A robust penalty coupling of non-matching isogeometric Kirchhoff–Love shell patches in large deformations

Leonetti, Leonardo; Liguori, Francesco S.; Magisano, Domenico; Kiendl, Josef; Reali, Alessandro; Garcea, Giovanni

doi:10.1016/j.cma.2020.113289

Cited by 51 publications

(26 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We begin by reordering the matrix A ∈ R ndof×ndof stemming from (26) in blocks as follows: where the subscripts i and refer to internal and interface dofs, respectively, where an example is depicted in Fig. 4.…”

Section: The Schur Complement Reductionmentioning

confidence: 99%

“…Finally, penalty methods are widely used in the engineering community due to their conceptual simplicity, see the seminal work [2]. Furthermore, they can be easily and efficiently incorporated into a numerical code, where we refer to [1,13,16,23,26] for more insights and some applications in the context of isogeometric Kirchhoff-Love shells. Nonetheless, a major drawback of this approach resides in their lack of robustness with respect to the choice of penalty parameters.…”

Section: Introductionmentioning

confidence: 99%

“…The contribution in [16] partially addresses these issues by introducing suitably scaled penalty parameters and a single problem-independent userdefined coefficient. This work was recently extended in [26] to alleviate locking by introducing independent fields related to the coupling terms and by exploiting reduced integration techniques. Our contribution falls into this realm.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A projected super-penalty method for the $$C^1$$-coupling of multi-patch isogeometric Kirchhoff plates

2021

View full text Add to dashboard Cite

This work focuses on the development of a super-penalty strategy based on the $$L^2$$ L 2 -projection of suitable coupling terms to achieve $$C^1$$ C 1 -continuity between non-conforming multi-patch isogeometric Kirchhoff plates. In particular, the choice of penalty parameters is driven by the underlying perturbed saddle point problem from which the Lagrange multipliers are eliminated and is performed to guarantee the optimal accuracy of the method. Moreover, by construction, the method does not suffer from boundary locking, especially on very coarse meshes. We demonstrate the applicability of the proposed coupling algorithm to Kirchhoff plates by studying several benchmark examples discretized by non-conforming meshes. In all cases, we recover the optimal rates of convergence achievable by B-splines where we achieve a substantial gain in accuracy per degree-of-freedom compared to other choices of the penalty parameters.

show abstract

Section: The Schur Complement Reductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A projected super-penalty method for the $$C^1$$-coupling of multi-patch isogeometric Kirchhoff plates

2021

View full text Add to dashboard Cite

show abstract

“…Integration points and weights are easily provided by the algorithm given in [5]. The proposed reduced integration rule is accurate and does not give stability problems [18]. However, this does not solve the convergence issue in large deformation problems for high values of the penalty parameter.…”

Section: Penalty Formulation With Reduced Integration and Mixed Integmentioning

confidence: 99%

“…However, they are used to evaluate the tangent global stiffness matrix, making the performance of the iterative process almost unaffected by the penalty parameter α. As a consequence we can now use high values of α without compromising the iterative effort to gain equilibrium [18].…”

Section: Penalty Formulation With Reduced Integration and Mixed Integmentioning

confidence: 99%

Robust and Efficient Large Deformation Analysis of Kirchhoff–love Shells: Locking, Patch Coupling and Iterative Solution

Magisano¹,

Liguori²,

Leonetti³

et al. 2021

14th WCCM-ECCOMAS Congress

View full text Add to dashboard Cite

Isogeometric Kirchhoff-Love elements have received an increasing attention in geometrically nonlinear analysis of thin walled structures. They make it possible to meet the C 1 requirement in the interior of surface patches, to avoid the use of finite rotations and to reduce the number of unknowns compared to shear flexible models. Locking elimination, patch coupling and iterative solution are crucial points for a robust and efficient nonlinear analysis and represent the main focus of this work. Patch-wise reduced integrations are investigated to deal with locking in large deformation problems discretized via a standard displacement-based formulation. An optimal integration scheme for third order C 2 NURBS, in terms of accuracy and efficiency, is identified, allowing to avoid locking without resorting to a mixed formulation. The Newton method with mixed integration points (MIP) is used for the solution of the discrete nonlinear equations with a great reduction of the iterative burden and a superior robustness with respect to the standard Newton scheme. A simple penalty approach for coupling adjacent patches, applicable to either smooth or non-smooth interfaces, is proposed. An accurate coupling, also for a nonmatching discretization, is obtained using an interface-wise reduced integration while the MIP iterative scheme allows for a robust and efficient solution also with very high values of the penalty parameter.

show abstract

References

2022

IGA: Non‐conforming Coupling and Shape Optimization of Complex Multipatch Structures

View full text Add to dashboard Cite

A robust penalty coupling of non-matching isogeometric Kirchhoff–Love shell patches in large deformations

Cited by 51 publications

References 53 publications

A projected super-penalty method for the $$C^1$$-coupling of multi-patch isogeometric Kirchhoff plates

A projected super-penalty method for the $$C^1$$-coupling of multi-patch isogeometric Kirchhoff plates

Robust and Efficient Large Deformation Analysis of Kirchhoff–love Shells: Locking, Patch Coupling and Iterative Solution

References

Contact Info

Product

Resources

About