By Tod A. Laursen
This booklet 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 strong and structural research, in addition to for engineers and scientists facing applied sciences within which tribological reaction needs to be characterised, the publication contains an introductory yet exact review of nonlinear finite aspect formulations earlier than facing touch and influence particularly. issues encompassed comprise the continuum mechanics, mathematical constitution, variational framework, and finite point implementations linked to contact/impact interplay. also, vital and at present rising study themes in computational touch mechanics are brought, encompassing such themes as tribological complexity, conservative remedy of inelastic influence interplay, and novel spatial discretization strategies.
Read or Download Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis PDF
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This publication comprehensively treats the formula and finite point approximation of touch and influence difficulties in nonlinear mechanics. meant for college students, researchers and practitioners attracted to numerical sturdy and structural research, in addition to for engineers and scientists facing applied sciences within which tribological reaction has to be characterised, the publication contains an introductory yet targeted evaluation of nonlinear finite point formulations ahead of facing touch and impression in particular.
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Additional resources for Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis
A convenient approach to a broader understanding of this concept is to begin with the Cauchy stress tensor u, and to associate this object with the spatial configuration. 1. In the current context, we interpret the components of u, denoted as O"ij, as representing forces per unit areas in the spatial configuration at a given spatial point :1:. It will be necessary to consider related measures of stress defined in terms of the other configurations we have discussed; in particular, the reference and rotated configurations are of particular interest.
171) and dB(O) = VO(X B ), B = 1, .. ,nnp, where X b are the reference coordinates of node B. 172) • We are now in a position to summarize the discrete equations that will result from Eq. 169). Before doing so, let us develop one more notational necessity. 174) Note that indices i and j are spatial indices in general. It is useful in generating matrix equations to have indices referring not to nodes A and 44 2. Finite Element Formulations in Nonlinear Solid Mechanics B or spatial directions i and j, but rather to degree of freedom numbers in the problem.
The volume-preserving portion of F, denoted as F, can therefore be defined as F:= J-l/3F. 2 The IBVP in the Finite Strain Case 37 Direct calculation readily reveals that det[Fl = 1, as required. 146), will generically be denoted by overbars. This idea is incorporated directly into the definition ofthe hyperelastic stored energy function W, assumed here to be additively decomposed into a volumetric part U and a deviatoric part W. Explicitly, we take W = U(J e) + W(b e), where U(r) := ~K D(Je 2 -1) -lnr] W(b e) := ~It (trWl- 3) .