By Tod A. Laursen
This e-book comprehensively treats the formula and finite aspect approximation of touch and effect difficulties in nonlinear mechanics. meant for college kids, researchers and practitioners drawn to numerical sturdy and structural research, in addition to for engineers and scientists facing applied sciences during which tribological reaction has to be characterised, the publication contains an introductory yet exact assessment of nonlinear finite aspect formulations prior to facing touch and effect in particular. issues encompassed contain the continuum mechanics, mathematical constitution, variational framework, and finite aspect implementations linked to contact/impact interplay. also, vital and presently rising examine issues in computational touch mechanics are brought, encompassing such themes as tribological complexity, conservative therapy of inelastic impression interplay, and novel spatial discretization strategies.
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Additional info for Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis
7». , fixing the reference coordinate X), and then considering successive (partial) time derivatives of the motion cp(X, t). 57) and A(X,t) 8 82 = 8t(V(X,t» = 8t2 (CP(X,t». 58) that V and A take X as their first argument; hence their designation as material quantities. A Lagrangian description of motion, in which reference coordinates are the independent variables, would most naturally use these measures of velocity and acceleration. An Eulerian description, on the other hand, would in general require measures written in terms of points ID, without requiring explicit knowledge of material points X.
80) 26 2. 81) where dA is the differential reference area spanned by dR 1 and dR2 , and N is the reference unit normal to this area. 81) via nda = JF-TNdA. 82) is sometimes referred to as Nanson's formula, and is important (among other reasons) because it provides the appropriate change of variables formula for surface integrals in the reference and current configurations. In the current context, the primary interest is in computing the product of the traction acting on the plane at x and the differential area under consideration.
The elastic deformation Fe, which gives rise to the stress-strain relations as will be seen shortly, then has the effect of deforming these non conforming regions into 36 2. 6. Schematic representation of the multiplicative decomposition of the deformation gradient. The circles denote neighborhoods of the point X in the various configurations. Note that the intermediate (stress free) configuration is inherently nonconforming. the (conforming) spatial configuration, where equilibrium is in general imposed.