TY - JOUR
T1 - Finite element methods for Timoshenko beam, circular arch and Reissner-Mindlin plate problems
AU - Cheng, Xiao Liang
AU - Han, Weimin
AU - Huang, Hong Ci
N1 - Funding Information:
The work was supported by Research Grant Council of Hong Kong.
PY - 1997/3/17
Y1 - 1997/3/17
N2 - In this paper some finite element methods for Timoshenko beam, circular arch and Reissner-Mindlin plate problems are discussed. To avoid locking phenomenon, the reduced integration technique is used and a bubble function space is added to increase the solution accuracy. The method for Timoshenko beam is aligned with the Petrov-Galerkin formulation derived in Loula et al. (1987) and can be naturally extended to solve the circular arch and the Reissner-Mindlin plate problems. Optimal order error estimates are proved, uniform with respect to the small parameters. Numerical examples for the circular arch problem shows that the proposed method compares favorably with the conventional reduced integration method.
AB - In this paper some finite element methods for Timoshenko beam, circular arch and Reissner-Mindlin plate problems are discussed. To avoid locking phenomenon, the reduced integration technique is used and a bubble function space is added to increase the solution accuracy. The method for Timoshenko beam is aligned with the Petrov-Galerkin formulation derived in Loula et al. (1987) and can be naturally extended to solve the circular arch and the Reissner-Mindlin plate problems. Optimal order error estimates are proved, uniform with respect to the small parameters. Numerical examples for the circular arch problem shows that the proposed method compares favorably with the conventional reduced integration method.
KW - Bubble function space
KW - Circular arch problem
KW - Finite element method
KW - Locking phenomenon
KW - Reduced integration technique
KW - Reissner-Mindlin plate problem
KW - Timoshenko beam problem
UR - http://www.scopus.com/inward/record.url?scp=0031095491&partnerID=8YFLogxK
U2 - 10.1016/S0377-0427(97)00159-3
DO - 10.1016/S0377-0427(97)00159-3
M3 - Journal article
AN - SCOPUS:0031095491
SN - 0377-0427
VL - 79
SP - 215
EP - 234
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 2
ER -