Effect of Mass Matrix Formulation Schemes on Dynamics of Structures

Finite element modeling for dynamic analysis of large and complex structures such as ship hulls, offshore structures, aerospace structures etc, introduces a very large computational overhead due to presence of large number of elements and nodes. Proper representation of mass and inertia properties is critical for accuracy and reliability of results. Different mass representation schemes have influences on assembling time, storage space of matrices, and solution time. Errors in natural frequencies and mode shapes precipitate to significant errors in dynamic response analysis. To arrive at efficient error analysis procedures for vibration analysis, detailed studies on performance of the various mass lumping schemes are necessary. Investigations conducted in the present study are aimed at understanding the influence of the mass lumping and its distribution based on accuracy of the results of the dynamic analysis. Detailed studies have been conducted to investigate the performance of the existing methods of representation of mass that are generally employed for free vibration and dynamic response analysis of structures using finite element method (FEM). A number of configuration for free vibration analysis of beams, plates, and plates under plane stress state have been solved using different finite elements, mesh configurations schemes in ANSYS. Results of some configuration are validated with analytical solution wherever possible, results for other configuration are compared with results obtained from the computer program given by K. J. Bathe - modified to accept banded matrices apart from skyline form. The investigation also includes shape distortion and its effect on vibration characteristics. The studies show that the mass lumping scheme used has significant influence over the accuracy of the results of dynamic analysis.
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