This book provides an extensive introduction to the mechanics of
anti-sandwiches: non-classical composites with multiple homogeneous
layers but widely differing parameters concerning their geometry and
materials. Therefore, they require special attention in the context of
structural mechanics.
The theoretical framework presented here is based on a five parametric,
planar continuum, which is a pragmatic version of the COSSERAT shell.
The direct approach used here is enlarged where constraints are
introduced to couple layers and furnish a layer-wise theory.
Restrictions are made in terms of linearity - geometrical and physical.
After having defined appropriate variables for the kinematics and
kinetics, linear elastic material behaviour is considered, where the
constitutive tensors are introduced in the context of isotropy. The
basics are presented in a clear and distinct manner using index-free
tensor notation. This format is simple, concise, and practical.
Closed-form solutions of such boundary value problems are usually
associated with serious limitations on the boundary conditions, which
constitutes a serious disadvantage. To construct approximate solutions,
a variational method is employed as the basis for computational
procedures where the Finite Element Method is applied. Therefore, the
introduction of the vector-matrix notation is convenient. Based on the
plane considerations, a finite eight-node SERENDIPITY element with
enlarged degrees of freedom is realised. To avoid artificial stiffening
effects, various integration types are applied, and the solutions
generated are subsequently verified with closed-form solutions for
monolithic limiting cases.
Within this setting, it is possible to efficiently calculate the global
structural behaviour of Anti-Sandwiches, at least up to a certain
degree. The power of the proposed method in combination with the
numerical solution approach is demonstrated for several case and
parameter studies. In this regard, the optimal geometrical and material
parameters to increase stiffness are analysed and the results for the
kinematic and kinetic quantities are discussed.
