Hybrid-Mixed Quadrilateral Element for Laminated Plates Composed of Functionally Graded Materials
A hybrid-mixed four-node quadrilateral element for the three-dimensional stress analysis of laminated functionally graded plates through the use of the method of sampling surfaces is developed. The sampling surfaces formulation is based on choosing inside the n <sup>th</sup> layer I<sub>n</sub> not equally spaced sampling surfaces parallel to the middle surface, in order to introduce the displacements of these surfaces as basic plate variables. The sampling surfaces are located inside each layer at Chebyshev polynomial nodes that allows one to uniformly minimize the error due to the Lagrange interpolation. To avoid shear locking and have no spurious zero energy modes, the assumed natural strain concept is employed. The developed assumed natural strain four-node quadrilateral plate element passes the bending patch tests for laminated and functionally graded plates and exhibits a superior performance in the case of coarse distorted mesh configurations. It can be useful for the three-dimensional stress analysis of thick and thin laminated functionally graded plates because the sampling surfaces formulation gives the possibility to obtain the numerical solutions with a prescribed accuracy, which asymptotically approach the three-dimensional exact solutions of elasticity as the number of sampling surfaces tends to infinity.