Non-conforming solid elements for the analyses of bending deformation of isotropic/orthotropic materials with the smallest DOF

摘要

This paper proposes both a 3-D 10-node equivalent solid element and a 2-D 5-node equivalent solid element. These proposed elements have the smallest number of degree of freedom among 3-D/2-D solid elements, taking into consideration bending deformation as well as extensional and shear deformations of solids. The proposed elements exhibit greater bending stiffness than the conventional 2-D/3-D solid elements, due to the reduction of degrees of freedom. This phenomenon of greater stiffness was corrected by using a modification of Gauss sampling points. The quantity of modification is expressed as a function of material properties. Adopting this kind of modification, we can show that even the conventional 4-node elements can be applied to the analysis, of bending problem successfully in proper fine mesh. The proposed elements pass the patch test and have no spurious zero energy modes. The effectiveness of MQ10 element (Q10 with the modification) is tested in several examples. The results of static and free vibration analyses of isotropic/orthotropic plates using MQ10 elements show good agreements with those using 20-node element. In addition, damped/undamped forced motion analyses using MQ10 elements were carried out, and compared with those of a 20-node element. [References: 8]