ULiege - Aerospace & Mechanical Engineering http://metafor.ltas.ulg.ac.be/dokuwiki/ 2026-05-15T09:40:43+00:00 http://metafor.ltas.ulg.ac.be/dokuwiki/ http://metafor.ltas.ulg.ac.be/dokuwiki/_media/logo.png text/html 2016-03-30T13:23:04+00:00 Anonymous (anonymous@undisclosed.example.com) http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/integration/scheme/coupledtm?rev=1459344184&do=diff Thermomechanical coupled integration scheme Description Used if MDE_NDYT=1. The mechanical scheme must be quasi-static (MDE_NDYN=0). The thermal scheme is trapezoidal (MDE_THTY=1) or generalized midpoint (MDE_THTY=0) (see Global Parameters [REMOVED]). Data set Old Metafor Version <= 2422 text/html 2022-12-21T10:35:06+00:00 Anonymous (anonymous@undisclosed.example.com) http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/integration/scheme/dynexpl?rev=1671618906&do=diff Explicit dynamic integration schemes Description The equilibrium equation between internal forces $F^{int}$, inertial forces $Ma$ (where $M$ is the diagonalized mass matrix and $a$ the acceleration) and external forces $F^{ext}$ : $$Ma+F^{int}=F^{ext}$$ Central difference method Relations between displacements $x$$v$$a$$$v(t^{n+1/2}) = v(t^{n-1/2}) + (t^{n+1}-t^n) a(t^n) $$$$x(t^{n+1}) = x(t^n) + (t^{n+1}-t^n) v(t^{n+1/2}) $$$$a(t^{n+1}) = (F^{ext}(t^{n+1}) - F^{int}(t^{n+1}))/M $$$$(1-\alp… text/html 2017-06-16T08:28:56+00:00 Anonymous (anonymous@undisclosed.example.com) http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/integration/scheme/dynimpl?rev=1497601736&do=diff Implicit dynamic integration schemes Description This method can manage several sub-methods :Newmark, HHT, Chung Hulbert, generalized midpoint rule, conservative scheme. Alpha-Generalized Family Concerning Chung and Hulbert scheme, the equilibrium equation is rewritten pondering inertia forces by the parameter $\alpha_M$$\alpha_F$$t^{n+1}$$$(1-\alpha_M) \boldsymbol{F}^{\text{inert}}(t^{n+1}) + \alpha_M \boldsymbol{F}^{\text{inert}}(t^n) + (1-\alpha_F) \boldsymbol{F}^{\text{int}}(t^{n+1}) + \… text/html 2016-03-30T13:23:04+00:00 Anonymous (anonymous@undisclosed.example.com) http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/integration/scheme/dynimplexpl?rev=1459344184&do=diff Dynamic implicit/explicit integration scheme Description Can shift from implicit scheme to explicit scheme and reciprocally. Data set Old Metafor Version <= 2422 See dynamic implicit and explicit for a description of schemes and the definition of density and initial velocities. text/html 2016-03-30T13:23:04+00:00 Anonymous (anonymous@undisclosed.example.com) http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/integration/scheme/quasistatique?rev=1459344184&do=diff Quasi-static integration schemes Description In this case, inertial forces $F^{inert}$ are neglected. The equation $F^{int}=F^{ext}$ is then solved iteratively for each time test required. Data set Old Metafor Version <= 2422 No commands are required, quasi-static integration is the default one. If the parameter text/html 2024-06-07T13:58:44+00:00 Anonymous (anonymous@undisclosed.example.com) http://metafor.ltas.ulg.ac.be/dokuwiki/doc/user/integration/scheme/staggeredtm?rev=1717768724&do=diff Thermomechanical staggered integration scheme Description Old Metafor Version <= 2422 Used if MDE_NDYT=2. The mechanical scheme must be quasi-static (MDE_NDYN=0) or alpha genealized (MDE_NDYN=2). The thermal scheme is trapezoidal (MDE_THTY=1) or generalized midpoint (