G.  Cocchetti

M.  Pagani

U.  Perego

PEREGO, UMBERTO

COCCHETTI, GIUSEPPE

PAGANI, MARA

Archivio istituzionale della ricerca - Politecnico di Milano

11th World Congress on Computational Mechanics (WCCM XI)5th European Conference on Computational Mechanics (ECCM V)6th European Conference on Computational Fluid Dynamics (ECFD VI)July 20–25, 2014, Barcelona, SpainSELECTIVE MASS SCALING FOR SOLID-SHELLELEMENTS IN EXPLICIT DYNAMICS ANALYSESU. Perego1, G. Cocchetti1 and M. Pagani 21 Department of Civil and Environmental Engineering, Politecnico di Milano, p.zza L. da Vinci32, 20133 Milano, Italy, umberto.perego@polimi.it, giuseppe.cocchetti@polimi.it,http://www.dica.polimi.it2 Comsol s.r.l., v.le Duca degli Abruzzi 103, 25124 Brescia, Italy, mara.pagani@comsol.com,http://www.comsol.itKey words: Explicit Dynamics, Solid-Shell Elements, Selective Mass Scaling.In view of the current trends in the development of computing architectures, evolving inthe direction of finer and finer parallelization, often with the aid of co-processors or graph-ics card units with limited availability of on-board memory, explicit dynamics methodsfor the solution of highly nonlinear structural problems are gaining increasing attention.As it is well known, however, explicit methods are only conditionally stable and mayrequire extremely small time steps, approximately linearly decreasing in size with thesmallest element geometrical dimension in the mesh. The problem is particularly evi-dent when solid-shell elements are employed, since they present a thickness which can bea small fraction of the element in-plane dimensions. Solid-shell elements are becomingincreasingly popular as they make use of displacement degrees of freedom only and cannaturally incorporate complex three-dimensional material behaviors, even though theiruse in explicit dynamics has been seldom considered, in view of this limitation on thecritical time-step.A common way to increase the critical time step size is to scale the model inertia, whilekeeping the stiffness constant. In doing this, the objective is to reduce the high frequencymodes only, while leaving the lower ones unaltered. In particular, in inertia dominatedproblems, it is essential to leave the inertia associated to translational rigid body modesunaltered. To obtain this, several selective mass scaling techniques have been proposedin the literature (see e.g. [1, 2, 3, 4]). The common drawback of these approaches is thatthe resulting selectively scaled mass matrix is no more diagonal, even when starting froma lumped mass matrix, thus requiring the solution of a linear system for the accelerationcomputation at each time step.A different approach, specifically conceived for solid-shell elements and inspired to thescaling of rotational inertia usually adopted in classical shell elements, has been proposedU. Perego, G. Cocchetti and M. Paganiin [5]. The method is based on a linear transformation of degrees of freedom and hasthe advantage that it can be used keeping the diagonal structure of the mass matrix. Ananalytical estimate of the maximum eigenfrequency for the simple case of parallelepipedelements was also provided. An empirical strategy for the definition of the optimal selec-tive scaling factor was proposed in [6], still restricted, however, to parallelepiped elements.The case of arbitrarily distorted solid-shell elements is discussed here, together with a morerigorous strategy for the definition of the optimal scaling factor. Following the approachproposed in [7], an effective procedure for the estimation of the critical time step forthe scaled distorted element is proposed, based on a one-Gauss point integration. It isalso shown how the selective mass scaling can be equivalently interpreted as a geometricscaling in the thickness direction, thus providing a natural definition of the optimal scalingparameter: the maximum value of the scaling factor is the one which makes the currentelement thickness of the same magnitude of the average in-plane dimensions. Numericaltests allow to assess the accuracy and effectiveness of the proposed strategy.REFERENCES[1] R.W. Macek and B.H. Aubert. A mass penalty technique to control the critical timeincrement in explicit dynamic finite element analyses, Earthquake Engineering andStructural Dynamics, Vol. 24(10), 1315–1331, 1995.[2] L. Olovsson, K. Simonsson and M. Unosson. Selective mass scaling for explicit finiteelement analyses. International Journal for Numerical Methods in Engineering, Vol.63(10), 1436–1445, 2005.[3] H. Askes, D. Nguyen and A. Tyas. Increasing the critical time step: micro-inertia,inertia penalties and mass scaling. Computational Mechanics, Vol. 47(6), 657–667,2011.[4] A. Tkachuk and M. Bischoff. Variational methods for selective mass scaling. Compu-tational Mechanics, Vol. 52(3), 563–570, 2013.[5] G. Cocchetti, M. Pagani and U. Perego. Selective mass scaling and critical time-step estimate for explicit dynamics analyses with solid-shell elements. Computers &Structures, Vol. 127, 39–52, 2013.[6] M. Pagani, S. Reese and U. Perego. Computationally efficient explicit nonlinear anal-yses using reduced integration-based solid-shell finite elements. Computer Methodsin Applied Mechanics and Engineering, Vol. 268, 141–159, 2014.[7] D.P. Flanagan and T. Belytschko. Eigenvalues and Stable Time Steps for the UniformStrain Hexahedron and Quadrilateral. Journal of Applied Mechanics, 51(1), 35–40,1984.2

Selective mass scaling for solid-shell elements in explicit dynamics analyses

https://re.public.polimi.it/retrieve/handle/11311/884366/26734/2014_Perego_Cocchetti_Pagani_WCCM-ECCOMAS.pdf

Selective mass scaling for solid-shell elements in explicit dynamics analyses

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