Grid-stiffened Composite Structures Research Articles

Buckling optimization of non-uniform curved grid-stiffened composite structures (NCGCs) with a cutout using conservativeness-relaxed globally convergent method of moving asymptotes

There are renewed interests in grid-stiffened composite structures due to the high structural stability and damage tolerance enabled by multiple intersected stiffeners. The limited design space of repeated straight grid patterns has been remarkably expanded by introducing non-uniform curved grid-stiffened composite structures (NCGCs). In this work, curved stiffener layout optimization for NCGCs with a central cutout is investigated to maximize the critical buckling load under a given weight constraint. The design framework is developed by calling ABAQUS for simulating stiffened models and using numerical sensitivities in order to adopt gradient-based optimization algorithm, where the computational time depends not only on simulation but also the number of design variables. To increase the efficiency, an improvement is proposed based on globally convergent method of moving asymptotes (GCM), as one of the most popularly used structural optimization algorithms, by relaxing the conservativeness (CR-GCM) with an additional relaxation factor and an adaptive limit of the iteration number. Numerical examples show that optimal curved stiffeners around the cutout have the ability to remarkably increase the structural buckling load and the proposed CR-GCM demonstrates the ability of better balancing the computational efficiency and convergence in the optimization process.

Buckling Analysis and Configuration Optimum Design of Grid-Stiffened Composite Panels

To allow an efficient preliminary design, a grid pattern or configuration optimization strategy is proposed for grid-stiffened composite structures under the constraint of sustaining the buckling resistant capability. This is achieved by first introducing a configuration vector for representing stiffeners in a grid unit, which is applicable for the description of iso-grid, ortho-grid -grid, and bi-grid. The parametric equivalent stiffener model of the structure is derived by the smearing method, and the global and local buckling loads are calculated for the different grid configurations. The artificial bee colony algorithm was used as an optimizer to address the discrete design variable space, including a grid-unit size, height, and thickness of stiffeners that could be specified by designers or manufacturing requirements. Two test examples validated the effectiveness of the approach. The results suggested that both optimal and suboptimal solutions can be considered effectively as design options in the preliminary stage of design for such types of structures.

Streamline stiffener path optimization (SSPO) for embedded stiffener layout design of non-uniform curved grid-stiffened composite (NCGC) structures

A bio-inspired concept of non-uniform curved grid-stiffened composite structures with embedded stiffeners (embedded NCGCs) is proposed in the paper. Shallow curved stiffeners are embedded in the laminate skin to form an integrated structure to improve the skin–stiffener deformation compatibility. A method named streamline stiffener path optimization (SSPO) based on multiscale modeling is proposed for curved stiffener layout design of embedded NCGCs. Firstly, the homogenization-based global/local analysis is used to calculate structural responses on a global unstiffened model with the equivalent material properties obtained from local representative cell configurations (RCCs). Secondly, the discrete distribution of 2D curved stiffener paths is transformed into a continuous distribution of the streamline function values (SFVs) on a 3D level set surface. The stiffener path description using the streamline function is similar as the level set method with specific constraints. Projections of points with the same integral SFVs will form one stiffener path. Thirdly, optimal curved stiffener layout is achieved using shape design of local parallelogram representative cell configurations with analytical sensitivities calculated using the affine mapping from the square master domain to the parallelogram RCCs. Fourthly, stiffener spacing and angle constraints are added for manufacturing considerations and local buckling resistance, and optimization design is implemented to maximize the buckling load within a given weight. Finally, numerical examples of a square laminated panel under uniaxial and biaxial compressions validate the effectiveness of the proposed SSPO method and indicate the significant improvement of the buckling loads by steering the stiffener paths.

Sensitivity analysis for optimization design of non-uniform curved grid-stiffened composite (NCGC) structures

Conventional grid-stiffened composite structures are designed with straight and uniformly distributed stiffeners. In this paper, a new concept of non-uniform curved grid-stiffened composite structures (NCGCs) with curved non-uniformly distributed stiffeners is proposed, which can significantly boost the design space and flexibility for high efficient composite structures. Under the framework of homogenization-based global/local analysis, optimization design of NCGCs can be solved as material/sizing and shape optimization of local representative cell configurations (RCCs). In the presented contribution, efficient analytical sensitivities with respect to both the skin/stiffener material/sizing parameters and the RCC shape parameters are derived systemically. Sensitivities with respect to the RCC shape parameters are highlighted and derived based on linear membrane and bending transformations between physical and master domains by an affine mapping for the assumed parallelogram RCCs. Optimal material properties, sizes or curved stiffener layout can be efficiently obtained by using the proposed sensitivity calculation method. The accuracy is validated using numerical examples with analytical and finite difference solutions. Finally, a design study of a NCGC panel with linearly varying stiffener angles is presented to demonstrate the feasibility and efficiency of the proposed method.

Scaling effects in the manufacture and testing of grid-stiffened composite structures

Scaling effects in the manufacture and testing of glass fiber-reinforced epoxy grid-stiffened structures have been investigated in this study. Four nominally identical scaled sizes of mold have been manufactured, in which the length, width, height, and internal channel sizes were varied to achieve ¼, ½, ¾ and full-scale stiffened structures. The panels were manufactured on a glass mold using the vacuum-assisted resin transfer molding technique, enabling the flow front to be monitored throughout the filling process. Grid-stiffened beams were removed from the cured panels and tested in flexure on scaled bending fixtures. The vacuum-assisted resin transfer molding manufacturing study on the four scaled sizes indicated that resin infusion incurred more rapidly in the smallest mold, possibly due to difficulties in accurately cutting the glass fabric, which in turn reduced the effective areal density of the fabric, thereby modifying its effective permeability. The flow rates and velocities of the resin fronts in the larger mold sizes were similar, suggesting that an appropriately scaled mold can be used to successfully predict the infusion process in more representative structures. Flexural tests on the grid-stiffened samples highlighted a similar response in the three largest samples, with the smallest sample again offering a modified response. Similar failure mechanisms, including fracture of the grid structure, debonding at the skin-core interface, and flexural failure in the center of the sample, were observed in all of the samples.

