| Fiber-reinforced composite material (hereinafter referred to as composite material) with its superior high strength, high stiffness, functional applications and design ability has been widely used in various industries and has attracted wide academical attention. However, with the increasing demands of lightweight structure in aerospace engineering, the single use of new materials or single use of innovative structural configuration can not meet the above requirements sufficiently. An urgent need to find a new method to realize the lightweight design of the composite structures, which can further explore the potential of the composite structures from the structures configuration and fiber laying parameters on the two geometrical scales. Therefore, the present paper is based on the geometrical multi-scale structural and material optimization theory, with the structure topology configuration on the macro-structural scale and the fiber laying angle on micro-material scale as the independent variables on the two geometrical scales, systematically carried out the multi-scale integrated optimization design of composite material and structure represented by composite frame structure. The main research contents are as follows. Considering the manufacturing process constraint, adopting the nonlinear Heaviside function, the paper proposes an improved discrete material optimization model which is labeled as HPDMO model, which can considerably improve the convergence rate of the optimal results compared with the traditional DMO models. Based on the improved discrete material optimization model, the void material is added into the optional discrete material set to realize the topology change of the composite structure. The integrated optimization design of the material and structure model for discrete composite planar structure, shell and frame is established. Considering the common six manufacturing constraints in aerospace engineering, the specific manufacturing constraints are explicitly expressed as series of linear inequalities or equalities adopting discrete material optimization model variables. Therefore, the integrated multi-scale design optimization of composite frame with specific manufacturing constraints is established. The optimization objective function has multiple local minimum and initial design variable depending problems, when the fiber winding angles are directly regarded as design variables. Based on the jointed parameter method, the global jointed parameter optimization design method is proposed for composite frame optimization with fiber winding angle and equivalent structural stiffness parameter as design variables. The specifically contents are as follows.(1) An improved discrete composite optimization model HPDMO. Considering the fiber ply angle manufacturing process and cost constraints, the ply angles are required to be easily manufactured with the characteristic of discrete angle combinations (such as [0°,±45°,90°]). Based on the discrete material optimization and topology optimization technology, the low convergence rate difficulty of the fiber ply angel optimization results in the discrete material optimization model (DMO) indicates that the fiber plying angle is not clear in the low convergence elements. This brings the inconvenience for the optimal structure design and processing. In addition, the optimum design results can not directly be applied to practical engineering. Therefore, the present paper adopts the improved Heaviside function, and proposes an improved HPDMO (Heaviside Penalization of Discrete Material Optimization) discrete optimization model, and carries out the explicit sensitivity analysis. Adopting the continuous penalty strategy, the ply angle and the distribution of the composite material are introduced for the widely used composite plate and shell structure, as independent variables in two geometric scales (material and structural scales). An optimization model based on the minimum structural compliance with a specified composite volume constraint is established. Optimization results show that, the improved HPDMO model can not only considerably improve the convergence rate of the optimal results compared with the traditional DMO models, but also can provide better performance of the composites structural design. (The second chapter)(2) Integrated optimization design of composite frame based on modified discrete interpolation scheme. For composite frame structure, considering the manufacturing process constraints, the discrete fiber winding angle [0°,±45°,90°] on micro-material scale and the geometrical parameter of components of the frame on the macro-structural scale are introduced as the independent variables on the two geometrical scales. Based on the improved HPDMO interpolation scheme, the optimization models based on the minimum structural compliance and maximum fundamental frequency with the specified fiber material volume constraint has been established, respectively. The sensitivity information about the two geometrical scale design variables are also deduced considering the characteristics of discrete fiber winding angle based on semi-analytically sensitivity method. The optimization model considers the comparison of continue and discrete fiber winding angle effect on objective function. The optimization results of the fiber winding angle and the macro structural topology on the two single geometrical scales, together with the integrated two-scale optimization are separately studied and compared in the paper. The paper shows that the integrated multi-scale optimization can further improve the potential of lightweight design and frequency performance of the composite frame. (The third chapter)(3) Integrated optimization design of composite frame with specific manufacturing constraints. For the requirements of manufacturing constraints in aerospace engineering, the present paper has considered the six specific manufacturing constraints in the manufacturing process of the fiber-reinforced composite laminate. And explicitly gives the specific manufacturing constraints as series of linear inequalities or equalities by considering typical failure modes, such as:continuity constraint; symmetry constraints; 10% constraint; the first floor damage constraints, which provides the possibility for discrete composite optimization design to solve the above large-scale constraints problem. Based on gradient optimization algorithm, the integrated optimization design model with minimum structural compliance and maximum fundamental frequency is proposed subject to constraints on the composite structural volume. The geometrical parameter of the frame components in the macro-structural scale and the discrete fiber winding angle in the micro-material scale are introduced as the independent design variables in the two geometrical scales. The linear constraints and composite integrated optimization problems are solved by Sequential Linear Programming (SLP) optimization algorithm. The influence of different constrained parameters on objective function has been studied. The comparison between single-scale optimization and integration optimization has been compared. (The fourth chapter)(4) Optimization design of composite frame based on jointed parameterized method. Based on the existing extensive literature results, the optimization objective function has multiple local minimum, when the filament winding angles are considered as design variables, and thus the traditional gradient-based optimization algorithm may be not effective and can only get local optimum solution and which is difficult to meet the requirements of engineering. Therefore, for fiber-reinforced composites frame structure, the present paper proposes a new jointed parameter optimization scheme. Firstly, adopting layer-wise constant shear beam theory, the equivalent elastic modulus and shear modulus of the composite beam with single layer can be integral expressed as filament winding angle function. For circular cross section composite beam, the equivalent structural stiffness parameter has been expressed as the integral of the equivalent elastic and shear modulus through thickness direction. Secondly, the optimization problem in the fiber winding angle space is established, based on the fact that when considering structural stiffness parameters (tension stiffness, bending stiffness, torsional stiffness) as the design variables, the optimization problem's feasible domains are convexity, the objective sensitivity information with respect to design variables has been solved by using the semi-analysis method in two kinds of optimization problems, i.e., the filament winding angle space and equivalent structural stiffness parameter space optimization. Thirdly, based on the equivalent structural stiffness parameter, the sub-optimization problem between structural filament winding angle and equivalent structural stiffness parameter has been presented to realize the independent implementation of filament winding angle space and structural stiffness parameter space optimization problem and design variables feasible region switches from a non-convex domain to a convex domain. Lastly, the optimum structural stiffness parameter in the stiffness space should be mapped to fiber winding angel space, which is regarded as the new starting point in the filament winding angel space, then the jointed parameter method is realized for composite frame optimization, which greatly increase the possibility to get the global optimum solution when the filament winding angle are the design variables. Which also provides a useful theory basis and realizing technology for composite frame structure optimization. (The fifth chapter)... |
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