Sub-modelling and boundary conditions with -type hybrid-equilibrium plate-membrane elements

Ramsay, A. C. A.; Maunder, E. A. W.

doi:10.1016/j.finel.2006.08.002

Cited by 6 publications

(4 citation statements)

References 5 publications

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“…Such domains are more problematic to analyse using hybrid equilibrium elements if we maintain the constraint of preserving a strong form of equilibrium. However, other work has indicated some directions in which to proceed, for example, map the geometry, but retain Cartesian stress fields within elements , or adopt a curvilinear reference frame for the stress fields . Problems can then arise with enforcing strict codiffusivity of tractions, and some relaxation of local equilibrium may then follow as a result.…”

Section: Introductionmentioning

confidence: 78%

The stability of stars of simplicial hybrid equilibrium finite elements for solid mechanics

Maunder

Almeida

Pereira

2015

Int. J. Numer. Meth. Engng

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Summary In this paper, we define the spurious kinematic modes of hybrid equilibrium 2D and 3D simplicial elements of general degree and present the results of studies on the stability of star patches of such elements. The approach used in these studies is based on first establishing the kinematic properties of a pair of elements that share an interface. This approach is introduced by its application to star patches of hybrid equilibrium triangular plate elements for modelling membrane and plate bending problems and then generalised to 3D continua. It is then shown how the existence of spurious kinematic modes depends on the topological and geometrical properties of a patch, as well as on the degree of the polynomial approximation functions of stress and displacement. Copyright © 2015 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 78%

The stability of stars of simplicial hybrid equilibrium finite elements for solid mechanics

Maunder

Almeida

Pereira

2015

Int. J. Numer. Meth. Engng

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“…To analyze a separate finely meshed region of interest, a submodel was created as part of an entire finite element model to produce more accurate results. The boundaries of the submodel were critically evaluated from an engineering point of view [28]. In addition, there are some studies to enlighten the application procedures of this modeling technique into biological problems [29,30].…”

Section: Discussionmentioning

confidence: 99%

Numerical simulation of the effect of time-to-loading on peri-implant bone

Akça

Eser

Canay

2010

Medical Engineering & Physics

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“…At present, the multiscale methods include the local mesh refinement method [29,30], the substructure method [31,32] and the sub-model method [33,34] have attracted much attention and been widely used in modeling the macro-and microscopic mechanical behavior of composite structures [35]. The sub-model method, which separates the areas that need to be focused on from the overall model, establishes refined modeling on the sub-model, and solves the overall model and the sub-model simultaneously [36,37], is one of the promising candidate to simulate the multiscale behaviors of HTS magnets. The coupling between the overall model and the sub-model is realized by establishing interface between the macroscopic model and the microscopic model [35].…”

Section: Introductionmentioning

confidence: 99%

Multiscale modeling on the multi-physical behaviors of high temperature superconducting magnets based on a combined global homogenization and local refinement scheme

Wang,

Jing

2024

Supercond. Sci. Technol.

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The safe and stable operation is a crucial issue in the development of high-field high temperature superconducting (HTS) magnets. In this paper, we construct a multiscale model which couples the homogenized global (macroscopic) behavior and the refined local (mesoscopic) characteristics to simulate the coupled electromagnetic-mechanical-thermal behaviors of the HTS magnets. In the model, the numerical homogenization method is adopted to simulate the macroscopic behavior of the magnets and identify the “dangerous region” of the magnet which are prone to damage or quench. Then, a refined local sub-model which coupling with the macroscopic homogenization model is established by considering the microstructure and physical parameters of each components of the HTS tapes in the “dangerous region”. Thus, a combined global homogenization and local refinement scheme which balances the computational efficiency and numerical accuracy is developed to simulate the coupled multi-physical behaviors of the HTS magnets including the quench and its propagation. Our results show that the refined local sub-model can simulate the electromagnetic field and the stress-strain at the scale of the tape more accurately. Characteristics, such as the discontinuous stress distribution across the interfaces between different layers and the current shunt from the HTS layer to metallic layers during the quench process of HTS tapes, which are beyond the capability of the homogenization model, have also been well depicted by the refined sub-model.

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Sub-modelling and boundary conditions with -type hybrid-equilibrium plate-membrane elements

Cited by 6 publications

References 5 publications

The stability of stars of simplicial hybrid equilibrium finite elements for solid mechanics

The stability of stars of simplicial hybrid equilibrium finite elements for solid mechanics

Numerical simulation of the effect of time-to-loading on peri-implant bone

Multiscale modeling on the multi-physical behaviors of high temperature superconducting magnets based on a combined global homogenization and local refinement scheme

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