TY - JOUR

T1 - Least-squares finite element approximations to the Timoshenko beam problem

AU - Jou, Jang

AU - Yang, Suh Yuh

PY - 2000/10/6

Y1 - 2000/10/6

N2 - In this paper a least-squares finite element method for the Timoshenko beam problem is proposed and analyzed. The method is shown to be convergent and stable without requiring extra smoothness of the exact solutions. For sufficiently regular exact solutions, the method achieves optimal order of convergence in the H1-norm for all the unknowns (displacement, rotation, shear, moment), uniformly in the small parameter which is generally proportional to the ratio of thickness to length. Thus the locking phenomenon disappears as the parameter tends to zero. A sharp a posteriori error estimator which is exact in the energy norm and equivalent in the H1-norm is also briefly discussed.

AB - In this paper a least-squares finite element method for the Timoshenko beam problem is proposed and analyzed. The method is shown to be convergent and stable without requiring extra smoothness of the exact solutions. For sufficiently regular exact solutions, the method achieves optimal order of convergence in the H1-norm for all the unknowns (displacement, rotation, shear, moment), uniformly in the small parameter which is generally proportional to the ratio of thickness to length. Thus the locking phenomenon disappears as the parameter tends to zero. A sharp a posteriori error estimator which is exact in the energy norm and equivalent in the H1-norm is also briefly discussed.

UR - http://www.scopus.com/inward/record.url?scp=0034299560&partnerID=8YFLogxK

U2 - 10.1016/S0096-3003(99)00139-3

DO - 10.1016/S0096-3003(99)00139-3

M3 - 期刊論文

AN - SCOPUS:0034299560

SN - 0096-3003

VL - 115

SP - 63

EP - 75

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 1

ER -