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 students, researchers and practitioners drawn to numerical sturdy and structural research in addition to engineers and scientists facing applied sciences within which tribological reaction has to be characterised, the publication comprises an introductory yet designated evaluate of nonlinear finite point formulations earlier than facing touch and impression particularly. subject matters encompassed contain continuum mechanics, mathematical constitution, variational framework and finite point implementations linked to contact/impact interplay. also, very important and at present rising learn subject matters in computational touch mechanics are brought, encompassing such themes as tribological complexity, conservative therapy of inelastic impression interplay and novel spatial discretization innovations.
Read or Download Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis PDF
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Additional resources for Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis
The interested reader should consult [HugOO] for details. 2 A Point of Departure: Reformulation of the IBVP for the Finite Strain Case With some foundation now established through consideration of the small strain problem, one may readily introduce changes to this framework introduced by finite deformations. Virtually all of the physical ideas summarized in the last section survive, but more generality is required in definition of the general kinematic framework, the stress and strain measures, and the constitutive descriptions to be utilized.
167) resulting in satisfaction ofthis condition. Note that the only restriction on the tp h is that they must result in satisfaction of the homogeneous boundary condition on r u; they are otherwise arbitrary. ), find r,of E for each time t such that: 1 et ""; (0) [pw h • a h + [\7w h ] : u h ] dv =! wh . ""; (0) f dv + 1 ""; (f .. 169), u h refers to the Cauchy stress field computed from the discrete mapping r,of through the constitutive relations, while a h is the discrete material acceleration.
This integrator is second order accurate and unconditionally stable for linear problems, meaning that the spectral radii of the integrator remain less than 1 in modulus for any time step ilt. 1. • Central differences (a = 1,(3 = 0,,), = 1/2). This integrator is second order accurate and only conditionally stable, meaning that linearized stability is only retained when ilt is less than some critical value. 2. 1 Implicit Methods To introduce the concept of an implicit finite element method we examine the trapezoidal rule, which is simply that member of the Newmark family obtained by setting (3 = 1/4 and')' = 1/2.