By Günter Hofstetter (eds.)
The booklet offers state of the art works in computational engineering. concentration is on mathematical modeling, numerical simulation, experimental validation and visualization in engineering sciences. specifically, the next issues are awarded: constitutive types and their implementation into finite point codes, numerical types in nonlinear elasto-dynamics together with seismic excitations, multiphase types in structural engineering and multiscale versions of fabrics platforms, sensitivity and reliability research of engineering buildings, the applying of medical computing in city water administration and hydraulic engineering, and the applying of genetic algorithms for the registration of laser scanner aspect clouds.
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Extra resources for Computational Engineering
14: Ri ; TOL D 10 3 and Ri ; TOL D 10 7 (both 32 W. Fellin and A. 39), err " D Extrapolated Euler, TOL D 10 10 Euler steps It. No. 1 2 3 4 5 6 err " "num "an "an i R 380:8 124:6 6:040 1:629 1:195 5:573 0:124 10 10 10 2 7 18 It. No. 1 2 3 4 5 6 err " 10 i R 261:1 52:07 1:267 8:024 10 4 3:218 10 10 4:629 10 20 5:400 10 11 with AERR D 10 6 ). The Newton iteration shows quadratic convergence when the numerical residual Ri is near the analytic residual Ran . We loose the quadratic convergence when the residual is of the same order as the tolerance of the time integration.
10 Numerical Approximation of the Jacobian Working out the Jacobian analytically for a complex constitutive model can be a tedious task or sometimes even not feasible. Thus we want to use a numerical approximation. #/ ; dt @T @D which is a good approximation to the variational equation for small #. 88) we see that B D C for # ! 0. If # is sufficiently small, B. t /= t will be thus a good approximation to the Jacobian. 11 Example We investigate a simple but illustrative example to study some numerical aspects.
Switching to semi-implicit integration in numerically stiff regions is worth thinking about. However, as these regions are typically small and any switch algorithm will take some extra time, the effect on the overall performance is assumed to be small. 4 Application to Elasto-Plasticity Here we show the applicability of the numerical time integration strategies to an extended von Mises elasto-plastic model. For the sake of simplicity we will formulate the model in principal stresses, which is sufficient as we will calculate the stress response of an unconfined compression test.