A mass lumping scheme for the second-order numerical manifold method. (March 2019) - Zhang, Guohua; Yang, Yongtao; Zheng, Hong
Highlights: A mass lumping scheme suitable for the second-order numerical manifold method is proposed. The second-order numerical manifold method is further applied for dynamic analysis of structures. Accuracy of the proposed mass lumping scheme is demonstrated. Abstract: The numerical manifold method (NMM) has been employed to solve many types of engineering problems. To improve accuracy of the traditional NMM, a second-order NMM with six-node triangular mesh was recently proposed. This second-order NMM is further applied for structural dynamic problems in this study. In order to reduce time consumption in solving large scale simultaneous algebraic equations, a mass lumping scheme which is suitable for the second-order NMM is proposed. A series of numerical examples show that natural frequencies of structures assessed from the proposed lumped mass matrix (LMM) are more accurate than those from the consistent mass matrix (CMM). In addition, even in the implicit time integration scheme to predict dynamic responses of structures, the CMM can be replaced by the proposed LMM without losing accuracy.