アイソパラメトリック要素の剛性マトリックスの数値積分法に関する考察第 2 報 : 平面板の曲げにおけるロッキングと低減積分の効果

抄録

Solutions by isoparametric plate bending elements in thin plate situations diverge form the ones predicted by kirchhoff's theory. This phenomenon is known as the locking phenomenon. In this part, the influence of integration schemes of stiffness matrices on the locking is investigated. The elements considered here are three-, four-, six-, eight- and nine-node elements. The numerical integration schemes considered here are exact integration, uniform reduced integration and selective reduced integration. It is theorectically clarified that the condition that transverse shear energy is zero in thin plate situations yields equations of linearly dependent relation for displacement degrees-of-freedom whose number are equal to the rank of transverse shear stiffness matrices and, thus, the condition which must be satisfied to avoid the locking is that transverse shear stiffness matrices are singular. Square plates subjected to a concentrated load at the center are analysed and the rank of transverse shear stiffness matrices, displacements and strain energy are calculated. According to the results obtained, it is shown that in many cases reduced integration introduces singularities in transverse shear stiffness matrices and, therefore, the locking is avoided.