An isogeometric formulation with a three-variable high order shear deformation theory for free vibration analysis of FG porous plates reinforced by graphene platelets

  • Lieu B. Nguyen Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, 01 Vo Van Ngan street, Thu Duc city, Ho Chi Minh city, Vietnam
  • Thi Bui Viet Center of Construction Inspection and Consulting, CCIC, Thu Dau Mot University, 6 Tran Van On street, Thu Dau Mot city, Binh Duong province, Vietnam
  • Hong-Yen Nguyen Board of Directors Office, Binh Duong University, 504 Binh Duong avenue, Thu Dau Mot city, Binh Duong province, Vietnam

Abstract

We present a generalized three-variable high order shear deformation theory (THSDT) using isogeometric analysis (IGA) to analyze free vibration of functionally graded porous (FGP) plates reinforced by graphene platelets (GPLs) in this work. It is named as FGP-GPLs for a short. The proposed theory only has got three degrees of freedom (DOFs) per node as the same way of numerically solutions in three-dimensional (3D) solids. THSDT fulfills the classical plate theory (CPT), the first-order shear deformation theory (FSDT) and even the higher-order shear deformation theory (HSDT). IGA is chosen to analyze because of its noteworthy advantages in numerical computational sides of plate problems. In addition, the displacement field of THSDT needs the high continuity in approximated formulation with high-order derivatives for a weak form of fourth order equation. According to IGA formulation based on the generalized THSDT, the shear locking phenomenon is free. The variables of THSDT are less than HSDTs which contain five DOFs per node. The influences of weight fractions, the coefficient porosity, dispersion patterns of GPLs and distribution types of porosity on structure’s natural frequencies are studied through some numerical examples. In order to prove the reliability and accuracy of present method, the numerical results are compared to available published works.

Keywords:

FG-porous plate; graphene platelet reinforcements; three-variable high order shear deformation theory (THSDT); isogeometric analysis; free vibration.

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Published
15-04-2021
How to Cite
Nguyen, L. B., Viet, T. B., & Nguyen, H.-Y. (2021). An isogeometric formulation with a three-variable high order shear deformation theory for free vibration analysis of FG porous plates reinforced by graphene platelets. Journal of Science and Technology in Civil Engineering (STCE) - NUCE, 15(2), 51-66. https://doi.org/10.31814/stce.nuce2021-15(2)-05
Section
Research Papers