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

Abstract

In the present manuscript, a Layer-Wise (LW) generalized model 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 by means of the Generalized Differential Quadrature (GDQ) method, whereas the numerical integrations are computed employing the Generalized Integral Quadrature (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 from refined 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.

Natural Frequency Response of FG-CNT Coupled Curved Beams in Thermal Conditions

“…These studies focused on static and dynamic behavior [7][8][9], transverse vibration [10], and forced vibration [11], using viscously damped interlayer [8,12] among others. Among the most recent works, we can find studies focusing on the dynamic response of coupled curved beams, including both singly curved [13][14][15][16] and doubly curved systems [17][18][19].…”

On the Importance of the Recovery Procedure in the Semi-Analytical Solution for the Static Analysis of Curved Laminated Panels: Comparison with 3D Finite Elements

“…The recovery procedure has been demonstrated to be an effective tool for the reconstruction of the three-dimensional response of doubly-curved shell structures with advanced lamination schemes, starting from numerical solutions of refined formulations based on HSDTs. In some previous works [100,101], the recovery procedure has been applied to some two-dimensional GDQ-based numerical solutions for the prediction of the static response of doubly-curved shells with generally anisotropic materials. However, the effects of this procedure on two-dimensional semi-analytical solutions have not been checked.…”