Equivalent single layer higher order theory based on a weak formulation for the dynamic analysis of anisotropic doubly-curved shells with arbitrary geometry and variable thickness

In the present work a novel approach is presented for the modal analysis of shells with arbitrary geometry, general boundary conditions and variable thickness. The Equivalent Single Layer (ESL) methodology is followed for the definition of the fundamental set of equations. Shell reference surface is defined with respect to a proper curvilinear coordinate system. The skewness of the shell is set following an isogeometric NURBS-based approach, and a blending coordinate transformation is derived. Structures with general curvatures are considered characterized by a variable thickness along the two parametric lines, combining power and sinusoidal variations. Displacement-based fundamental equations are derived from the Hamiltonian Principle, taking a weak formulation based on a lagrangian interpolation of the unknown variables. A generalized higher order assumption is considered for the definition of the field variable along the thickness of the structure unlike other previous works. The proposed approach can handle coupled unsymmetric lamination schemes, including completely anisotropic layers with general orientations. Different external constraints are set along mapped edges. Some examples of investigations have been considered, and mode frequencies and shapes are provided for each case. The results are compared with refined finite element-based solutions and a great accuracy is seen between the various approaches.