Numerical procedure to couple shell to solid elements by using Nitsche’s method

Yamamoto, Takeki; Yamada, Takahiro; Matsui, Kazumi

doi:10.1007/s00466-018-1585-6

Cited by 10 publications

(4 citation statements)

References 48 publications

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“…We note that different approaches to handle mixed-dimensional couplings have been proposed in literature. They include the use of special transition finite elements [12], handling multipoint constraint equations [4], applying formulations based on Nitche's method [13], and iterative procedures that couple a global two-dimensional model with a local three-dimensional model via using overlapping decompositions [5]. We note that the use of transition finite elements involves the burden of constructing new finite element types and also complicates the preprocessing step of analysis, as special connectivity of degrees of freedom has to be applied over a local mesh consisting of them.…”

Section: Introductionmentioning

confidence: 99%

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The coupling of solids and shells by conjugate approximations

Malinen¹,

Råback²

2023

RakMek

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In order to get detailed information about deformations of structures efficiently, it may be necessary to use finite element models which combine three-dimensional discretizations of solidswith approximations of two-dimensional models for shells. Here we show how the idea of conjugate approximations can be used as a means to obtain a formulation of mixed-dimensional coupling between shells and solids. Our method is consistent with respect to the principle of virtual workand does not depend on additional computational parameters, an augmentation of a potential-energy functional by introducing new unknowns, or computations over auxiliary meshes.

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Section: Introductionmentioning

confidence: 99%

“…As an alternate to using the Lagrange multipliers, the penalty methods have also been applied to handle multipoint constraint equations, but the questions of consistency and computational accuracy may then arise. For a sampling of earlier work on the subject of this paper, see, for example, papers cited in [13].…”

Section: Introductionmentioning

confidence: 99%

The coupling of solids and shells by conjugate approximations

Malinen¹,

Råback²

2023

RakMek

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“…The coupling on the element interfaces ensures displacement compatibility and stress equilibrium. To this end, multi-point constraints [7], Lagrange multipliers [8,9], Nitsche's method [10] or the Arlequin method [11] can be employed. Methods that utilize the superposition of mathematical models [12,13] can also be classified within this category, where the solution space u is decomposed into local and global contributions u local and u global , resulting in u = u global + u local .…”

Section: Introductionmentioning

confidence: 99%

Two-scale analysis and design of spaceframes with complex additive manufactured nodes

Oztoprak¹,

Paolini²,

D’Acunto³

et al. 2023

Preprint

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The advancements in additive manufacturing (AM) technology have allowed for the production of geometrically complex parts with customizable designs. This versatility benefits large-scale spaceframe structures, as the individual design of each structural node can be tailored to meet specific mechanical and other functional requirements. To this end, however, the design and analysis of such space-frames with distinct structural nodes needs to be highly automated. A critical aspect in this context is automated integration of the local 3D features into the 1D large-scale models. In the present work, a two-scale modeling approach is developed to improve the design and linear-elastic analysis of space frames with complex additively manufactured nodes. The mechanical characteristics of the 3D nodes are numerically reduced through an automated dimensional reduction process based on the Finite Cell Method (FCM) and substructuring. The reduced stiffness quantities are assembled in the large-scale 1D model which, in turn, enables efficient structural analysis. The response of the 1D model is passed on to the local model, enabling fully resolved 3D linear-elastic analysis. The proposed approach is numerically verified on a simplified beam example. Furthermore, the workflow is demonstrated on a tree canopy structure with additively manufactured nodes with bolted connections. The form of the large-scale structure is found based on the Combinatorial Equilibrium Modeling framework, and the different designs of the local structural nodes are based on generative exploration of the design space. It is demonstrated that the proposed methodology effectively automates the design and analysis of space-frame structures with complex, distinct structural nodes.

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“…By coupling this shell model to a fully 3D phase‐field description, the reduced computational effort of a structural element is preserved while refraining from any assumptions or simplifications in the phase‐field. Although the idea of combining solid and structural elements to describe various parts of a structure, such as done for instance in References 59‐63, or even different parts within each other for reinforced structures as for example, in References 64‐66 is not new, the idea to combine solid and structural elements for different fields of a coupled BVP has not been presented before.…”

Section: Introductionmentioning

confidence: 99%

Phase‐field modeling of brittle fracture along the thickness direction of plates and shells

Ambati

Heinzmann

Seiler

et al. 2022

Numerical Meth Engineering

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The prediction of fracture in thin-walled structures is decisive for a wide range of applications. Modeling methods such as the phase-field method usually consider cracks to be constant over the thickness which, especially in load cases involving bending, is an imperfect approximation. In this contribution, fracture phenomena along the thickness direction of structural elements (plates or shells) are addressed with a phase-field modeling approach. For this purpose, a new, so called "mixed-dimensional" model is introduced, which combines structural elements representing the displacement field in the two-dimensional shell midsurface with continuum elements describing a crack phase-field in the three-dimensional solid space. The proposed model uses two separate finite element discretizations, where the transfer of variables between the coupled twoand three-dimensional fields is performed at the integration points which in turn need to have corresponding geometric locations. The governing equations of the proposed mixed-dimensional model are deduced in a consistent manner from a total energy functional with them also being compared to existing standard models. The resulting model has the advantage of a reduced computational effort due to the structural elements while still being able to accurately model arbitrary through-thickness crack evolutions as well as partly along the thickness broken shells due to the continuum elements. Amongst others, the higher accuracy as well as the numerical efficiency of the proposed model are tested and validated by comparing simulation results of the new model to those obtained by standard models using numerous representative examples.

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Numerical procedure to couple shell to solid elements by using Nitsche’s method

Cited by 10 publications

References 48 publications

The coupling of solids and shells by conjugate approximations

The coupling of solids and shells by conjugate approximations

Two-scale analysis and design of spaceframes with complex additive manufactured nodes

Phase‐field modeling of brittle fracture along the thickness direction of plates and shells

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