An Optimal Support Size Selection for Interpolatory Lumped-Mass Meshfree Collocation in Structural Vibration Analysis

The accuracy of meshfree collocation methods is highly sensitive to the support size, yet a theoretically grounded approach for its optimal selection remains lacking. To address this issue in structural vibration analysis, an optimal support size selection method for the interpolatory lumped-mass meshfree collocation method is presented. Guided by the discrete governing equations and local truncation error theory, a frequency error expression is derived. The intrinsic relationship among the error expression, the support size and the second order derivatives of the shape functions is then investigated to identify the factors governing frequency accuracy. This analysis enables the proposed method to select the optimal support size, thereby improving the scheme’s frequency accuracy. Results show that the frequency accuracy is directly governed by the error expression, where a smaller coefficient consequently yields higher accuracy. Importantly, the approach does not depend on the specific problem. Optimal performance is achieved through a straightforward comparison of the error expression results for candidate support sizes. Additionally, the interpolatory lumped-mass meshfree collocation method effectively eliminates the spurious modes often generated by the conventional lumped-mass meshfree collocation approach. The validity of the theoretical analysis is conclusively demonstrated through a series of numerical examples.