Are Higher-Order Theories and Layer-wise Zig-Zag Theories Necessary for N-Layer Composite Laminates?
Qifeng Fan1, Yaping Zhang2, Leiting Dong1,3, Shu Li1, Satya N. Atluri4
School of Aeronautic Science and Engineering, Beihang University, China
Taizhou Polytechnic College, China
Corresponding Author, Email: dong.leiting@gmail.com
Department of Mechanical Engineering, Texas Tech University, USA
Although “higher-order” and layer-wise “higher-order” plate and shell
theories for composite laminates are widely popularized in the current literature,
they involve (1) postulating very complex assumptions of plate/shell kinematics in
the thickness direction, (2) defining generalized variables of displacements, strains,
and stresses, and (3) developing very complex governing equilibrium, compatibility,
and constitutive equations in terms of newly-defined generalized kinemaic and
generalized kinetic variables. Their industrial applications are thus hindered by
their inherent complexity, and the fact that it is difficult for end-users (front-line
structural engineers) to completely understand all the newly-defined FEM DOFs
in higher-order and layer-wise theories. In an entirely different way, the authors
developed very simple lowest-order (8-node hexahedral), and higher-order
(32-node hexahedral) 3-D continuum solid-shell elements, based on the theory of
3D solid mechanics, for static and dynamic analyses of composite laminates. The
shear-locking of the lower-order 8-node hexahedral element is alleviated by independently
assuming locking-free strain fields for each element. Over-integration
is used to evaluate the element stiffness matrices of laminated structures with an
arbitrary number of laminae, while only one element is used in the thickness direction
without increasing the number of degrees of freedom. A stress-recovery
approach is used to compute the distribution of transverse stresses by considering
the equations of 3D elasticity. Comprehensive numerical results are presented for
static, free vibration, and transient analyses of different laminated plates and shells,
which agree well with existing solutions in the published literature, or solutions
of very-expensive 3D models (where 3D elements are used to model each layer)
by using commercial FEM codes. Because the proposed methodology merely involves
simple displacement DOFs at each node, relies only on the simple theory of
solid mechanics, and is capable of accurately and efficiently predicting the static and dynamical behavior of composite laminates in a very simple and cost-effective
manner, it is thus believed by the authors that the development of “higher-order” or
“layer-wise higher-order” theories are not entirely necessary for analyses of laminated
plates and shells.
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