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A segmentation-free isogeometric extended mortar contact method
This paper presents a new isogeometric mortar contact formulation based on an
extended finite element interpolation to capture physical pressure
discontinuities at the contact boundary. The so called two-half-pass algorithm
is employed, which leads to an unbiased formulation and, when applied to the
mortar setting, has the additional advantage that the mortar coupling term is
no longer present in the contact forces. As a result, the computationally
expensive segmentation at overlapping master-slave element boundaries, usually
required in mortar methods (although often simplified with loss of accuracy),
is not needed from the outset. For the numerical integration of general contact
problems, the so-called refined boundary quadrature is employed, which is based
on adaptive partitioning of contact elements along the contact boundary. The
contact patch test shows that the proposed formulation passes the test without
using either segmentation or refined boundary quadrature. Several numerical
examples are presented to demonstrate the robustness and accuracy of the
proposed formulation.Comment: In this version, we have removed the patch test comparison with the
classical mortar method and removed corresponding statements. They will be
studied in further detail in future work, so that the focus is now entirely
on the new IGA mortar formulatio
Π‘ΠΊΡΠ½ΡΠ΅Π½Π½ΠΎ-Π³ΡΠ°Π½ΠΈΡΠ½ΠΎΠ΅Π»Π΅ΠΌΠ΅Π½ΡΠ½Π° ΡΡ Π΅ΠΌΠ° ΠΌΠ΅ΡΠΎΠ΄Ρ Π΄Π΅ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡΡ ΠΎΠ±Π»Π°ΡΡΡ Π΄Π»Ρ ΠΏΠ»ΠΎΡΠΊΠΈΡ Π·Π°Π΄Π°Ρ ΡΠ΅ΠΎΡΡΡ ΠΏΡΡΠΆΠ½ΠΎΡΡΡ Π· Π½Π΅ΡΡΠΌΡΡΠ½ΠΈΠΌΠΈ ΡΠΎΠ·Π±ΠΈΡΡΡΠΌΠΈ ΠΏΡΠ΄ΠΎΠ±Π»Π°ΡΡΠ΅ΠΉ
Π ΠΎΠ·Π³Π»ΡΠ΄Π°ΡΡΡΡΡ ΡΠ·Π°Π³Π°Π»ΡΠ½Π΅Π½Π½Ρ ΠΏΠ°ΡΠ°Π»Π΅Π»ΡΠ½ΠΎΡ ΠΠ΅ΠΉΠΌΠ°Π½Π°-ΠΠ΅ΠΉΠΌΠ°Π½Π° ΡΠ° ΠΏΠΎΡΠ»ΡΠ΄ΠΎΠ²Π½ΠΎΡ ΠΡΡΡΡ
Π»Π΅-ΠΠ΅ΠΉΠΌΠ°Π½Π° ΡΡ
Π΅ΠΌ ΠΌΠ΅ΡΠΎΠ΄Ρ Π΄Π΅ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡΡ ΠΎΠ±Π»Π°ΡΡΡ Π΄Π»Ρ ΠΏΠ»ΠΎΡΠΊΠΎΡ Π·Π°Π΄Π°ΡΡ ΡΠ΅ΠΎΡΡΡ ΠΏΡΡΠΆΠ½ΠΎΡΡΡ Π·Π° Π½Π΅ΡΡΠΌΡΡΠ½ΠΈΡ
ΡΡΡΠΎΠΊ Π½Π° ΠΌΠ΅ΠΆΡ ΠΏΡΠ΄ΠΎΠ±Π»Π°ΡΡΠ΅ΠΉ. ΠΠ· Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½ΡΠΌ ΠΌΠΎΡΡΠ°ΡΠ½ΠΈΡ
Π΅Π»Π΅ΠΌΠ΅Π½ΡΡΠ² ΡΠΌΠΎΠ²ΠΈ ΡΠ΄Π΅Π°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΌΠ΅Ρ
Π°Π½ΡΡΠ½ΠΎΠ³ΠΎ ΠΊΠΎΠ½ΡΠ°ΠΊΡΡ ΠΏΡΠ΄ΠΎΠ±Π»Π°ΡΡΠ΅ΠΉ Π½Π°Π±Π»ΠΈΠΆΠ°ΡΡΡΡΡ ΡΠ»Π°Π±ΠΊΠΈΠΌΠΈ ΡΠΌΠΎΠ²Π°ΠΌΠΈ. Π§ΠΈΡΠ»ΠΎΠ²Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΈ ΠΎΡΡΠΈΠΌΠ°Π½Ρ Π· Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½ΡΠΌ Π»ΡΠ½ΡΠΉΠ½ΠΈΡ
Π³ΡΠ±ΡΠΈΠ΄Π½ΠΈΡ
