Anisogrid composite lattice shells and their composite bolted joints: theoretical and numerical modeling, structural analysis and optimization

The present Thesis aims to define a new methodology for the optimal design of anisogrid composite lattice structures in the framework of aerospace and aeronautic industries, such as rocket interstages, payload adapters and fuselage segments along with the theoretical background complete development of accurate and computationally-light FE modeling techniques for the analysis of bolted joints utilized for the assembly of the anisogrid lattice shells in the overall structure where they are employed. In particular, the outlined research activities received the financial support of Avio SpA through a PhD grant funding. In fact, Avio SpA is in charge of designing and manufacturing with anisogrid technology the Interstage 2/3 of Vega C, the new generation of European launcher developed by the Italian Space Agency and the European Space Agency. In the field of anisogrid composite lattice structures optimization methods, this Thesis presents a comprehensive optimal design methodology which is capable of determining the minimum mass configuration of the lattice shell accounting for the contemporaneous action of different external load typologies and multiple stiffness constraints. The outlined method makes use of a full FE parametric model of both the cylindrical and the conical configurations of the anisogrid structures which was fully coupled with an optimization technique based on the NSGA-II genetic algorithm. As a consequence, it is possible to overcome all the restrictions of the continuous approaches to the design related to the assessment of the buckling failure and the ones of the discrete approaches which correctly describe the structural behavior of the anisogrid lattice structure but that have been utilized with still limited optimization margins. Indeed, using the discrete approach to exactly evaluate the critical buckling load in the design analysis, regardless of the specific buckling failure mode, it is possible to realize a comprehensive analysis of the buckling failure of anisogrid lattice structures taking into account all possible buckling modes deriving from different load conditions, including those which cannot be adequately described by means of an analytical formulation, and thus reliably optimize the lattice shell. Some numerical case studies related to actual industrial cases are proposed, multiple external loads and stiffness constraints applied simultaneously to the anisogrid lattice structures are considered in order to demonstrate the potentialities of this optimal design methodology. Moreover, with reference to the bolted joints used in the final assembly of the anisogrid composite lattice structures, it is required the proper simulation of these connections since this aspect represents a critical issue for the structural integrity of the entire project. As a consequence, stemming from this specific problem and considering the wide and relevant employment of composite bolted joints in the aeronautic and aerospace fields, an efficient and reliable design tool capable of returning accurate results in terms of junction stiffness, without making computationally heavier the global FE model, turns out to be a potential great benefit in this context. Thus, the theoretical framework that is the basis of an original FE modeling technique for composite bolted joints is presented. This FE modeling technique is founded on the new definition of a Spot Joint Element representative of the structural behavior of a region surrounding the spot joint comprising the bolt and a circular portion of the connected plates. The enhanced version implements a stiffness matrix whose terms are obtained according to the analytical solution of the composite bolted joint theoretical reference model. The theoretical model consists in an annular plate, with rectilinear orthotropic material properties, featuring a rigid core at the inner radius and fully clamped conditions at the outer edge undergoing different external loads: (i) transversal load, (ii) in-plane load, (iii) in-plane bending moment and (iv) torsional moment. The bolted joint element is realized through a suitable assembly of beam-type elements and, even if this FE tool features a reduced number of DOFs with respect to a complex 3D model, it preserves a substantial accuracy in the simulation of bolted joint connections. The obtainment of the novel Spot Joint Element stiffness matrix required the analytical solution of the composite bolted joint theoretical reference model; in this regard, the main complication with respect to the previous version of this FE simulation tool is represented by the fact of considering rectilinear orthotropic material properties, that are intrinsically symmetric in a Cartesian coordinate system, for an annular plate, i.e. an axisymmetric geometry. This aspect introduces a circumferential variation of the composite annular plate bending stiffnesses and of the displacement components as a consequence. This makes it impossible the chance to obtain closed form solutions, as for the classical version of the Spot Joint Element where the theoretical reference model featured isotropic material properties. Therefore, the constitutive equations of the rectilinear orthotropic circular plate are determined in the frame of the Classical Lamination Plate Theory and are further derived according to First-order Shear Deformation Plate Theory in order to make wider the range of applicability of the presented method. In particular, the circumferentially variable stiffness terms of this typologies of plates are outlined. Initial efforts towards the analytical solution of the composite bolted joint theoretical reference model made use of vector approach: the governing equation was determined for thin-plates from the equilibrium and the compatibility equations of the laminate circular plate. Then, as regards the transversal load condition and considering the lack of closed form solutions, the governing equation was solved through the application of Galerkin method. Approximation functions compliant with the displacement constraints introduced by the joint theoretical model are derived and utilized in the application of Galerkin method. Nevertheless, the solution method founded on the vector approach can hardly be enlarged to the other load conditions needed to characterize the new spot joint theoretical reference model. Indeed, Galerkin method necessitates of approximation functions that are compliant with both essential and natural boundary conditions of the problem and their search results demanding for load conditions more complicated than the transversal load one. Consequently, the solution strategy was further improved exploiting the energy approach; a solution methodology based on the Ritz method along with the virtual displacements principle is outlined. The Ritz formulation of the problem is presented in general form and, subsequently, it is particularized for the four load conditions required by the theoretical reference model. Two symmetrical lay-ups commonly employed in literature regarding composite bolted joints are considered in the results presentation. Besides, the results concerning the transversal load condition and the in-plane bending moment load condition demonstrated the necessity of accounting for the composite plate shear deformability when dealing with higher values of the plate slenderness ratio, in order to extend and make more flexible the usage of both the analytical method and of the Spot Joint Element. In the end, a first application of the composite bolted joint element, considering only the in-plane load condition, with the analytic solution embedded into the FE stiffness matrix of the new version of Spot Joint Element, is reported. The comparison between a complex 3D model and the presented FE modeling approach demonstrate the benefits achievable through the employment of this simulation technique in terms of reduced computational weight with no accuracy loss.