Algorithms and methodologies ============================ Modal analysis -------------- [:external:ref:`R5.01.01 `] Modal solvers and generalized problem solving (GEP) [:external:ref:`R5.01.02 `] Solving the quadratic modal problem (QEP) [:external:ref:`R5.01.03 `] Modal parameters and the norm of eigenvectors [:external:ref:`R5.01.04 `] Procedure for counting eigenvalues [:external:ref:`R5.07.01 `] Calculating non-linear modes Transient dynamic analysis ----------------------------- [:external:ref:`R4.05.01 `] Seismic response by transient analysis [:external:ref:`R5.05.01 `] Solving a second order differential equation using the NIGAM method [:external:ref:`R5.05.02 `] Algorithms for directly integrating the DYNA_LINE_TRAN operator [:external:ref:`R5.05.04 `] Modeling damping in linear dynamics [:external:ref:`R5.05.05 `] Dynamic nonlinear algorithm [:external:ref:`R5.06.03 `] Modeling shocks and friction in transient analysis by modal recombination [:external:ref:`R5.06.04 `] DYNA_TRAN_MODAL operator time integration algorithms Dynamic frequency analysis ------------------------------- [:external:ref:`R5.05.03 `] Harmonic response Spectral analysis and random response -------------------------------------- [:external:ref:`R4.05.02 `] Stochastic approach for seismic analysis [:external:ref:`R4.05.03 `] Seismic response by spectral method [:external:ref:`R7.10.01 `] Analysis of random responses Dynamic substructuring ---------------------------- [:external:ref:`R4.06.02 `] Modal calculation by classical dynamic substructuring [:external:ref:`R4.06.03 `] Cyclic dynamic substructuring [:external:ref:`R5.06.01 `] Model reduction in linear and non-linear dynamics: RITZ method Extrapolation of experimental measurements --------------------------------------- [:external:ref:`R7.20.02 `] Extrapolation of measurements on a numerical model in dynamics Soil-structure interaction ------------------------- [:external:ref:`R4.05.04 `] Soil-structure interaction with spatial variability (operator DYNA_ISS_VARI) [:external:ref:`R4.05.05 `] Generation of seismic signals [:external:ref:`R4.05.06 `] Equivalent linear method for wave propagation in 1D [:external:ref:`R4.05.07 `] Nonlinear soil-structure interaction with the Laplace-Temps method [:external:ref:`R4.05.08 `] Method for taking into account the Floor-Material interaction [:external:ref:`R5.05.09 `] Calculation of reconstituted signals and the transfer function matrix Mechanics of rupture ----------------------- [:external:ref:`R7.02.01 `] Rate of energy release in linear thermoelasticity [:external:ref:`R7.02.03 `] Rate of energy restoration in non-linear thermoelasticity [:external:ref:`R7.02.04 `] Beremin model [:external:ref:`R7.02.05 `] Calculation of stress intensity coefficients in planar linear thermoelasticity [:external:ref:`R7.02.06 `] Bordet and Rice and Tracey models [:external:ref:`R7.02.07 `] Rate of energy restoration in thermo-elasto-plasticity - approach GTP [:external:ref:`R7.02.08 `] Calculation of stress intensity factors by extrapolation of the displacement field [:external:ref:`R7.02.09 `] Weibull model identification [:external:ref:`R7.02.10 `] Simplified analysis of defect harmfulness by the K-beta method [:external:ref:`R7.02.13 `] Crack propagation algorithms with X- FEM [:external:ref:`R7.02.16 `] Gp method: an energetic approach to the prediction of cleavage [:external:ref:`R7.02.17 `] Equivalent crack from a damage field [:external:ref:`R7.02.18 `] Hydro-mechanical element coupled with XFEM [:external:ref:`R7.02.19 `] Cohesive elements with X- FEM [:external:ref:`R7.02.20 `] Computation of T-stress by extrapolation of displacement field Recaliation -------- [:external:ref:`R4.03.06 `] Recalibration algorithm Probabilistic methods ---------------------- [:external:ref:`R4.03.05 `] Probabilistic parametric and non-parametric models in dynamics Boundary and link conditions ------------------------------------- [:external:ref:`R3.03.01 `] Dualization of boundary conditions [:external:ref:`R3.03.02 `] Solid body bond conditions [:external:ref:`R3.03.03 `] 2D-Beam and 3D-Beam Connections [:external:ref:`R3.03.05 `] Elimination of dualized boundary conditions [:external:ref:`R3.03.06 `] Hull-beam connection [:external:ref:`R3.03.08 `] RBE3 linear kinematic relationships [:external:ref:`R3.03.09 `] 3D Harlequin Connector — Beam Nonlinear mechanics ---------------------- [:external:ref:`R5.03.01 `] Quasi-static nonlinear algorithm (operator STAT_NON_LINE) [:external:ref:`R5.03.03 `] Taking into account the hypothesis of plane constraints in nonlinear behaviors [:external:ref:`R5.03.14 `] Implicit and explicit integration of nonlinear behavioral relationships [:external:ref:`R5.03.80 `] Load control methods [:external:ref:`R5.03.81 `] Method IMPLEX [:external:ref:`R7.01.02 `] Modelling of prestressed cables Algebraic solvers -------------------- [:external:ref:`R6.01.02 `] Overview of the conjugate gradient: GCPC Aster and the use of PETSc [:external:ref:`R6.02.01 `] About GAUSS decomposition methods [:external:ref:`R6.02.02 `] Linear solver using the multifrontal method MULT_FRONT [:external:ref:`R6.02.03 `] Overview of direct linear solvers and the use of MUMPS [:external:ref:`R6.03.01 `] Solving non-regular systems by a method of decomposition into singular values Fatigue ------- [:external:ref:`R7.04.01 `] Estimation of lifespan in fatigue with a large number of cycles and in oligocyclic fatigue [:external:ref:`R7.04.02 `] Estimation of fatigue under random stress [:external:ref:`R7.04.04 `] Multi-axial fatigue initiation criteria Thermo-hydro-mechanical coupled ------------------------------ [:external:ref:`R7.01.10 `] THHM Modeling: Generalities and Algorithms [:external:ref:`R7.01.34 `] SUSHI finite volume diagrams for modeling miscible unsaturated flows Contact and friction --------------------- [:external:ref:`R5.03.50 `] Discreet formulation of touch-friction [:external:ref:`R5.03.52 `] Contact elements derived from a continuous hybrid formulation [:external:ref:`R5.03.53 `] Contact in big swings with X- FEM [:external:ref:`R5.03.54 `] