Static Analysis of Anisotropic Doubly-Curved Shell Subjected to Concentrated Loads Employing Higher Order Layer-Wise Theories

In the presentmanuscript,a Layer-Wise(LW)generalizedmodel is proposed for the linear static analysis of doublycurved shells constrained with general boundary conditions under the influence of concentrated and surface loads.The unknown field variable is modelled employing polynomials of various orders,each of them defined within each layer of the structure.As a particular case of the LW model,an Equivalent Single Layer(ESL)formulation is derived too.Different approaches are outlined for the assessment of external forces,as well as for non-conventional constraints.The doubly-curved shell is composed by superimposed generally anisotropic laminae,each of them characterized by an arbitrary orientation.The fundamental governing equations are derived starting from an orthogonal set of principal coordinates.Furthermore,generalized blending functions account for the distortion of the physical domain.The implementation of the fundamental governing equations is performed bymeans of the Generalized Differential Quadrature(GDQ)method,whereas the numerical integrations are computed employing theGeneralized IntegralQuadrature(GIQ)method.In the post-processing phase,an effective procedure is adopted for the reconstruction of stress and strain through-the-thickness distributions based on the exact fulfillment of three-dimensional equilibrium equations.A series of systematic investigations are performed in which the static response of structures with various curvatures and lamination schemes,calculated by the present methodology,have been successfully compared to those ones obtained fromrefined finite element three-dimensional simulations.Even though the present LW approach accounts for a two-dimensional assessment of the structural problem,it is capable of well predicting the three-dimensional response of structures with different characteristics,taking into account a reduced computational cost and pretending to be a valid alternative to widespread numerical implementations.

Static Analysis of Doubly-Curved Shell Structures of Smart Materials and Arbitrary Shape Subjected to General Loads Employing Higher Order Theories and Generalized Differential Quadrature Method

The article proposes an Equivalent Single Layer(ESL)formulation for the linear static analysis of arbitrarily-shaped shell structures subjected to general surface loads and boundary conditions.A parametrization of the physical domain is provided by employing a set of curvilinear principal coordinates.The generalized blendingmethodology accounts for a distortion of the structure so that disparate geometries can be considered.Each layer of the stacking sequence has an arbitrary orientation and is modelled as a generally anisotropic continuum.In addition,re-entrant auxetic three-dimensional honeycomb cells with soft-core behaviour are considered in the model.The unknown variables are described employing a generalized displacement field and pre-determined through-the-thickness functions assessed in a unified formulation.Then,a weak assessment of the structural problem accounts for shape functions defined with an isogeometric approach starting fromthe computational grid.Ageneralizedmethodology has been proposed to define two-dimensional distributions of static surface loads.In the same way,boundary conditions with three-dimensional features are implemented along the shell edges employing linear springs.The fundamental relations are obtained from the stationary configuration of the total potential energy,and they are numerically tackled by employing the Generalized Differential Quadrature(GDQ)method,accounting for nonuniform computational grids.In the post-processing stage,an equilibrium-based recovery procedure allows the determination of the three-dimensional dispersion of the kinematic and static quantities.Some case studies have been presented,and a successful benchmark of different structural responses has been performed with respect to various refined theories.