Get Analysis and Simulation of Contact Problems PDF

By T.A. Laursen (auth.), Peter Wriggers Professor Dr., Udo Nackenhorst Professor Dr. (eds.)

ISBN-10: 3540317600

ISBN-13: 9783540317609

ISBN-10: 3540317619

ISBN-13: 9783540317616

Contact mechanics was once and is a vital department in mechanics which covers a large box of theoretical, numerical and experimental investigations. during this rigorously edited booklet the reader will receive a cutting-edge evaluate on formula, mathematical research and numerical answer strategies of touch difficulties. The contributions accrued during this quantity summarize the lectures provided throughout the 4th touch Mechanics overseas Symposium (CMIS) held in Hannover, Germany, 2005, by means of top scientists within the zone of touch mechanics.

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Example text

Thus, in the combined finite-discrete element method a finite-strain elasticity element formulation is adopted. This is best demonstrated on a constant strain triangle. The matrix of the deformation gradient tensor for this element is obtained as follows   ∂xc ∂xc  ∂xi ∂yi  ˆix ˆjx −1  = x1c − x0c x2c − x0c (1) F=  ∂yc ∂yc  ˆiy ˆjy y1c − y0c y2c − y0c ∂xi ∂yi where the transformation matrix is given by ˆix ˆiy ˆjx ˆjy = x1i − x0i y1i − y0i x2i − x0i y2i − y0i (2) and x0i ,y0i x1i ,y1i , x2i , y2i , x0c , y0c ,x1c ,y1c ,x2c , y2c are initial and current coordinates of node 0, 1 and 2 respectively.

T. Laursen. Computational Contact and Impact Mechanics. Springer Berlin Heildelberg, 2002. 11. M. Puso and T. Laursen. A mortar segment-to-segment contact method for large deformation solid mechanics. Comput. Methods Appl. Mech. , 193(68):601-629, 2004. 12. G. Stadler. Semismooth Newton and augmented Lagrangian methods for a simplified friction problem. SIAM J. , 15(1):39-62, 2004. 13. K. Willner. Kontinuums- und Kontaktmechanik. Springer, 2003. 14. P. Wriggers. Computational Contact Mechanics. J.

For the stress-strain relation of the material, we consider σ = (λ + 2/3µ) tr(ε) − 3αθ + 2µdev(ε). α denotes the thermal expansion coefficient. The balance conditions are given by −div(σ) = 0 and div(q) = r, where q = −Kgrad(θ) denotes the heat flux, the mass density and r the heat source. On the contact zone, we use the heat law qc = kc [θ] with the contact heat flux qc = q · n. , [14], where λm denotes the mechanical Lagrange multiplier. Let λθ = p∈S qp ψp be the thermal part of the Lagrange multiplier representing the heat flux qc .

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Analysis and Simulation of Contact Problems by T.A. Laursen (auth.), Peter Wriggers Professor Dr., Udo Nackenhorst Professor Dr. (eds.)


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