/ALE/SOLVER/FINT

Block Format Keyword This option defines the numerical method for internal force integration. This is relevant only for brick element and ALE legacy solver (momentum equation solved with FEM).

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/ALE/SOLVER/FINT
Iform

Definition

Field Contents SI Unit Example
Iform Integration method (internal force for brick elements) flag.
= 0
Set to 3.
= 1
Volume integration of the stress tensor using a shape function.
= 2
Surface integration for the hydrostatic stress tensor only.
= 3 (Default)
Surface integration for the stress tensor.

(Real)

Comments

  1. Momentum equation has local form:

    ∂ ρ u ∂ t + d i v ( ρ u u ) = d i v ( σ ) + ρ g MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai abgkGi2kabeg8aYjaahwhaaeaacqGHciITcaWG0baaaiabgUcaRiaa dsgacaWGPbGaamODamaabmaabaGaeqyWdiNaaCyDaiaahwhaaiaawI cacaGLPaaacqGH9aqpcaWGKbGaamyAaiaadAhadaqadaqaaiaaho8a aiaawIcacaGLPaaacqGHRaWkcqaHbpGCcaWHNbaaaa@5135@

    Iform is a flag defining the numerical method to compute d i v ( σ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGKbGaam yAaiaadAhadaqadaqaaiaaho8aaiaawIcacaGLPaaaaaa@3D12@ when integrated over the cell with legacy solver (nodal velocities).
    Iform=1
    F int = ∫ Ω d i v ( σ ) d V MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWHgbWaaS baaSqaaiGacMgacaGGUbGaaiiDaaqabaGccqGH9aqpdaWdXaqaaiaa dsgacaWGPbGaamODaiaacIcacaWHdpGaaiykaaWcbaGaeuyQdCfaba aaniabgUIiYdGccaWGKbGaamOvaaaa@474B@
    Was the default method up to Radioss version 2019.
    Iform=2
    F int = - ∫ ∂ Ω p d S + ∫ Ω d i v ( σ ) d V MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWHgbWaaS baaSqaaiGacMgacaGGUbGaaiiDaaqabaGccqGH9aqpcaqGTaWaa8qm aeaacaWGWbaaleaacqGHciITcqqHPoWvaeaaa0Gaey4kIipakiaads gacaWHtbGaey4kaSYaa8qmaeaacaWGKbGaamyAaiaadAhacaGGOaGa aC4WdiaacMcaaSqaaiabfM6axbqaaaqdcqGHRiI8aOGaamizaiaadA faaaa@50BE@
    The integration method used with obsolete card /CAA (Obsolete)
    Iform=3
    F int = ∫ ∂ Ω ( - p I + σ d e v ) d S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWHgbWaaS baaSqaaiGacMgacaGGUbGaaiiDaaqabaGccqGH9aqpdaWdXaqaamaa bmaabaGaaeylaiaadchacaWHjbGaey4kaSIaaC4WdmaaBaaaleaaca WGKbGaamyzaiaadAhaaeqaaaGccaGLOaGaayzkaaaaleaacqGHciIT cqqHPoWvaeaaa0Gaey4kIipakiaadsgacaWHtbaaaa@4C6D@
    The integration method used as of Radioss version 2020.

    For volume integration, shape functions are used to compute at node, N:

    F int i N = σ i k ∂ Φ N ∂ x k | 0 | Ω | MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWHgbWaa0 baaSqaaiGacMgacaGGUbGaaiiDaaqaaiaadMgacaWGobaaaOGaeyyp a0Jaeq4Wdm3aaSbaaSqaaiaadMgacaWGRbaabeaakmaaeiaabaWaaS aaaeaacqGHciITcqqHMoGrdaWgaaWcbaGaamOtaaqabaaakeaacqGH ciITcaWG4bWaaSbaaSqaaiaadUgaaeqaaaaaaOGaayjcSdWaaSbaaS qaaiaaicdaaeqaaOWaaqWaaeaacqqHPoWvaiaawEa7caGLiWoaaaa@509D@

    Where, i = 1 , 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGPbGaey ypa0JaaGymaiaacYcacaaIZaaaaa@3B84@

    The value ∂ Φ N ∂ x k | 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaabcaqaam aalaaabaGaeyOaIyRaeuOPdy0aaSbaaSqaaiaad6eaaeqaaaGcbaGa eyOaIyRaamiEamaaBaaaleaacaWGRbaabeaaaaaakiaawIa7amaaBa aaleaacaaIWaaabeaaaaa@4166@ is taken at the integration point. It is assumed that:

    ∂ Φ N 1 ∂ x j = − ∂ Φ N 7 ∂ x j   ;   ∂ Φ N 2 ∂ x j = − ∂ Φ N 8 ∂ x j   ;   ∂ Φ N 3 ∂ x j = − ∂ Φ N 5 ∂ x j   ;   ∂ Φ N 4 ∂ x j = − ∂ Φ N 6 ∂ x j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai abgkGi2kabfA6agnaaBaaaleaacaWGobGaaGymaaqabaaakeaacqGH ciITcaWG4bWaaSbaaSqaaiaadQgaaeqaaaaakiabg2da9iabgkHiTm aalaaabaGaeyOaIyRaeuOPdy0aaSbaaSqaaiaad6eacaaI3aaabeaa aOqaaiabgkGi2kaadIhadaWgaaWcbaGaamOAaaqabaaaaOGaaeiiai aacUdacaqGGaWaaSaaaeaacqGHciITcqqHMoGrdaWgaaWcbaGaamOt aiaaikdaaeqaaaGcbaGaeyOaIyRaamiEamaaBaaaleaacaWGQbaabe aaaaGccqGH9aqpcqGHsisldaWcaaqaaiabgkGi2kabfA6agnaaBaaa leaacaWGobGaaGioaaqabaaakeaacqGHciITcaWG4bWaaSbaaSqaai aadQgaaeqaaaaakiaabccacaGG7aGaaeiiamaalaaabaGaeyOaIyRa euOPdy0aaSbaaSqaaiaad6eacaaIZaaabeaaaOqaaiabgkGi2kaadI hadaWgaaWcbaGaamOAaaqabaaaaOGaeyypa0JaeyOeI0YaaSaaaeaa cqGHciITcqqHMoGrdaWgaaWcbaGaamOtaiaaiwdaaeqaaaGcbaGaey OaIyRaamiEamaaBaaaleaacaWGQbaabeaaaaGccaqGGaGaai4oaiaa bccadaWcaaqaaiabgkGi2kabfA6agnaaBaaaleaacaWGobGaaGinaa qabaaakeaacqGHciITcaWG4bWaaSbaaSqaaiaadQgaaeqaaaaakiab g2da9iabgkHiTmaalaaabaGaeyOaIyRaeuOPdy0aaSbaaSqaaiaad6 eacaaI2aaabeaaaOqaaiabgkGi2kaadIhadaWgaaWcbaGaamOAaaqa baaaaaaa@8735@

    This assumption is exact for parallelepipedic shape only, which is why the new default value method is set to surface integration (Iform=3).