ΡΠΊΡΠ½ΡΠ΅Π½Π½ΠΎ-Π³ΡΠ°Π½ΠΈΡΠ½ΠΎΠ΅Π»Π΅ΠΌΠ΅Π½ΡΠ½ΠΈΡ
Π°ΠΏΡΠΎΠΊΡΠΈΠΌΠ°ΡΡΠΉ. ΠΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½ΠΎ ΡΠΊΡΡΡΡ Π½Π°Π±Π»ΠΈΠΆΠ΅Π½ΠΎΠ³ΠΎ ΡΠΎΠ·Π²βΡΠ·ΠΊΡ Π²ΡΠ΄ ΠΊΡΠ»ΡΠΊΠΎΡΡΡ ΠΌΠΎΡΡΠ°ΡΠ½ΠΈΡ
Π΅Π»Π΅ΠΌΠ΅Π½ΡΡΠ² Ρ ΠΉΠΎΠ³ΠΎ Π·Π±ΡΠΆΠ½ΡΡΡΡ ΠΏΡΠΈ Π·Π³ΡΡΠ΅Π½Π½Ρ Π½Π΅ΡΡΠΌΡΡΠ½ΠΈΡ
ΡΡΡΠΎΠΊ ΠΌΠ΅ΡΠΎΠ΄Ρ ΡΠΊΡΠ½ΡΠ΅Π½Π½ΠΈΡ
Π΅Π»Π΅ΠΌΠ΅Π½ΡΡΠ² Ρ ΠΏΡΡΠΌΠΎΠ³ΠΎ ΠΌΠ΅ΡΠΎΠ΄Ρ Π³ΡΠ°Π½ΠΈΡΠ½ΠΈΡ
Π΅Π»Π΅ΠΌΠ΅Π½ΡΡΠ².A generalization of parallel Neumann-Neumann and sequential Dirichlet-Neumann domain decomposition schemes for a plane elasticity problem with nonconforming meshes on the common boundary of subdomains is proposed. These schemes are based on approximation of ideal mechanical contact conditions of subdomains by weak contact conditions using the mortar element method. Numerical solution is obtained by using linear hybrid finite-boundary element approximation. The quality of the approximate solution depending on a number of mortar elements and its convergence in nonconforming meshes of the method of finite elements and the direct method of boundary-value elements are investigated.ΠΠ°Π½ΠΎ ΠΎΠ±ΠΎΠ±ΡΠ΅Π½ΠΈΠ΅ ΠΏΠ°ΡΠ°Π»Π»Π΅Π»ΡΠ½ΠΎΠΉ ΠΠ΅ΠΉΠΌΠ°Π½Π°-ΠΠ΅ΠΉΠΌΠ°Π½Π° ΠΈ ΠΏΠΎΡΠ»Π΅Π΄ΠΎΠ²Π°ΡΠ΅Π»ΡΠ½ΠΎΠΉ ΠΠΈΡΠΈΡ
Π»Π΅-ΠΠ΅ΠΉΠΌΠ°Π½Π° ΡΡ
Π΅ΠΌ ΠΌΠ΅ΡΠΎΠ΄Π° Π΄Π΅ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΈΠΈ ΠΎΠ±Π»Π°ΡΡΠΈ Π΄Π»Ρ ΠΏΠ»ΠΎΡΠΊΠΎΠΉ Π·Π°Π΄Π°ΡΠΈ ΡΠ΅ΠΎΡΠΈΠΈ ΡΠΏΡΡΠ³ΠΎΡΡΠΈ Π² ΡΠ»ΡΡΠ°Π΅ Π½Π΅ΡΠΎΠ²ΠΌΠ΅ΡΡΠ½ΡΡ
ΡΠ΅ΡΠΎΠΊ Π½Π° ΠΎΠ±ΡΠ΅ΠΉ Π³ΡΠ°Π½ΠΈΡΠ΅ ΠΏΠΎΠ΄ΠΎΠ±Π»Π°ΡΡΠ΅ΠΉ. Π’Π°ΠΊΠΎΠ΅ ΠΎΠ±ΠΎΠ±ΡΠ΅Π½ΠΈΠ΅ ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΎ Π½Π° ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΠΈ ΡΡΠ»ΠΎΠ²ΠΈΠΉ ΠΈΠ΄Π΅Π°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΊΠΎΠ½ΡΠ°ΠΊΡΠ° ΠΏΠΎΠ΄ΠΎΠ±Π»Π°ΡΡΠ΅ΠΉ ΡΠ»Π°Π±ΡΠΌΠΈ ΡΡΠ»ΠΎΠ²ΠΈΡΠΌΠΈ Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΠΌΠ΅ΡΠΎΠ΄Π° ΠΌΠΎΡΡΠ°ΡΠ½ΡΡ
ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ². Π§ΠΈΡΠ»Π΅Π½Π½ΠΎΠ΅ ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΎ Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ Π»ΠΈΠ½Π΅ΠΉΠ½ΡΡ
Π³ΠΈΠ±ΡΠΈΠ΄Π½ΡΡ
ΠΊΠΎΠ½Π΅ΡΠ½ΠΎ-Π³ΡΠ°Π½ΠΈΡΠ½ΠΎ-ΡΠ»Π΅ΠΌΠ΅Π½ΡΠ½ΡΡ
Π°ΠΏΠΏΡΠΎΠΊΡΠΈΠΌΠ°ΡΠΈΠΉ. ΠΠ·ΡΡΠ΅Π½Ρ Π²Π»ΠΈΡΠ½ΠΈΠ΅ Π½Π° ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° ΠΌΠΎΡΡΠ°ΡΠ½ΡΡ
ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ², ΡΡ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΡ ΡΠ΅ΡΠ΅Π½ΠΈΡ ΠΏΡΠΈ ΡΠ³ΡΡΠ΅Π½ΠΈΠΈ ΠΈ ΡΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΠΈ Π½Π΅ΡΠΎΠ²ΠΌΠ΅ΡΡΠ½ΡΡ
ΡΠ΅ΡΠΎΠΊ
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