Three-dimensional problems in the theory of elasticity

Abstract

2505. Three-dimensional problems in th e th eory of elast icity and furth ermoreIt is easy to see thatReplacing te nsor t and its first invariant by the following expressions we find j rrn .t ,uido= (1 ) g ooDevp] . J 15 1-v E Proceeding to the second term in formula (1.2.18) we notice that the stre ss tensor calculated in terms of ui is equal to

Influence of particle size distribution on nanopowder cold compaction processes

“…The theoretical model of [12,13] includes the contact interaction laws, such as the modified Hertz law, which describes the elastic repulsion of particles, the linearized Cattaneo -Mindlin law [14,15], which describes the "friction" forces at particle shift, the Lurie law [16], which describes the contact elasticity to the particle rolling, as well as modified Hamaker's formula [17], which describes the dispersion attractive forces, and (in the case of II type systems) the possibility of interparticle solid bridges formation [10]. Note that the dispersion attractions and the agglomeration tendency for the nanosized powders, as distinct from powders of micron (or larger) sizes, take on special significance and, in particular, owing to introduction this factors the size effect in compaction processes, well-known from the experimental studies [1][2][3]6], is reproduced by the granular dynamics method.…”

Quasistatic problems for piecewise-continuously growing solids with integral force conditions on surfaces expanding due to additional material influx

“…The radii of the ends of the cone and the value of forces acting on it depend on a real parameter t. This formal coincidence is gained by substituting in the problem (3) the values P • to the value of tensile force related to the shear modulus, and the tensor T • to the stress tensor related to the shear modulus. We can construct the closed analytical solution of the described classical problem if we combine known specific solutions of the theory of elasticity [14]. We will not trace out the constructed analytical solution in this succinct paper.…”

Stability of E. Reyssner’s plates on the elastic non-winkler foundation

“…Stress-strain state of three-dimensional elastic layer is described by the solution of homogeneous equations of the theory of elasticity in displacements [2]:…”

“…Expressions (10) (11) identically satisfy the conditions (2). Other conditions on the ends of the plate and layer allow to solve the problem of the of bifurcation forms of balance of system and to determine the value of the parameter O.…”