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2 Computer Assisted Mechanics and Engineering Sciences

2 1998

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Numerical results on the locking for cylindrical shells

Chinosi C., Della Croce L., Scapolla T.

Computer Assisted Mechanics and Engineering Sciences

1998

Vol. 5, nr 1

31-44

We investigate the performance of the Naghdi shell model using a family of hierarchic high order finite elements. We solve two cylindrical shell problems representative of extermely discriminating situations: the membrane dominated Scordelis-Lo problem and a bending dominated problem already tested by Leino and Pitkaranta. As it is well know, these problems are hard tests for shell elements, especially when the thickness of the shell is approaching to zero, since the presence of hidden constraints can lead to numerical convergence problems, known as shear and membrane locking. The numerical results show the robustness of the finite elements developed, able to avoid the locking behavior.

Hierarchic finite elements for thin plates and shells

Chinosi C., Della Croce L., Scapolla T.

Computer Assisted Mechanics and Engineering Sciences

1998

Vol. 5, nr 2

151-160

We consider the numerical approximation of thin plate and shell structures. The plate model is described following the Reissner -Mindlin assumptions while the shell is described using the Naghdi formulation. It is well known that the numerical approximation with standard finite elements suffers of the so-called locking phenomenon, i. e., the numerical solution degenerates as the thickness of the structure becomes smaller. Plates exhibit shear locking and shells show both shear and membrane locking. Several techniques to avoid the numerical locking have been proposed. Here we solve the problems using a family of high order hierarchic finite elements. We present several numerical results that show the robustness of the finite elements, able to avoid in many circumstances the locking behavior.