An Adaptive hp–DG–FE Method for Elliptic Problems: Convergence and Optimality in the 1D Case

Abstract The goal of this paper is to present various types of iterative solvers: gradient iteration, Newton’s method and a quasi-Newton method, for the finite element solution of elliptic problems arising in Gao type beam models (a geometrical type of nonlinearity, with respect to the Euler–Bernoulli hypothesis). Robust behaviour, i.e., convergence independently of the mesh parameters, is proved for these methods, and they are also tested with numerical experiments.

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A novel model of Z-pin insertion in prepreg based on fracture mechanics

Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture ◽

10.1177/09544054211014442 ◽

2021 ◽

pp. 095440542110144

Author(s):

Guobiao Ji ◽

Liang Cheng ◽

Shaohua Fei ◽

Jiangxiong Li ◽

Yinglin Ke

Keyword(s):

Fracture Toughness ◽

Fracture Mechanics ◽

Analytical Model ◽

Model Parameters ◽

Force Model ◽

Fe Model ◽

Cohesive Elements ◽

Fe Method ◽

Insertion Force ◽

Mechanics Model

Through-thickness reinforcement is a promising solution to the problem of delamination susceptibility in laminated composites. Modeling Z-pin–prepreg interaction is essential for accurate robotics-assisted Z-pin insertion. In this paper, a novel Z-pin insertion force model combining the classical cohesive finite element (FE) method with a dynamic analytical fracture mechanics model is proposed. The velocity-dependent cohesive elements, in which the fracture toughness is provided by the analytical model, are implemented in Z-pin insertion FE model to predict the crack initiation and propagation. Then Z-pin insertion experiments are performed on prepreg sample with metallic Z-pins at different velocities to identify the analytical model parameters and validate the simulation predictions offered by the model. Dynamics of Z-pin interaction with inhomogeneous prepreg is described and the effects of insertion velocity on prepreg contact force are studied. Results show that the force model agrees well with experiments and the fracture toughness rises with the increasing Z-pin insertion velocity.

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Multiple solutions for nonlocal elliptic problems with concave–convex nonlinearities and weights

Operator Theory ◽

10.1515/9783110598193-016 ◽

2021 ◽

pp. 207-218

Author(s):

Safia Benmansour ◽

Atika Matallah ◽

Mustapha Meghnafi

Keyword(s):

Multiple Solutions ◽

Elliptic Problems

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Non-compact Elliptic Problems

Singularly Perturbed Methods for Nonlinear Elliptic Problems ◽

10.1017/9781108872638.002 ◽

2021 ◽

pp. 1-53

Keyword(s):

Elliptic Problems

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Development and analysis of composite overwrapped pressure vessels for hydrogen storage

Journal of Composite Materials ◽

10.1177/00219983211033568 ◽

2021 ◽

pp. 002199832110335

Author(s):

Osman Kartav ◽

Serkan Kangal ◽

Kutay Yücetürk ◽

Metin Tanoğlu ◽

Engin Aktaş ◽

...

Keyword(s):

Hydrogen Storage ◽

Damage Model ◽

Pressure Vessels ◽

Filament Winding ◽

Burst Pressure ◽

Fe Model ◽

Fe Method ◽

Liner Material ◽

Mechanical Performances ◽

Metallic Liner

In this study, composite overwrapped pressure vessels (COPVs) for high-pressure hydrogen storage were designed, modeled by finite element (FE) method, manufactured by filament winding technique and tested for burst pressure. Aluminum 6061-T6 was selected as a metallic liner material. Epoxy impregnated carbon filaments were overwrapped over the liner with a winding angle of ±14° to obtain fully overwrapped composite reinforced vessels with non-identical front and back dome layers. The COPVs were loaded with increasing internal pressure up to the burst pressure level. During loading, deformation of the vessels was measured locally with strain gauges. The mechanical performances of COPVs designed with various number of helical, hoop and doily layers were investigated by both experimental and numerical methods. In numerical method, FE analysis containing a simple progressive damage model available in ANSYS software package for the composite section was performed. The results revealed that the FE model provides a good correlation as compared to experimental strain results for the developed COPVs. The burst pressure test results showed that integration of doily layers to the filament winding process resulted with an improvement of the COPVs performance.

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