Abstract
For the analysis of thick laminated composite structures this paper proposes a partial mixed 3βD element. The variational principle of this new element is obtained by modifying the HellingerβReissner principle. The functional of the present stationary principle is constructed by treating three displacements (u, v, w) and two transverse shear stresses (Ο~xz~, Ο~yz~) as independent of each other. Hence the nodal variables of the present mixed element contain three displacements and two transverse shear stresses. The other stresses (Ο~x~, Ο~y~, Ο~xy~, Ο~z~) are computed from the assumed displacement field and nodal displacement field and nodal displacements. The present element can satisfy the requirements of (1)transverse shear stress continuity between laminate layers and (2)boundary conditions of free transverse shear stresses on the top and bottom surfaces. These requirements are violated by conventional displacement finite elements. Since the stiffness matrix of the present element is formulated by combining a displacement model and a mixed model, it is definite, rather than indefinite as for the conventional mixed elements. Also, these two transverse shear stresses are part of the solution variables and are solved directly together with displacements. Examples are presented to demonstrate the accuracy and efficiency of this proposed partial mixed 3βD element in the analysis of thick laminated composite structures.