先进复合材料格栅加筋结构优化设计与损伤分析
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摘要
先进复合材料格栅加筋结构(AGS)综合新材料技术和新结构设计的优点,不仅具有一般复合材料结构的比强度和比刚度高的特点,同时拥有环境鲁棒性、自动化制造技术等独特的优势,已被广泛应用于航天航空结构中,成为最具发展前途的新型结构形式之一。本文根据航天和航空飞行器中复合材料AGS板/壳构件和结构的特点,从总体和局部,统观和精细等层次,对该结构的分析模型、理论、方法和破坏过程开展了较为深入的研究,并独立开发了相应的分析软件包AGSANS。该项研究是国家重点基础研究发展计划973计划课题“超轻多孔材料和结构创新构型的多功能化基础研究”(2006CB601205)和国家自然科学基金面上项目“含损伤先进复合材料格栅加筋结构(AGS)破坏机理研究”(10302004)子课题的重要研究内容之一,同时还得到中国运载火箭研究院十五攻关预研项目《先进复合材料格栅加筋结构的力学分析与优化设计》的资助。本论文主要研究工作如下:
1.复合材料AGS结构优化设计混合遗传算法
复合材料AGS结构优化设计是一个非线性优化问题,且存在多约束、离散和连续变量并存等难点。基于这些难点,本文将遗传算法与单纯形法相结合提出了一种混合遗传算法,可以较快得到全局最优解。同时将遗传算法进行了改进,也对单纯形法中存在的若干问题给出了解决方案。优化目标为给定外载下使复合材料AGS圆柱壳的重量最小,同时满足稳定性和应变约束条件。其中,对AGS结构的分析是基于等效刚度模型。设计变量包括连续变量(肋骨厚度、斜肋铺设角度)和离散变量(蒙皮铺层、肋骨高度、斜肋间距)。通过对有无强度约束和不同加筋形式对优化结果的影响分析,发现整体稳定性为控制AGS圆柱壳结构安全度的最主要约束因素,等格栅结构在侧压下是最有效的结构形式。
2.复合材料AGS圆柱壳的鲁棒优化设计方法
通常在制造过程中,对构件尺寸和位置都规定了公差,因此,在进行结构设计时有必要将这些因素考虑在内。为此,本文基于上述混合遗传算法提出了一种针对非完善复合材料AGS圆柱壳的鲁棒优化设计方法,同时考虑了优化目标和约束的鲁棒性。为了简化运算过程,提高优化分析效率,通过敏度分析方法选取对优化结果影响较大的设计变量作为鲁棒优化设计变量(本问题为肋骨高度和斜肋铺设角度)。典型算例结果表明,鲁棒优化设计结果与传统确定性优化结果相比差别较大,表明鲁棒设计是很必要的。此外,AGS圆柱壳对初始几何非圆度缺陷不敏感。
3.复合材料三角形精细Mindlin加筋板/壳单元
由于AGS结构的复杂性和肋骨往往较高,以往的有限元分析模型都存在各种不足。本文构造了用于复合材料AGS结构分析的复合材料三角形精细Mindlin加筋板/壳单元,并推导了考虑几何大变形的非线性有限元列式。在构造过程中假定肋骨和蒙皮横向位移相同,但转角采用相同形函数分别插值,这样既保证两者变形协调性,又放松了肋骨转动的约束。在此单元中,肋骨放置的数量、位置和角度可以任意,为结构的单元网格剖分带来了很大的便利。通过算例计算结果对比,表明本单元具有较好收敛性能,并能够精确计算加筋结构的位移和面内应力,对于高肋格栅加筋结构表现出了独特的优越性。另外,基于该单元还对正交格栅加筋板和等格栅圆柱壳进行了特征值屈曲和后屈曲分析。
4.复合材料AGS结构的损伤累积扩展分析
由于复合材料AGS结构损伤行为的复杂性,有关该方面的报道还很少。本文基于精细加筋单元模型提出了一种用于AGS结构的损伤启始和扩展分析方法。该方法同时考虑了层内损伤和层间损伤,其中,层内损伤包括蒙皮纤维破坏、蒙皮基体开裂、蒙皮纤维-基体剪切破坏以及肋骨纤维破坏,而层间损伤为蒙皮分层损伤。对于层内损伤采用材料常数退化准则;而对于分层损伤,提出了一种新的等效刚度退化准则。另外基于三角形单元提出了一种适用于薄板和中厚层合板的层间剪切应力有限差分计算方法。通过典型算例证明了该损伤模型用于AGS结构分析的有效性,并详细分析了中心含孔复合材料正交各向异性格栅加筋曲板和光板在轴压下的损伤扩展机理和行为。
5.复合材料AGS结构混合分析模型
结合等效刚度模型和精细加筋单元模型构造了一种混合分析模型,即对于需要特殊研究的局部区域应用精细加筋单元离散,而在其他区域应用等效刚度板壳单元离散。这样不仅可以有效地分析AGS结构的局部力学性能,还可降低模型化的工作量,提高计算效率。计算结果表明格栅形状、肋骨间距和高度对等效刚度模型计算结果精度有重要的影响,并通过对带孔复合材料AGS板孔边特殊点应力值的分析,明确了混合法的使用限制。
Advanced composite grid stiffened (AGS) structures not only inherit the traditional excellent qualities of fiber-reinforced composite materials, e.g. high specific strength and stiffness, but also exhibit many unique advantages by combining new material technology and new structure design concepts, e.g. environmental robustness and automatic manufacturing. AGS structures appear to be a promising concept and have been widely used in aircraft and spacecraft design. According to the characteristic of composite AGS plate/shell, this dissertation investigates the model, theory, method and failure process for the AGS structures from global-local and macroscopic-microscopic views. In addition, a corresponding software (AGSANS) is developed. This study is a sub-part of the project of National Basic Research Program