Three-dimensional free vibration analyses of preloaded cracked plates of functionally graded materials via the mls-ritz method

Chiung Shiann Huang*, Hao Ting Lee, Pin Yu Li, Ming Ju Chang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this study, the moving least squares (MLS)-Ritz method, which involves combining the Ritz method with admissible functions established using the MLS approach, was used to predict the vibration frequencies of cracked functionally graded material (FGM) plates under static loading on the basis of the three-dimensional elasticity theory. Sets of crack functions are proposed to enrich a set of polynomial functions for constructing admissible functions that represent displacement and slope discontinuities across a crack and appropriate stress singularity behaviors near a crack front. These crack functions enhance the Ritz method in terms of its ability to identify a crack in a plate. Convergence studies of frequencies and comparisons with published results were conducted to demonstrate the correctness and accuracy of the proposed solutions. The proposed approach was also employed for accurately determining the frequencies of cantilevered and simply supported side-cracked rectangular FGM plates and cantilevered internally cracked skewed rhombic FGM plates under uniaxial normal traction. Moreover, the effects of the volume fractions of the FGM constituents, crack configurations, and traction magnitudes on the vibration frequencies of cracked FGM plates were investigated.

Original languageEnglish
Article number7712
JournalMaterials
Volume14
Issue number24
DOIs
StatePublished - 1 Dec 2021

Keywords

  • Cracked FGM plates
  • Enriched basis functions
  • MLS-Ritz method
  • Threedimensional elasticity
  • Vibrations

Fingerprint

Dive into the research topics of 'Three-dimensional free vibration analyses of preloaded cracked plates of functionally graded materials via the mls-ritz method'. Together they form a unique fingerprint.

Cite this