A condensed algorithm for adaptive component mode synthesis of viscoelastic flexible multibody dynamics

• Published in: International journal for numerical methods in engineering Vol. 122; no. 2; pp. 609 - 637
• Main Authors: Tang, Yixuan, Hu, Haiyan, Tian, Qiang
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 30.01.2021; Wiley Subscription Services, Inc
• Subjects: absolute nodal coordinate formulation; Accuracy; Adaptive algorithms; Adaptive systems; Algorithms; Component mode synthesis; condensed algorithm for adaptive component mode synthesis; Configurations; Damping; flexible multibody dynamics; Geometric nonlinearity; Iterative algorithms; Iterative methods; Modal choice; modal reductions; Multibody systems; Static equilibrium; Stiffness; Subsystems; viscoelastic damping; Viscoelasticity
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6552

A condensed algorithm for adaptive component mode synthesis is proposed to compute the dynamics of viscoelastic flexible multibody systems efficiently and accurately. As studied, the continuous use of modes derived from the initial configuration will lead to poor convergence when dealing with geometric nonlinearity caused by large deformations and overall rotations. The modal reduction at a series of quasi‐static equilibrium configurations should be updated accordingly. According to the loss rate of system energy in the updating process of modal bases, an adaptive mode selection is proposed to reserve the optimal modal bases with their modal number automatically so as to achieve a high‐accuracy simulation. In the proposed condensed iteration algorithm, the order of reduced dynamic equations in the Newton‐Raphson is far less than the number of the unknowns to be discrete in generalized‐α scheme. Using an analytical mapping between the two parts of unknowns, the new algorithm solves a small part of the unknowns iteratively and solves the others noniteratively. Therefore, the saving of time cost comes not only from the proposed adaptive component mode synthesis, but also from the proposed condensed iteration algorithm. The modal bases of subsystems are updated by a series of frame‐like quasi‐static equilibrium configurations independently, in conjunction with the Craig‐Bampton method. Thus, the challenges in the model reduced of extensive ranges of stiffness and damping are removed via the successively updated modal bases. Finally, three numerical tests are made to illuminate the high accuracy and efficiency of the new algorithm proposed.