Monolithic formulation of electromechanical systems within the context of hybrid finite elements

Agrawal, Manish; Jog, C. S.

doi:10.1007/s00466-016-1356-1

Cited by 12 publications

(4 citation statements)

References 16 publications

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“…The key notion is the choice and evaluation of stress interpolation functions which is inspired from the work of Jog [29,30] in context of conventional FEA framework. The efficient FE implementation of the stated approach for large-deformation contact mechanics [2], structural acoustics [32], electromagnetic analysis [31], analysis of electromechanical systems [1], and coupled fluid-structure problem [38] confirms the effectiveness and robustness of the method. In the present study, the systematic evaluation of stress interpolation functions specific to the NURBS interpolations and its effective implementation in a two-dimensional linear elasticity regime is investigated.…”

Section: Introductionmentioning

confidence: 86%

“…Moreover, with a comparative perspective, the IGA or proposed hybrid IGA performs superior to its FEA or hybrid FEA counterpart. In the second case, the nearly incompressible behavior is investigated by setting the Poisson's ratio close to the value 1 2 . The convergence curves specific to = 0.4999 are presented in the Figure 14b.…”

Section: Infinite Plate With a Hole Problemmentioning

confidence: 99%

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A novel hybrid isogeometric element based on two-field Hellinger-Reissner principle to alleviate different types of locking

Bombarde¹,

Gautam²,

Nandy³

2021

Preprint

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In the present work, a novel class of hybrid elements is proposed to alleviate the locking anomaly in non-uniform rational B-spline (NURBS)-based isogeometric analysis (IGA) using a two-field Hellinger-Reissner variational principle. The proposed hybrid elements are derived by adopting the independent interpolation schemes for displacement and stress field. The key highlight of the present study is the choice and evaluation of higher-order terms for the stress interpolation function to provide a locking-free solution. Furthermore, the present study demonstrates the efficacy of the proposed elements with the treatment of several two-dimensional linear-elastic benchmark problems alongside the conventional single-field IGA, Lagrangian-based finite element analysis (FEA), and hybrid FEA formulation. It is shown that the proposed class of hybrid elements performs effectively for analyzing the nearly incompressible problem domains that are severely affected by volumetric locking along with the thin plate and shell problems where the shear and membrane locking is dominant. A better coarse mesh accuracy of the proposed method in comparison with the conventional formulation is demonstrated through various numerical examples. Moreover, the formulation is not restricted to the locking-dominated problem domains but can also be implemented to solve the problems of general form without any special treatment. Thus, the proposed method is robust, most efficient, and highly effective against different types of locking.

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Section: Introductionmentioning

confidence: 86%

Section: Infinite Plate With a Hole Problemmentioning

confidence: 99%

A novel hybrid isogeometric element based on two-field Hellinger-Reissner principle to alleviate different types of locking

Bombarde¹,

Gautam²,

Nandy³

2021

Preprint

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show abstract

“…Vector field problems require a special type of formulations due to their special continuity requirements at material interfaces. In [25,4,27,1,26], the potential formulation is used in nodal framework. But this potential formulation failed in eliminating the problem of spurious eigenvalues in sharp corner objects.…”

Section: Introductionmentioning

confidence: 99%

Comparative Performance of Novel Nodal-to-Edge finite elements over Conventional Nodal element for Electromagnetic Analysis

Kamireddy¹,

Chavan²,

Nandy³

2022

Preprint

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In nodal based finite element method (FEM), degrees of freedom are associated with the nodes of the element whereas, for edge FEM, degrees of freedom are assigned to the edges of the element. Edge element is constructed based on Whitney spaces. Nodal elements impose both tangential and normal continuity of vector or scalar fields across interface boundaries. But in edge elements only tangential continuity is imposed across interface boundaries, which is consistent with electromagnetic field problems. Therefore the required continuities in the electromagnetic analysis are directly obtained with edge elements whereas in nodal elements they are attained through potential formulations. Hence, while using edge elements, field variables are directly calculated but with nodal elements, post-processing is required to obtain the field variables from the potentials. Here, we present the finite element formulations with the edge element as well as with nodal elements. Thereafter, we have demonstrated the relative performances of different nodal and edge elements through a series of examples. All possible complexities like curved boundaries, non-convex domains, sharp corners, non-homogeneous domains have been addressed in those examples. The robustness of edge elements in predicting the singular eigen values for the domains with sharp edges and corners is evident in the analysis. A better coarse mesh accuracy has been observed for all the edge elements as compared to the respective nodal elements. Edge elements are also not susceptible to mesh distortion.

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“…These methods solve the problem partially by pushing the spurious mode to the higher end of the spectrum. In order to capture singular eigen value in case of sharp edges and corners, in the regularization method we have to use a penalty parameter varying from 0 at the sharp edge to 1 at a large distance from the sharp edge.Also, in order to take care of inherent tangential continuity and normal discontinuity across material interface, potential formulation is used in nodal finite element framework [24], [4], [26], [1], [25]. In [19], a two field variation formulation in electromagnetics which can predict the eigen frequencies very accurately with correct multiplicities.…”

Section: Introductionmentioning

confidence: 99%

A Novel Conversion Technique from Nodal to Edge Finite Element Data Structure for Electromagnetic Analysis

Kamireddy,

Nandy

2021

Preprint

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Standard nodal finite elements in electromagnetic analysis have well-known limitation of occurrence of spurious solution. In order to circumvent the problem, a penalty function method or a regularization method is used with potential formulation. These methods solve the problem partially by pushing the spurious mode to the higher end of the spectrum. But it fails to capture singular eigen values in case of the problem domains with sharp edges and corners. To circumvent this limitation, edge elements have been developed for electromagnetic analysis where degree of freedoms are along the edges. But most of the preprocessors develop complex meshes in nodal framework. In this work, we have developed a novel technique to convert nodal data structure to edge data structure for electromagnetic analysis. We have explained the conversion algorithm in details, mentioning associated complexities with relevant examples. The performance of the developed algorithm has been demonstrated extensively with several examples.

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Monolithic formulation of electromechanical systems within the context of hybrid finite elements

Cited by 12 publications

References 16 publications

A novel hybrid isogeometric element based on two-field Hellinger-Reissner principle to alleviate different types of locking

A novel hybrid isogeometric element based on two-field Hellinger-Reissner principle to alleviate different types of locking

Comparative Performance of Novel Nodal-to-Edge finite elements over Conventional Nodal element for Electromagnetic Analysis

A Novel Conversion Technique from Nodal to Edge Finite Element Data Structure for Electromagnetic Analysis

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