The Augmented Lagrangian Method as a Framework for Stabilised Methods in Computational Mechanics

Burman, Erik; Hansbo, Peter; Larson, Mats G.

doi:10.1007/s11831-022-09878-6

Cited by 19 publications

(8 citation statements)

References 100 publications

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“…Therefore, we next outline a model formulation based on inequality constraints h(x, y,t) − h b (Z(t), x, y) ≤ 0, cf. developments and results of contact dynamics in continuum mechanics [9].…”

Section: Design-of-experiment: Sampling Contraction Geometriesmentioning

confidence: 99%

“…So either λ = 0 or h = h b . Moreover, the Lagrange multiplier equation (18e) and in fact the entire (conservative part of the) system can be derived from an augmented Lagrangian formulation (by combining the work in [5], [9], [21]), which aids both numerical formulation and implementation. The numerical implementation of such fully nonlinear wave-to-wire models using this inequality constrained formulation is in progress within the finite-element environment Firedrake ( [22], [1], [2], [21]).…”

Section: Design-of-experiment: Sampling Contraction Geometriesmentioning

confidence: 99%

“…• Potential-flow or Boussinesq-type wave modelling for wave-energy devices will be discussed with a new formulation of the coupled wave and buoy motion using an augmented Lagrangian, see [9], [21] ( §IV).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Power optimisation of a rogue-wave energy device in a contraction

Bokhove,

Thompson

2024

Preprint

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We consider optimisation of a wave-energy device placed in a contraction consisting of unidirectional wave-induced buoy motion coupled to a tubular electromagnetic generator. First, optimisation of the generator is achieved by using three induction coils instead of one. Second, geometric optimisation is explored for two contraction-shape parameters. Finally, we discuss the advantages of using nonlinear Boussinesq-type wave models and their coupling to the buoy with an inequality constraint.

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Section: Design-of-experiment: Sampling Contraction Geometriesmentioning

confidence: 99%

Section: Design-of-experiment: Sampling Contraction Geometriesmentioning

confidence: 99%

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Power optimisation of a rogue-wave energy device in a contraction

Bokhove,

Thompson

2024

Preprint

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“…In the table, the solution obtained from the SCA [8] and other algorithms, i.e. augmented Lagrange multiplier (ALM) [48] and improved SCA (ISCA) [49], are also reported. The results demonstrate that APSOIIM provides a better solution in terms of both accuracy and efficiency levels.…”

Section: Gear Train Design Problemmentioning

confidence: 99%

An adaptive particle swarm optimization with information interaction mechanism

Liu,

Wei,

Zhang

2024

Mach. Learn.: Sci. Technol.

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The Particle Swarm Optimization (PSO) algorithm is easy to implement owing to its simple framework, and has been successfully applied to many optimization problems. However, the standard PSO easily falls into the local optimum and has weak search ability. To enhance the optimization ability of the algorithm, this paper proposes an adaptive particle swarm optimization with information interaction mechanism (APSOIIM). First, a chaotic sequence strategy was used to produce uniformly distributed particles and enhance their convergence speed at the initialization stage of the algorithm. Then, an interaction information mechanism is introduced to enhance the diversity of the population with the progress of the search, which can effectively interact with the best information of neighboring particles to maintain the balance between exploration and exploitation. Besides, the convergence was proven to verify the robustness and efficiency of the proposed APSOIIM algorithm. Finally, the proposed APSOIIM was applied to solve the CEC2014 benchmark functions and CEC2017 benchmark functions as well as famous engineering optimization problems. The experimental results show that the proposed APSOIIM has significant advantages over the compared algorithms.

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“…The Lagrange multiplier method transforms an optimization problem with constraints into an unconstrained problem, and satisfies the constraints of the original problem by introducing Lagrange multipliers. Moreover, this method has the advantages of simple algorithm and easy implementation, and performs well in convex optimization problems [42,43]. To realize the accurate fitting of the particle contour, the discrete points comprising the contour are fitted and segmented by setting appropriate error and threshold values.…”

Section: Microstructural Modelingmentioning

confidence: 99%

Experimental and Numerical Investigation into the Mechanical Behavior of Composite Solid Propellants Subject to Uniaxial Tension

Wu,

Jiang,

et al. 2023

Materials

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To further explore the quasi-static mechanical characteristics of composite solid propellants at low strain rates, an investigation was conducted on the mechanical behavior and damage mechanisms of a four-component hydroxy-terminated polybutadiene (HTPB) propellant by means of experiments and numerical simulation. A uniaxial tensile test and scanning electron microscope (SEM) characterization experiment were carried out. A microstructural model, which accurately represents the mesoscopic structure, was developed via the integration of micro-CT scanning and image-processing techniques. The constructed microstructural model was utilized to conduct a numerical simulation of the mechanical behavior. The experimental results demonstrated that the maximum tensile strength increases with increasing strain rate, and the primary cause of propellant failure at low strain rates is the dewetting phenomenon occurring at the interface between the larger particles and the matrix. The maximum tensile strength is 0.48 MPa when the strain rate is 0.00119 s−1, and the maximum tensile strength is 0.37 MPa when the strain rate is 0.000119 s−1. The simulation results indicated a consistent trend in variation when comparing the simulation and experimental curves. This suggested that the established model exhibits a high level of reliability, and provides a promising approach for carrying out microstructural simulations of heterogeneous propellants in future. The mechanical behavior of the propellant can be effectively described by utilizing a mesoscopic finite element model that incorporates the superelastic constitutive model of the matrix and the bilinear cohesive model. This framework facilitates the representation of mesoscopic damage evolution, which consequently provides insights into the damage mechanism. Additionally, the utilization of such models assists in compensating for the limitations of damage evolution characterization experiments.

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The Augmented Lagrangian Method as a Framework for Stabilised Methods in Computational Mechanics

Cited by 19 publications

References 100 publications

Power optimisation of a rogue-wave energy device in a contraction

Power optimisation of a rogue-wave energy device in a contraction

An adaptive particle swarm optimization with information interaction mechanism

Experimental and Numerical Investigation into the Mechanical Behavior of Composite Solid Propellants Subject to Uniaxial Tension

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