Buckling optimization design of curved stiffeners for grid-stiffened composite structures

Grid-stiffened composite structures not only allow for significant structural weight reduction but also are competitive in terms of structural stability and damage tolerance compared with conventional stiffened candidates. As the development of Automated Fibre Placement (AFP) technology matures, a unitized construction of skin and stiffeners is easily manufacturable. In this paper, a curved stiffener layout is optimized to enhance the structural buckling resistance. A linear variation of stiffener angles is used, resulting in the formation of a locally rhombic lattice pattern. Due to the spatial variation of angle and spacing induced by the use of curved stiffeners, analytic solutions for the responses are not generally applicable. Thus, global and local buckling loads are calculated based on finite element models by a previously-developed global/local coupled strategy. Since the stiffeners are not explicitly modelled in the finite element calculations, a fixed mesh is used for gradient-based optimization. Both parametric design and optimization are performed in order to find the optimal curved grid pattern, whose practical performances are assessed by post-buckling analysis. A comparison between the performances of structures with curved stiffeners, with straight stiffeners, and variable-stiffness skins with curved fibres, demonstrates the potential of curved stiffener configurations in improving the structural efficiency.

An efficient semi-automated optimisation approach for (grid-stiffened) composite structures: Application to Ariane 6 Interstage

Grid-stiffened composite structures offer an interesting competitive design solution for many primary and secondary aerospace structures. Due to their inherent geometric complexity, however, analysis and optimisation of these structures is not trivial. In the current work an efficient analysis technique and optimisation approach have been developed and applied to the 2/3 Interstage of the Ariane 6 Launcher. For the analysis method it was found that thermal pre-loading of the structure was critical for accurate prediction of the structural performance. The automatic optimisation was also able to find a design providing 20% weight savings versus a reference design found through trial and error.

Numerical optimization of soft-mold aided co-curing process of advanced grid-stiffened composite structures

The co-curing process for advanced grid-stiffened (AGS) composite structure is a promising manufacturing process, which could reduce the manufacturing cost, augment the advantages and improve the performance of AGS composite structure. An improved method named soft-mold aided co-curing process which replaces the expansion molds by a whole rubber mold is adopted in this paper. This co-curing process is capable to co-cure a typical AGS composite structure with the manufacturer’s recommended cure cycle (MRCC). Numerical models are developed to evaluate the variation of temperature and the degree of cure in AGS composite structure during the soft-mold aided co-curing process. The simulation results were validated by experimental results obtained from embedded temperature sensors. Based on the validated modeling framework, the cycle of cure can be optimized by reducing more than half the time of MRCC while obtaining a reliable degree of cure. The shape and size effects of AGS composite structure on the distribution of temperature and degree of cure are also investigated to provide insights for the optimization of soft-mold aided co-curing process.

Global and local buckling analysis of grid-stiffened composite panels

There is a renewed interest in grid-stiffened composite structures; they are not only competitive with conventional stiffened constructions and sandwich shells in terms of weight but also enjoy superior damage tolerance properties. In this paper, both global and local buckling is investigated for orthogrid- and isogrid-stiffened composite panels. Homogenized properties corresponding to classical lamination theory are obtained by matching the strain energy of stiffened and equivalent unstiffened cells, and then used in global buckling analysis. Bloch wave theory is adopted to calculate the local buckling load, where the interaction of adjacent cells is fully taken into account. Instead of considering skin buckling and stiffener crippling separately, the skin and stiffeners are assembled together at the level of a characteristic cell. The critical instabilities can be captured whether they are related to the skin, stiffener or their interaction. The proposed combination of global/local models can also be used to predict the material failure. Numerical examples of isotropic panels show that the local buckling loads predicted by the proposed method match detailed finite element calculations well for eccentric or symmetrically located stiffeners with different torsional stiffness. The proposed method is further validated using typical composite configurations of flat panels and circular cylinders.

Study of filament wound grid-stiffened composite cylindrical structures

Abstract Grid-stiffened composite structures are known for their very high efficiency under compressive loading environment. The grid of stiffening ribs is the primary feature in these structures and filament winding is employed as the most convenient manufacturing technique. Three different types of circular cylindrical structures – unstiffened shell (with skin only), lattice cylinder (with ribs only) and grid-stiffened shell (with skin and ribs) – are considered for experimental study and a series of these structures have been manufactured adopting a simplified and cheap manufacturing process. Different aspects of manufacturing that include tooling and other processing aspects are presented in this paper. Axial compression tests have been carried out and the results are compared with finite element analysis. Based on the test results and comparison with finite element analysis, conclusions are drawn on the efficacies of this relatively new class of structures.

Analytical/experimental investigation of energy absorption in grid-stiffened composite structures under transverse loading

In this paper we summarize preliminary results from an analytical/experimental study of the energy absorption characteristics of grid-stiffened composite structures under transverse loading. Tests and quasi-static finite element analysis simulations were carried out for isogrid E-glass/polypropylene panels in three-point bending. The results of the tests and simulations show that these types of structures have excellent damage tolerance and that most of the energy absorption occurs beyond initial failure. It is also observed that even though the peak load is greater for loading on the skin side, the specific energy absorption and the range of displacements over which energy is absorbed are significantly better when the load is applied on the rib side.