of China (973 Project) "Study on multi-functional innovation construction of extra-waighted and porous materials & structures" (No.2006CB601205) and National Science Foundation in China "The fracture mechanism of advanced grid stiffened structure (AGS) with damage" (No. 10302004). It is also supported by a grant from the National Key Technologies R&D Program of China Academy of Launch Vehicle Technology during the 10th Five-Year Plan Period "Optimal design and mechanics analysis for composite AGS structures". The main research work can be summarized as follows:
1. Hybrid Genetic Algorithm of Composite AGS Structures
Considering the characteristics for optimal design of AGS structures, such as nonlinear programming, multi-constraints, and mixed discrete-continuous design variables, etc, a new hybrid genetic algorithm (GA) is developed by combining the improving GA and simplex algorithm (SA), which achieves global optimal solutions more quickly. In the method, some solutions are offered for several traditional problems in SA. The present design problem is to minimize the weight of an AGS cylindrical shell under a given load condition with buckling and strength constraints. An equivalent stiffness model (ESM) is used to analyze the AGS structure. Continuous design variables (rib thickness and angle of diagonal ribs) and discrete variables (rib height, diagonal rib spacing and skin laminate stacking sequence) are both considered. Some numerical examples are discussed about the effects of strength constraints and grid configurations upon the optimal results. It is concluded that global buckling constraint is the key factor for identifying the safety of AGS cylindrical shell, and the triangular grid is the ideal configuration under transverse pressure.
2. Robust Design for Composite AGS Cylindrical Shell
Robust design for the structures is normally necessary, since the size and location of the members generally need high tolerance during manufacturing. Therefore, a robust optimization design method, based on the hybrid GA, for the AGS cylindrical shell with initial-imperfect is proposed, in which both robustness of objective function and constraint functions are considered. To simplify the optimization and reduce the computational cost, the two most sensitive variables, which are introduced in robust analysis, are distinguished from all utilizing sensitivity analysis. In the present analysis, they are rib height and angle of diagonal ribs. By optimizing an AGS cylindrical shell under axial compressure, it can be seen that the optimization results given by the proposed robust design method are quite different from the general deterministic optimization method, and the AGS structures are not sensitive to the initial imperfection.
3. Refined Triangular Composite Stiffened Mindlin Plate/Shell Element
Since the AGS structures are so complex and the ribs are normally higher than skin, the present finite element models are all insufficient. A new refined triangular composite stiffened Mindlin plate/shell element is formulated for simulating AGS structures. The corresponding expressions of geometric nonlinearity are also deduced. In the element, the rotations of the ribs and skin are interpolated, respectively, using the same shape functions, while their transverse deformations are regarded as equal. Therefore, the conditions of displacement compatibility are well maintained along the interface of rib and skin, and the rotational constraints of the stiffeners are released. There are no restrictions on the number and orientation of the ribs in establishing element mesh. The numerical results show its good convergence and effectiveness, especially for the case of the AGS structures of higher ribs. The element can be used to calculate the deformation and in-plane stress of stiffened structures accurately. The studies on the buckling and post-buckling behavior for ortho-grid plate and iso-grid cylindrical shell are also carried out.
4. Progressive Failure Methodology for Composite AGS Structures
Presenting, literatures on the failure analysis of AGS structures is minimal due to its complexity. In this study, a new progressive failure methodology is developed to simulate the onset and growth of multi-failure for composite AGS plates/shells on the basis of the refined stiffened element model (RSEM). The failure modes considered in this study are inter-laminar failure (i.e. delamination in skin) and intra-laminar failure including fiber failure, matrix cracking, fiber-matrix shear failure in skin, and fiber failure in the ribs. For intra-laminar failure modes, corresponding material degradation rules are introduced. However, a new equivalent degraded stiffness rule is proposed for delamination. Meanwhile, a scheme for calculating inter-laminar shear stresses of the triangular element is developed by employing a mixed approach of finite element and finite difference method, which is confirmed available for thin or moderate thick composite laminate plates. The methodology is validated by some typical examples and is employed to evaluate the progressive failure behavior of a composite orthotropic-grid curved panel with a centrally located cutout under compressive load.
5. Mixed Analytical Model of Composite AGS Structures
A new mixed analytical model by conjunction of ESM with RSEM is formulated to simulate the composite AGS structures. The strategy is to use SEM to model the local area, where the mechanical features attract more attention, while use ESM to model the non-local area. It can not only simulate the local behavior more exactly but also be more efficient. The numerical simulations show that the accuracy of ESM is remarkably influenced by the configuration of grid, distance and height of the ribs. The limitation of the mixed analytical model is also investigated by analyzing the stress of a special point at the edge of the cutout located at the central of a grid-stiffened plate.
1.复合材料AGS结构优化设计混合遗传算法
复合材料AGS结构优化设计是一个非线性优化问题,且存在多约束、离散和连续变量并存等难点。基于这些难点,本文将遗传算法与单纯形法相结合提出了一种混合遗传算法,可以较快得到全局最优解。同时将遗传算法进行了改进,也对单纯形法中存在的若干问题给出了解决方案。优化目标为给定外载下使复合材料AGS圆柱壳的重量最小,同时满足稳定性和应变约束条件。其中,对AGS结构的分析是基于等效刚度模型。设计变量包括连续变量(肋骨厚度、斜肋铺设角度)和离散变量(蒙皮铺层、肋骨高度、斜肋间距)。通过对有无强度约束和不同加筋形式对优化结果的影响分析,发现整体稳定性为控制AGS圆柱壳结构安全度的最主要约束因素,等格栅结构在侧压下是最有效的结构形式。
2.复合材料AGS圆柱壳的鲁棒优化设计方法
通常在制造过程中,对构件尺寸和位置都规定了公差,因此,在进行结构设计时有必要将这些因素考虑在内。为此,本文基于上述混合遗传算法提出了一种针对非完善复合材料AGS圆柱壳的鲁棒优化设计方法,同时考虑了优化目标和约束的鲁棒性。为了简化运算过程,提高优化分析效率,通过敏度分析方法选取对优化结果影响较大的设计变量作为鲁棒优化设计变量(本问题为肋骨高度和斜肋铺设角度)。典型算例结果表明,鲁棒优化设计结果与传统确定性优化结果相比差别较大,表明鲁棒设计是很必要的。此外,AGS圆柱壳对初始几何非圆度缺陷不敏感。
3.复合材料三角形精细Mindlin加筋板/壳单元
由于AGS结构的复杂性和肋骨往往较高,以往的有限元分析模型都存在各种不足。本文构造了用于复合材料AGS结构分析的复合材料三角形精细Mindlin加筋板/壳单元,并推导了考虑几何大变形的非线性有限元列式。在构造过程中假定肋骨和蒙皮横向位移相同,但转角采用相同形函数分别插值,这样既保证两者变形协调性,又放松了肋骨转动的约束。在此单元中,肋骨放置的数量、位置和角度可以任意,为结构的单元网格剖分带来了很大的便利。通过算例计算结果对比,表明本单元具有较好收敛性能,并能够精确计算加筋结构的位移和面内应力,对于高肋格栅加筋结构表现出了独特的优越性。另外,基于该单元还对正交格栅加筋板和等格栅圆柱壳进行了特征值屈曲和后屈曲分析。
4.复合材料AGS结构的损伤累积扩展分析
由于复合材料AGS结构损伤行为的复杂性,有关该方面的报道还很少。本文基于精细加筋单元模型提出了一种用于AGS结构的损伤启始和扩展分析方法。该方法同时考虑了层内损伤和层间损伤,其中,层内损伤包括蒙皮纤维破坏、蒙皮基体开裂、蒙皮纤维-基体剪切破坏以及肋骨纤维破坏,而层间损伤为蒙皮分层损伤。对于层内损伤采用材料常数退化准则;而对于分层损伤,提出了一种新的等效刚度退化准则。另外基于三角形单元提出了一种适用于薄板和中厚层合板的层间剪切应力有限差分计算方法。通过典型算例证明了该损伤模型用于AGS结构分析的有效性,并详细分析了中心含孔复合材料正交各向异性格栅加筋曲板和光板在轴压下的损伤扩展机理和行为。
5.复合材料AGS结构混合分析模型
结合等效刚度模型和精细加筋单元模型构造了一种混合分析模型,即对于需要特殊研究的局部区域应用精细加筋单元离散,而在其他区域应用等效刚度板壳单元离散。这样不仅可以有效地分析AGS结构的局部力学性能,还可降低模型化的工作量,提高计算效率。计算结果表明格栅形状、肋骨间距和高度对等效刚度模型计算结果精度有重要的影响,并通过对带孔复合材料AGS板孔边特殊点应力值的分析,明确了混合法的使用限制。
Advanced composite grid stiffened (AGS) structures not only inherit the traditional excellent qualities of fiber-reinforced composite materials, e.g. high specific strength and stiffness, but also exhibit many unique advantages by combining new material technology and new structure design concepts, e.g. environmental robustness and automatic manufacturing. AGS structures appear to be a promising concept and have been widely used in aircraft and spacecraft design. According to the characteristic of composite AGS plate/shell, this dissertation investigates the model, theory, method and failure process for the AGS structures from global-local and macroscopic-microscopic views. In addition, a corresponding software (AGSANS) is developed. This study is a sub-part of the project of National Basic Research Program of China (973 Project) "Study on multi-functional innovation construction of extra-waighted and porous materials & structures" (No.2006CB601205) and National Science Foundation in China "The fracture mechanism of advanced grid stiffened structure (AGS) with damage" (No. 10302004). It is also supported by a grant from the National Key Technologies R&D Program of China Academy of Launch Vehicle Technology during the 10th Five-Year Plan Period "Optimal design and mechanics analysis for composite AGS structures". The main research work can be summarized as follows:
1. Hybrid Genetic Algorithm of Composite AGS Structures
Considering the characteristics for optimal design of AGS structures, such as nonlinear programming, multi-constraints, and mixed discrete-continuous design variables, etc, a new hybrid genetic algorithm (GA) is developed by combining the improving GA and simplex algorithm (SA), which achieves global optimal solutions more quickly. In the method, some solutions are offered for several traditional problems in SA. The present design problem is to minimize the weight of an AGS cylindrical shell under a given load condition with buckling and strength constraints. An equivalent stiffness model (ESM) is used to analyze the AGS structure. Continuous design variables (rib thickness and angle of diagonal ribs) and discrete variables (rib height, diagonal rib spacing and skin laminate stacking sequence) are both considered. Some numerical examples are discussed about the effects of strength constraints and grid configurations upon the optimal results. It is concluded that global buckling constraint is the key factor for identifying the safety of AGS cylindrical shell, and the triangular grid is the ideal configuration under transverse pressure.
