Engineering computations: international journal for - download pdf or read online

By Adnan Ibrahimbegovic, Bostjan Brank

ISBN-10: 184544163X

ISBN-13: 9781845441630

Comprises prolonged models of the papers first awarded by means of numerous invited audio system on the NATO-sponsored complicated examine workshop on "Multi-physics and multi-scale machine types in non-linear research and optimum layout of engineering constructions below severe conditions", which was once held in Bled, Slovenia, from June thirteen to 17, 2004.

It additionally includes a couple of papers contributed by means of younger researchers, who all made brief displays in their learn works at that assembly.

The accumulated papers search to give the newest learn achievements in this presently very lively examine subject and comprise contributions on nonlinear structural research, on optimum layout of buildings and microstructures, in addition to at the structural parameters identity initially released as Engineering Computations (2005, Vol.22, No.5/6)

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Extra resources for Engineering computations: international journal for computer-aided engineering and software. Vol. 22, No. 5/6, Engineering structures: nonclinical analysis optimal design and identification

Example text

The divergence for “version 2” occurs at approximately 4 s, while “version 1” is perfectly stable up to 10 s. Up to the divergence of “version 2”, both schemes give exactly the same results (see Table III for the convergence characteristics). 9 s. 8. Conclusions A detailed development of the parametrization of constrained finite rotations for dynamics of shells is presented. We recognized that the incremental rotation vector parameterization is the most suitable choice for handling the dynamics of shells in the sense of: .

2001). Standard implementation is used for computing the translational motion components, and necessary modifications are proposed for computing the components related to the constrained rotation of the shell-director. Considering the typical time interval between tn and tnþ 1 the algorithmic problem _ n ; and acceleration, can be described as: given at time tn displacement, w n, velocity, w w¨n, of translational motion of the shell mid-surface, and shell-director, t n , its constrained rotation, Ln, velocity, t_ n ; and acceleration, t€ n , find such values of w and t at time tnþ 1 that EC 22,5/6 520 dPdyn jnþ1 þ dPstat jnþ1 ¼ 0 ð91Þ and update velocities and accelerations of displacements and shell director by using the corresponding Newmark approximations.

Equation (112) satisfy condition (111). Linearization of dt with respect to intrinsic rotational variables at time tnþ 1, which are qnþ 1 and unþ 1, is not zero. It can be shown that the following forms can be obtained from equation (112) h q i ~ Ddt · b ¼ dq Y nþ1 Dqnþ1 ð113Þ h u i ~ Ddt · b ¼ du Ynþ1 Dunþ1 ~ q and Y ~ u are again functions of qnþ 1 and unþ 1, respectively. where b [ R3 and Y nþ1 nþ1 ~ q is Full form of Y nþ1 ~ q ¼ q cos q 2 sin q {qnþ1 ^ qnþ1 ½ðL n eÞ · bŠ þ I ½ðL n ðqnþ1 £ eÞÞ · bŠ} Y nþ1 q3 2 sin q I½ðL n eÞ · bŠ q sin qð3 2 q 2 Þ 2 3q cos q þ {qnþ1 ^ qnþ1 ½ðL n ðqnþ1 £ eÞÞ · bŠ} q5 þ q cos q 2 sin q {½A þ A T ŠððL n e 1 Þ · bÞ þ ½B þ B T ŠððL n e 2 Þ · bÞ} q3 where q ¼ kqnþ1 k and matrices A, B are defined as ð114Þ Constrained finite rotations in dynamics 523 EC 22,5/6 524 2 A¼4 0 3 0 q1nþ1 q2nþ1 " 5; B¼ 2q1nþ1 2q2nþ1 0 0 # ;  ÃT qnþ1 ¼ q1nþ1 ; q2nþ1 ð115Þ ~ u is given in an analogous way.

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Engineering computations: international journal for computer-aided engineering and software. Vol. 22, No. 5/6, Engineering structures: nonclinical analysis optimal design and identification by Adnan Ibrahimbegovic, Bostjan Brank


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