Higher-continuity s-version of finite element method with B-spline functions

Magome, Nozomi; Morita, Naoki; Kaneko, Shigeki; Mitsume, Naoto

doi:10.1016/j.jcp.2023.112593

Cited by 5 publications

(1 citation statement)

References 80 publications

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“…It is worth noting that layer-wise mixed theory [12,13] can also address this issue. Recently, N. Magome [14] proposed a novel strategy called a B-splinebased SFEM to cover the problems stated above; it can also handle the accuracy of numerical integration and matrix singularity.…”

Section: Introductionmentioning

confidence: 99%

An Eight-Node Non-Conforming Generalized Partial Hybrid Element and Its Application in Stress Analysis of Repaired Composite Laminate Structures

Xing,

Li,

Wang

et al. 2024

Aerospace

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To ensure the overall continuity of displacement and out-of-plane stress in composite laminate structures and to quantitatively analyze the mechanical properties of composite materials after damage or repair, a finite element solution method is applied based on the modified generalized H–R variational principle. This method utilizes an eight-node non-conforming generalized partial hybrid element (NCGPME8). The partial hybrid model established with this hybrid element can accurately satisfy the out-of-plane stress boundary conditions of the structure, ensuring the continuity of out-of-plane stress. Numerical examples are used to validate that this hybrid model can effectively compute thick and thin laminate structures with high accuracy and rapid convergence of out-of-plane stress. Finally, considering the insensitivity to irregular meshes and the accuracy in calculating in-plane stress, this method is propagated by element coefficient deduction or element material replacement, then employed to analyze the in-plane and out-of-plane stress distributions of laminates with damage from stepwise grinding perforations, and laminates repaired in a stepwise fashion. Stress and displacement at different locations on the laminates are compared and analyzed, leading to a quantitative assessment of the impact of damage and repair on the stress distribution of the laminates.

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Section: Introductionmentioning

confidence: 99%

An Eight-Node Non-Conforming Generalized Partial Hybrid Element and Its Application in Stress Analysis of Repaired Composite Laminate Structures

Xing,

Li,

Wang

et al. 2024

Aerospace

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Strategy for simulating high-speed crack propagation in 3D-plate structures based on S-version FEM

He,

Kishi,

Morita

et al. 2024

International Journal of Mechanical Sciences

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Wave propagation analysis in the modified nonlinear time fractional Harry Dym equation: Insights from Khater II method and B-spline schemes

Khater

2024

Mod. Phys. Lett. B

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This study aims to investigate the modified nonlinear time fractional Harry Dym equation using analytical and numerical techniques. The modified nonlinear time fractional Harry Dym equation is a generalization of the classical Harry Dym equation, which describes the propagation of nonlinear waves in a variety of physical systems. The conformable fractional derivative is used to define the time fractional derivative in the equation, which provides a natural and straightforward approach. The Khater II method, a powerful analytical technique, is employed to obtain approximate solutions for the equation. Additionally, three numerical schemes, namely, Cubic-B-spline, Quantic-B-spline and Septic-B-spline schemes, are developed and implemented to solve the equation numerically. The numerical results are compared with other numerical solutions to assess the accuracy and efficiency of the proposed schemes. The physical meaning of the modified nonlinear time fractional Harry Dym equation is discussed in detail, and its relation to other nonlinear evolution equations is highlighted. The results of this study provide new insights into the behavior of nonlinear waves in physical systems and contribute to a better understanding of the physical characterizations of the modified nonlinear time fractional Harry Dym equation.

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Higher-continuity s-version of finite element method with B-spline functions

Cited by 5 publications

References 80 publications

An Eight-Node Non-Conforming Generalized Partial Hybrid Element and Its Application in Stress Analysis of Repaired Composite Laminate Structures

An Eight-Node Non-Conforming Generalized Partial Hybrid Element and Its Application in Stress Analysis of Repaired Composite Laminate Structures

Strategy for simulating high-speed crack propagation in 3D-plate structures based on S-version FEM

Wave propagation analysis in the modified nonlinear time fractional Harry Dym equation: Insights from Khater II method and B-spline schemes

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