Computational Contact and Impact Mechanics: Fundamentals of by Tod A. Laursen
By Tod A. Laursen
This publication comprehensively treats the formula and finite point approximation of touch and influence difficulties in nonlinear mechanics. meant for college kids, researchers and practitioners drawn to numerical good and structural research in addition to engineers and scientists facing applied sciences within which tribological reaction has to be characterised, the ebook comprises an introductory yet special evaluate of nonlinear finite aspect formulations earlier than facing touch and impression in particular. subject matters encompassed comprise continuum mechanics, mathematical constitution, variational framework and finite aspect implementations linked to contact/impact interplay. also, vital and at present rising learn subject matters in computational touch mechanics are brought, encompassing such issues as tribological complexity, conservative remedy of inelastic impression interplay and novel spatial discretization options.
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Extra info for Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis
118) where I is the identity mapping (consistent with the assumption that the reference configuration corresponds to the configuration of the body at t = 0). 117), the divergence operator is to be interpreted as being with respect to spatial coordinates a;. The acceleration a is referred to spatial 32 2. 61). pt, but relies upon it for its own definition. pt to be a function of reference coordinates X, the framework is inherently Lagrangian. 117) are written in terms of reference quantities, clearly exposes the structure of the problem to be approximated.
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.
Bij 8rpti. 2 The mvp in the Finite Strain Case 39 4. 2 for the kinematically linear problem, we turn now to development of a weak form for the finite strain problem. f. 35}). Note that the are material quantities, in that they are associated with points X E O. It is useful at times to consider spatial forms of the weighting functions, obtained by composition of;P with the 40 2. Finite Element Formulations in Nonlinear Solid Mechanics (unknown) mapping '1'-1. 158) for any a: = CPt(X). This causes the condition w = 0 on cpt(r u) to be satisfied, and provided the configuration mapping is smooth (which we assume to be the case), all required partial derivatives of w can be computed.