By Konstantin Naumenko, Marcus Aßmus
This quantity offers a set of contributions on complicated methods of continuum mechanics, which have been written to have fun the sixtieth birthday of Prof. Holm Altenbach. The contributions are on issues with regards to the theoretical foundations for the research of rods, shells and 3-dimensional solids, formula of constitutive types for complicated fabrics, in addition to improvement of latest methods to the modeling of wear and tear and fractures.
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Extra resources for Advanced Methods of Continuum Mechanics for Materials and Structures
K cannot be taken arbitrarily as they must obey a set of three partial differential equations (Eq. (37) in p. 49) of which the general integral is an arbitrary function of the six components EKL of the finite deformation. This is the requirement for Eq. (31) to be compatible with the existence of internal forces. This was noticed by Poincaré in his lectures on elasticity (Poincaré 1892, p. 77) but also by Kirchhoff (1852), C. Neumann (1860), and closer to the Cosserats by Cellérier (1893). The second remark relates to the stability of equilibrium and the notions of “bifurcation” equilibrium and “limit” equilibrium of Poincaré.
A. jK = J −1 x,K S KL x,L gjp = J −1 x,K p ∂W p x g . ji (cf. Eq. (61), or (62), p. 65) indicating that other components are easily deduced. In the above-specified conditions the mechanical equilibrium equations are obtained as (cf. Eq. (63)–(64), p. K (30) at internal points in the body and Ti = NK at its regular boundary of unit outward pointing normal of components NK in the undeformed configuration. In the rest of this chapter, the Cosserats deal with various matters that include a “paradox” previously dealt with by Poincaré, Kirchhoff and others, notions on stability, the choice of a natural state, the question of material symmetry, and the case of infinitesimal deformations.
57), which hold for an undeformed volume). Rejection of the assumption complicates the derivations but the final Eqs. (62)–(64) remain unchanged. The operator δ d dr = + v− δt dt dt ·∇ (65) is a generalization of the material-derivative operator (45) for the moving observation point. A. Ivanova et al. where Δs is the displacement with respect to the observation point of a material point that was in the observation point at time t. The above definition has the same physical meaning as (46). The material derivative characterizes the rate of change a property of the material point that was in the observation point at time t.
Advanced Methods of Continuum Mechanics for Materials and Structures by Konstantin Naumenko, Marcus Aßmus