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Partial mixed 3‐D element for the analysis of thick laminated composite structures
Author(s) -
Liao ChungLi,
Tsai J. S.
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620350709
Subject(s) - transverse plane , displacement field , finite element method , stiffness matrix , displacement (psychology) , shear (geology) , transverse shear , variational principle , boundary value problem , structural engineering , mathematical analysis , geometry , materials science , mathematics , engineering , composite material , psychology , psychotherapist
For the analysis of thick laminated composite structures this paper proposes a partial mixed 3‐D element. The variational principle of this new element is obtained by modifying the Hellinger–Reissner principle. The functional of the present stationary principle is constructed by treating three displacements ( u, v, w ) and two transverse shear stresses (τ xz , τ 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 (σ x , σ y , τ xy , σ 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 3‐D element in the analysis of thick laminated composite structures.