A stabilized iRBF mesh-free method for quasi-lower bound shakedown analysis of structures

Ho, Phuc L.H.; Le, Cuong

doi:10.1016/j.compstruc.2019.106157

Cited by 19 publications

(7 citation statements)

References 43 publications

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“…Andersen [8] notably introduced a primal-dual interior-point algorithm with second-order cones, enhancing shakedown analysis potential. Subsequent studies, conducted by researchers including [9][10][11][12][13], have provided further validation of these advancements.…”

Section: Introductionmentioning

confidence: 93%

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A polygonal finite element method for shakedown analysis of structures

Ho,

Le,

Nguyen

et al. 2023

Vietnam J. Mech.

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This study presents an innovative numerical method that combines the polygonal finite element method (Poly-FEM) with conic optimization techniques within the framework of structural shakedown analysis. The resulting optimization problem is formulated as a second-order cone programming (SOCP) problem and is efficiently solved using the MOSEK primal-dual interior-point solver. Numerical experiments validate the computational efficiency and efficacy of the proposed approach.

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Section: Introductionmentioning

confidence: 93%

“…Complementing FEM advancements, smoothed finite element methods (S-FEMs) have found application in this context [11,19,20]. Additionally, mesh-free methods have been effectively employed in shakedown analysis, as seen in the nodal natural element method [21] and the stabilized integrated radial basis function method [12].…”

Section: Introductionmentioning

confidence: 99%

A polygonal finite element method for shakedown analysis of structures

Ho,

Le,

Nguyen

et al. 2023

Vietnam J. Mech.

Self Cite

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“…Trong nội dung này, mô hình tính toán theo thích nghi động học giản yếu sẽ được thực hiện trên các bài toán biến dạng phẳng và so sánh với các kết quả đã được công bố trước đây. Với tiêu chuẩn von Mises được sử dụng, công thức biểu diễn dạng phá hoại biến đổi chiều lặp lại (3) có thể được giải quyết bằng công thức sau: Bài toán này đã được khảo sát rất rộng rãi với nhiều phương pháp xấp xỉ khác nhau, các kết quả số có thể tìm thấy trong rất nhiều công bố trước đây (Belytschko, 1972;Groβ-Weege, 1997;Garcea, Armentano, Petrolo, & Casciaro, 2005;Ho & Le, 2020;Nguyen & ctg., 2012). Bảng 1 trình bày kết quả của bài toán phân tích thích nghi tương ứng với các trường hợp tải trọng khác nhau.…”

Section: Ví Dụ Sốunclassified

Phân Tích Thích Nghi Kết Cấu 2d Sử Dụng Công Thức Động Học Giản Yếu

Dũng¹

2022

HCMCOUJS

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Tóm tắt Trong bài báo này trình bày thuật giải cho bài toán phân tích kết cấu 2D sử dụng công thức động học giản yếu. Phần tử trơn trên cạnh (ES-FEM) kết hợp với tối ưu nón bậc 2 sẽ được sử dụng trong thuật giải kết hợp công thức thích nghi động học giản yếu này. Nghiên cứu cho thấy trong phương pháp đề xuất, mặc dù tính chính xác tăng lên đáng kể nhưng số biến của bài toán tối ưu không tăng nhiều, đảm bảo tính hiệu quả về chi phí tính toán. ABSTRACT In this paper, a solution strategy for a kinematic shakedown analysis formulation has been described. ES-FEM used in combination with second-order cone programming in the frame work of the reduced shakedown kinematic formulation. Results in a comparative advantages that are the size of optimization problem is reduced and that accurate solutions can be obtained with minimal computational effort.

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“…Authors in [7,8] studied steel frames under static and earthquake loadings with limit load analysis methods. Various discretization techniques have been developed to treat the limit problems such as finite elements [9][10][11][12], meshfree methods [13][14][15][16][17], and isogeometric analysis [18].…”

Section: Introductionmentioning

confidence: 99%

Computation of Limit Loads for Bending Plates

Tran

Nguyen

2023

Eng. Technol. Appl. Sci. Res.

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The purpose of this paper is to present a method for calculating the upper bound limit loads of plate bending using a conforming Hsieh-Clough-Tocher (HCT) element. These limit loads can be obtained from Koiter’s kinematic shakedown theorem for the case of one load vertex instead of using the kinematic limit theorem. When combining this theorem with the approximated displacement field, the limit analysis turns into an optimization problem and can be effectively solved by Second-Order Cone Programming (SOCP). Several benchmark plate problems such as square, rectangular, and L-shape plates are investigated to illustrate the effectiveness of the proposed solution. The results of the proposed method show good agreement with the results of previous studies. The maximum error is only 2.91% for the fully clamped rectangular plate problem.

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A stabilized iRBF mesh-free method for quasi-lower bound shakedown analysis of structures

Cited by 19 publications

References 43 publications

A polygonal finite element method for shakedown analysis of structures

A polygonal finite element method for shakedown analysis of structures

Phân Tích Thích Nghi Kết Cấu 2d Sử Dụng Công Thức Động Học Giản Yếu

Computation of Limit Loads for Bending Plates

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