A QUADRILATERAL THIN-THICK PLATE BENDING ELEMENT BY USING AREA COORDINATE METHOD

In this paper,a new quadrilateral thin-thick plate bending element with only 12 degrees of freedom, TACQ,is developed by using the area coordinate method.The basic idea of above approach is as follows. Firstly, on the basis of Mindlin thick plate theory, deflection and shear strain fields are assumed independently. Then the rotation fields are derived from the shear strain and the deflection fields. Secondly, the shear strain along each side of the element is determined based on Timoshenko beam theory. Then the shear strain fields in the domain of the element are determined with rational interpolation. Thirdly, the deflection field of the element is obtained by using the point compatibility conditions of the deflection at the element nodes, and the side average compatibility conditions of the deflection and the normal rotation along each side.This approach has two characteristics. (1) The convergence is ensured because the point and side-average generalized compatibility conditions are satisfied. (2) The shear strain fields are degenerated to be zero under the thin plate situation, so there is no shear locking phenomenon. Numerical examples show that this element is effective for a large range of thickness-span ratio from very thin plate to thick plate.