caa a22 4500 445361352 CHVBK 20180317142916.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s11071-010-9898-9 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9898-9 Sparse matrix implicit numerical integration of the Stiff differential/algebraic equations: Implementation [Elektronische Daten] [Bassam Hussein, Ahmed Shabana] The finite element absolute nodal coordinate formulation (ANCF) is often used in modeling very flexible bodies in multibody system (MBS) applications. This formulation leads to a constant mass matrix, allowing for an efficient sparse matrix implementation. Nonetheless, the use of the ANCF finite elements to model stiff structures can lead to high frequencies associated with ANCF coupled deformation modes, as discussed in the literature. Implicit numerical integration methods can be effectively used to develop efficient procedures for the solution of MBS differential/algebraic equations. Most existing implicit integration algorithms, however, require numerical differentiation of the equations of motion, and some of these integration methods do not ensure that the kinematic algebraic constraint equations are satisfied at all levels (position, velocity, and acceleration). Because of these limitations, existing implicit integration methods can be less accurate and less efficient when used to solve large scale MBS applications. In order to circumvent this problem, the two-loop implicit sparse matrix numerical integration (TLISMNI) method was proposed for the solution of MBS differential/algebraic equations. The TLISMNI method does not require numerical differentiation of the forces and allows for an efficient sparse matrix implementation. This paper discusses TLISMNI implementation issues including the step size selection, the error control, and the effect of the numerical damping. The relation between the step size selection and the structure stiffness is also discussed. The use of the computer implementation described in this paper is demonstrated by solving very stiff structure problems using the Hilber-Hughes-Taylor (HHT) method, which includes numerical damping. An eigenvalue analysis and Fast Fourier Transform (FFT) are performed in order to identify the fundamental modes of deformation and demonstrate that the contributions of these fundamental modes can be erroneously damped out when some other implicit integration methods are used. The TLISMNI method, on the other hand, captures the contributions of these fundamental modes. The results, obtained using the TLISMNI method, are compared with the results obtained using other methods including the implicit HHT-I3 and the explicit Adams integration methods. The results obtained show that the TLISMNI method can be five times faster than the other two methods when no numerical damping is considered. Springer Science+Business Media B.V., 2010 Differential/algebraic equations nationallicence Implicit numerical integrations nationallicence Multibody systems nationallicence Sparse matrix implementation nationallicence Hussein Bassam Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 West Taylor Street, 60607, Chicago, IL, USA aut Shabana Ahmed Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 West Taylor Street, 60607, Chicago, IL, USA aut Nonlinear Dynamics Springer Netherlands 65/4(2011-09-01), 369-382 0924-090X 65:4<369 2011 65 11071 https://doi.org/10.1007/s11071-010-9898-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9898-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hussein Bassam Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 West Taylor Street, 60607, Chicago, IL, USA aut NATIONALLICENCE 700 1- Shabana Ahmed Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 West Taylor Street, 60607, Chicago, IL, USA aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 65/4(2011-09-01), 369-382 0924-090X 65:4<369 2011 65 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer