Joint parameters for strain-based geometrically nonlinear beam formulation: Multibody analysis and experiment

Otsuka, Kiyoshi; Dong, Shuonan; Fujita, Koji; Nagai, Hiroki; Makihara, Kanjuro

doi:10.1016/j.jsv.2022.117241

Cited by 5 publications

References 68 publications

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Nonlinear Dynamic Analysis Framework for Slender Structures Using the Modal Rotation Method

Shizuno,

Dong,

Kuzuno

et al. 2024

Journal of Computational and Nonlinear Dynamics

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Owing to their low induced drag, high-aspect-ratio wings are often applied to aircraft, particularly high-altitude long-endurance aircraft. An analytical method that considers geometrical nonlinearity is necessary for the analysis of high-aspect-ratio wings as they tend to undergo large deformations. Nonlinear shell/plate or solid finite element methods are widely used for the static analysis of wing strength. However, an increase in the number of elements drastically increases the computational costs of nonlinear finite element methods owing to the complexity of wing shapes. The modal rotation method (MRM) can avoid this additional expense by analyzing large deformations based on modes and stiffness matrices obtained from any linear or linearized model. However, MRM has only been formulated as a static analysis method. In this study, a novel modal-based dynamic analysis framework, referred to as dynamic MRM (DMRM), is developed to analyze slender cantilever structures. This paper proposes a method to discretize dynamics by capitalizing on the fact that MRM considers geometrical nonlinearity based on deformed shapes. Additionally, a formulation method for the work performed by an external force modeled as a follower force is proposed. The energy stored in the structure was consistent with the work performed by an external force in each performed simulation. The proposed DMRM selects the modes used for analyses and systematically determines a time step according to the modes. DMRM achieved a 95% reduction in the calculation time compared with a nonlinear plate finite element method in a performed simulation.

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Nonlinear Dynamic Analysis Framework for Slender Structures Using the Modal Rotation Method

Shizuno,

Dong,

Kuzuno

et al. 2024

Journal of Computational and Nonlinear Dynamics

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Moving Morphable Multi Components Introducing Intent of Designer in Topology Optimization

et al. 2023

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Topology optimization based on moving morphable components efficiently generates a topology that is expressed by a few geometrical design variables. However, conventional moving morphable components have three problems: lack of [Formula: see text] continuity between components, difficulty in describing a smooth rollup shape, and difficulty in generating a rigid joint to an optimized topology. In this study, a novel topology optimization framework was developed by introducing theories devised for multibody analysis. First, an adaptive moving morphable component based on absolute nodal coordinate formulation was proposed. Because both the position and gradient are used as design variables, [Formula: see text] continuity is ensured. Second, a position and gradient connection algorithm leveraging the linear constraint of the absolute nodal coordinate formulation was proposed to describe the smooth rollup shape. Third, a rigid joint was generated by introducing the gradient constraint equation in an optimizer. The developed framework exhibited superior convergence as compared with the conventional one in the benchmark short beam problem. It successfully generated an optimal topology with the intent of a designer (that is, designer-selected topology continuity and rigid joints), which facilitated the assembly and manufacturing of topologically optimized structural members to construct an entire aerospace structure.

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Moving Morphable Components Using Strain-Based Beam Geometry Description for Topology Optimization

Otsuka,

Yamashita,

Sugiyama

et al. 2024

AIAA Journal

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In the moving-morphable-component topology optimization, morphable components are introduced as a geometrical model mapped onto the background finite elements, and their shape parameters are utilized as design variables for topology optimization. Whereas a complex curved geometry ensuring [Formula: see text] continuity can be generated using existing curved components, the component curvatures cannot be selected as design variables in the existing methods; thus geometric constraints associated with curvatures cannot also be directly imposed. To address this issue, this study proposes a curvature-based morphable component by introducing the curvilinear geometry representation in the strain-based beam formulation. Since the proposed component is parameterized by curvatures using the curvilinear equation, the component curvatures can be utilized as the design variables. This allows for directly imposing curvature constraints on structural members, thereby accounting for the manufacturability of an optimal topology. It is demonstrated that a symmetric placement of the design variables using the midpoint curvilinear coordinate system is critical in ensuring convergence of the proposed curvature-based component optimization. The symmetric curvature component is further extended to account for multiple curvatures within a single component while ensuring [Formula: see text] continuity. Several examples are presented to demonstrate the benefits of the proposed multicurvature component for topology optimization.

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Joint parameters for strain-based geometrically nonlinear beam formulation: Multibody analysis and experiment

Cited by 5 publications

References 68 publications

Nonlinear Dynamic Analysis Framework for Slender Structures Using the Modal Rotation Method

Nonlinear Dynamic Analysis Framework for Slender Structures Using the Modal Rotation Method

Moving Morphable Multi Components Introducing Intent of Designer in Topology Optimization

Moving Morphable Components Using Strain-Based Beam Geometry Description for Topology Optimization

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