アイソパラメトリックMindlin板曲げ要素に関する研究 : (その1)9節点要素

抄録

An improved displacement finite element method for shear-deformable plate bending element is developed and applied to a 9-node, 27-degree-of-freedom quadrilateral element. Based on the concept of the so-called Kirchhoff-mode criterion, two rotations : (θ_x, θ_y) and a deflection : w are assumed to be quadratic and cubic, respectively, wherein additional internal variables are employed for the latter with the ordinary nodal displacement parameters. In the numerical energy integration method, the Lobatto's formula, which has integration points on the corners and mid-sides as well as the center of the element, is adopted instead of the Gauss-Ledendre's often used in the finite element analyses. It is shown that the present element has no spurious zero energy modes and hardly locks. Also, the continuity on inter-elements and the completeness of shape functions are, with the accuracy of the employed integration formula, particularly examined in order to see the covergence aspect. Several numerical experiments are performed and show that the present element gives excellent results for both thin and thick plates.