Metallurgy

Download Advanced Metallization and Interconnect Systems for Ulsi by R. C. Ellwanger, S. Q. Wang PDF

By R. C. Ellwanger, S. Q. Wang

ISBN-10: 155899341X

ISBN-13: 9781558993419

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Example text

The temporal discretisation of this system is often based on the generalised midpoint method. 16] n where n is the increment/time step number, t is the time at the start of the time step, ∆t is the length of the current time step and the parameter q Œ [0,1] determines where in the increment we want to fulfil the energy equilibrium. 5. 5 gives a second order accurate time stepping but the solution can show oscillations. , 1996). e. q = 1. 17] requires an iterative approach for solving the temperature at each time step.

There is only one term in the integrals that depends on z¢.

38]. The domain of the integral, the stresses, and the n+1i B-matrix depend on the deformation. 48] The last term is called the constitutive or material stiffness matrix. 50] Its evaluation depends on the computational algorithm used for the stress updating algorithm. This motivates the name ‘algorithmic’ constitutive matrix (Simo and Hughes, 1997, Simo and Taylor, 1985, Ponthot, 2002). 51] A modified Newton–Raphson approach may also be more efficient in mechanical analysis as stated for the thermal analysis earlier.

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