena which some experts on crystals call twins, like the “rotational twins” described by Barrett & Massalski [2, p. 406], things which seem to me more reminiscent of the multiple births we commonly describe by other words, like triplets or sextuplets. Whatever one calls them, they are of physical interest, as are other somewhat similar phenomena. My purpose is to present elements of thermoelasticity theory for things of this general kind.

Some surface defects in unstressed thermoelastic solids

Uniformity in shells

http://library.um.ac.id/free-contents/downloadpdf.php/buku/introduction-to-the-thermodynamics-of-solids-j-l-ericksen-664.pdf

J. L. Ericksen

Papers

Wave propagation in thin elastic shells

Simpler static problems in nonlinear theories of rods

Some surface defects in unstressed thermoelastic solids

Uniformity in shells

Introduction to the thermodynamics of solids / J.L. Ericksen