2. Robust Design for Composite AGS Cylindrical Shell
Robust design for the structures is normally necessary, since the size and location of the members generally need high tolerance during manufacturing. Therefore, a robust optimization design method, based on the hybrid GA, for the AGS cylindrical shell with initial-imperfect is proposed, in which both robustness of objective function and constraint functions are considered. To simplify the optimization and reduce the computational cost, the two most sensitive variables, which are introduced in robust analysis, are distinguished from all utilizing sensitivity analysis. In the present analysis, they are rib height and angle of diagonal ribs. By optimizing an AGS cylindrical shell under axial compressure, it can be seen that the optimization results given by the proposed robust design method are quite different from the general deterministic optimization method, and the AGS structures are not sensitive to the initial imperfection.
3. Refined Triangular Composite Stiffened Mindlin Plate/Shell Element
Since the AGS structures are so complex and the ribs are normally higher than skin, the present finite element models are all insufficient. A new refined triangular composite stiffened Mindlin plate/shell element is formulated for simulating AGS structures. The corresponding expressions of geometric nonlinearity are also deduced. In the element, the rotations of the ribs and skin are interpolated, respectively, using the same shape functions, while their transverse deformations are regarded as equal. Therefore, the conditions of displacement compatibility are well maintained along the interface of rib and skin, and the rotational constraints of the stiffeners are released. There are no restrictions on the number and orientation of the ribs in establishing element mesh. The numerical results show its good convergence and effectiveness, especially for the case of the AGS structures of higher ribs. The element can be used to calculate the deformation and in-plane stress of stiffened structures accurately. The studies on the buckling and post-buckling behavior for ortho-grid plate and iso-grid cylindrical shell are also carried out.
4. Progressive Failure Methodology for Composite AGS Structures
Presenting, literatures on the failure analysis of AGS structures is minimal due to its complexity. In this study, a new progressive failure methodology is developed to simulate the onset and growth of multi-failure for composite AGS plates/shells on the basis of the refined stiffened element model (RSEM). The failure modes considered in this study are inter-laminar failure (i.e. delamination in skin) and intra-laminar failure including fiber failure, matrix cracking, fiber-matrix shear failure in skin, and fiber failure in the ribs. For intra-laminar failure modes, corresponding material degradation rules are introduced. However, a new equivalent degraded stiffness rule is proposed for delamination. Meanwhile, a scheme for calculating inter-laminar shear stresses of the triangular element is developed by employing a mixed approach of finite element and finite difference method, which is confirmed available for thin or moderate thick composite laminate plates. The methodology is validated by some typical examples and is employed to evaluate the progressive failure behavior of a composite orthotropic-grid curved panel with a centrally located cutout under compressive load.
5. Mixed Analytical Model of Composite AGS Structures
A new mixed analytical model by conjunction of ESM with RSEM is formulated to simulate the composite AGS structures. The strategy is to use SEM to model the local area, where the mechanical features attract more attention, while use ESM to model the non-local area. It can not only simulate the local behavior more exactly but also be more efficient. The numerical simulations show that the accuracy of ESM is remarkably influenced by the configuration of grid, distance and height of the ribs. The limitation of the mixed analytical model is also investigated by analyzing the stress of a special point at the edge of the cutout located at the central of a grid-stiffened plate.
引文
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