Abstract
An extended edge-based smoothed discrete shear gap method (XES-DSG3) is proposed for free vibration analysis of cracked Reissner–Mindlin plate by implementing the edge-based strain smoothing operation into the discrete shear gap-based extended finiteelement method (XFEM-DSG3). In present method, the strain smoothing operation is implemented into the bending strain gradient matrices, in which the enriched functions are included. Then, the derivatives of element shape functions and derivatives of crack-tip singular enriched functions are not required in the computation. The calculation of element matrices is performed over the smoothing domains which are associated with edges of elements. The transverse shear locking of Reissner–Mindlin plate can be avoided by using the integration of discrete shear gap (DSG) method. Several numerical examples are investigated to illustrate the accuracy of XES-DSG3 for the free vibration analysis of cracked Reissner–Mindlin plate. Moreover, numerical results show that the present method is insensitive to mesh distortion and it is more stable than the pervious XFEM-DSG3.
| Original language | English |
|---|---|
| Pages (from-to) | 477-504 |
| Number of pages | 28 |
| Journal | Applied Mathematical Modelling |
| Volume | 51 |
| DOIs | |
| Publication status | Published - 1 Nov 2017 |
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An extended edge-based smoothed discrete shear gap method for free vibration analysis of cracked Reissner–Mindlin plate. / Yang, Gang; Hu, Dean; Han, Xu; Ma, Guowei.
In: Applied Mathematical Modelling, Vol. 51, 01.11.2017, p. 477-504.Research output: Contribution to journal › Article
TY - JOUR
T1 - An extended edge-based smoothed discrete shear gap method for free vibration analysis of cracked Reissner–Mindlin plate
AU - Yang, Gang
AU - Hu, Dean
AU - Han, Xu
AU - Ma, Guowei
PY - 2017/11/1
Y1 - 2017/11/1
N2 - An extended edge-based smoothed discrete shear gap method (XES-DSG3) is proposed for free vibration analysis of cracked Reissner–Mindlin plate by implementing the edge-based strain smoothing operation into the discrete shear gap-based extended finiteelement method (XFEM-DSG3). In present method, the strain smoothing operation is implemented into the bending strain gradient matrices, in which the enriched functions are included. Then, the derivatives of element shape functions and derivatives of crack-tip singular enriched functions are not required in the computation. The calculation of element matrices is performed over the smoothing domains which are associated with edges of elements. The transverse shear locking of Reissner–Mindlin plate can be avoided by using the integration of discrete shear gap (DSG) method. Several numerical examples are investigated to illustrate the accuracy of XES-DSG3 for the free vibration analysis of cracked Reissner–Mindlin plate. Moreover, numerical results show that the present method is insensitive to mesh distortion and it is more stable than the pervious XFEM-DSG3.
AB - An extended edge-based smoothed discrete shear gap method (XES-DSG3) is proposed for free vibration analysis of cracked Reissner–Mindlin plate by implementing the edge-based strain smoothing operation into the discrete shear gap-based extended finiteelement method (XFEM-DSG3). In present method, the strain smoothing operation is implemented into the bending strain gradient matrices, in which the enriched functions are included. Then, the derivatives of element shape functions and derivatives of crack-tip singular enriched functions are not required in the computation. The calculation of element matrices is performed over the smoothing domains which are associated with edges of elements. The transverse shear locking of Reissner–Mindlin plate can be avoided by using the integration of discrete shear gap (DSG) method. Several numerical examples are investigated to illustrate the accuracy of XES-DSG3 for the free vibration analysis of cracked Reissner–Mindlin plate. Moreover, numerical results show that the present method is insensitive to mesh distortion and it is more stable than the pervious XFEM-DSG3.
KW - Cracked Reissner–Mindlin plate
KW - Discrete shear gap method
KW - Extended finite element method
KW - Mesh distortion
KW - Strain smoothing
KW - Vibration analysis
UR - http://www.scopus.com/inward/record.url?scp=85029009172&partnerID=8YFLogxK
U2 - 10.1016/j.apm.2017.06.046
DO - 10.1016/j.apm.2017.06.046
M3 - Article
VL - 51
SP - 477
EP - 504
JO - Applied Mathematics Modelling
JF - Applied Mathematics Modelling
SN - 0307-904X
ER -