TY - JOUR
T1 - Improving the Bergan Wang Quadrilateral plate element by using the UI approach for analysis of isotropic and FGM sandwich plates
AU - Katili, Andi Makarim
AU - Katili, Irwan
N1 - Funding Information:
The authors gratefully acknowledges financial support from the Indonesian Ministry of Education, Culture, Research, and Technology through the PDUPT program (Grant number: NKB-852/UN2.RST/HKP.05.00/2022 ).
Publisher Copyright:
© 2022 Elsevier Ltd
PY - 2023/2
Y1 - 2023/2
N2 - This work presents the improvement of Bergan Wang Quadrilateral (BWQ) element using the UI (unified and integrated) approach. In this approach, a new formulation of quadrilateral plate element is developed with a single independent variable just like what Bergan and Wang applied to develop a non-conforming BWQ element. The difference between the two approaches lies in the formulation of transverse displacement w, wherein the UI approach transverse displacement w is expressed as the sum of transverse bending, and shear displacements (wb and ws) and the transverse bending displacement wb becomes the single independent variable. The transverse shear displacement ws is defined as the second derivative of the transverse bending displacement wb. The rotations, curvatures, and shear strains are the first, second, and third derivatives of the bending displacement wb. The resulting non-conforming element, called UI-Q4 element, has proper rank, no shear locking problem, and passes the patch test. To examine the element convergence and accuracy, standard benchmark problems of isotropic plates, i.e. square plates, Razzaque and Morley skew plates, and circular plates, are used. The UI-Q4 element shows very good performance, which is observed by comparing it with MITC4, DSQK and BWQ elements. Moreover, the application of UI-Q4 element for analysing functionally graded material (FGM) sandwich plate analysis also performs well and delivers results which are quickly converged to the reference values.
AB - This work presents the improvement of Bergan Wang Quadrilateral (BWQ) element using the UI (unified and integrated) approach. In this approach, a new formulation of quadrilateral plate element is developed with a single independent variable just like what Bergan and Wang applied to develop a non-conforming BWQ element. The difference between the two approaches lies in the formulation of transverse displacement w, wherein the UI approach transverse displacement w is expressed as the sum of transverse bending, and shear displacements (wb and ws) and the transverse bending displacement wb becomes the single independent variable. The transverse shear displacement ws is defined as the second derivative of the transverse bending displacement wb. The rotations, curvatures, and shear strains are the first, second, and third derivatives of the bending displacement wb. The resulting non-conforming element, called UI-Q4 element, has proper rank, no shear locking problem, and passes the patch test. To examine the element convergence and accuracy, standard benchmark problems of isotropic plates, i.e. square plates, Razzaque and Morley skew plates, and circular plates, are used. The UI-Q4 element shows very good performance, which is observed by comparing it with MITC4, DSQK and BWQ elements. Moreover, the application of UI-Q4 element for analysing functionally graded material (FGM) sandwich plate analysis also performs well and delivers results which are quickly converged to the reference values.
KW - FGM sandwich plates
KW - Finite element
KW - Free formulation concept
KW - Quadrilateral element
KW - UI approach
UR - http://www.scopus.com/inward/record.url?scp=85143613102&partnerID=8YFLogxK
U2 - 10.1016/j.tws.2022.110328
DO - 10.1016/j.tws.2022.110328
M3 - Article
AN - SCOPUS:85143613102
SN - 0263-8231
VL - 183
JO - Thin-Walled Structures
JF - Thin-Walled Structures
M1 - 110328
ER -