General formulation of C~0 bending models based on the rational w-θ constraint

摘要

With regard to the C~0 plate bending elements, the constraints resulting from the Kirchhoff condition are separated into two sets. The first set is called the zero θ constraint and should be released so that there is no shear locking. The second set is called the w-θ constraint and should be imposed to determine the element shear strain. We take the line segment integral of the Kirchhoff condition to establish the rational version of w-θ constraint which ensures the resulting element to pass the patch test. In such a way, the 4, 8 and 9-node C~0 bending models are presented as a general formulation. The resulting elements, in particular the 9-node one, show excellent numerical performance.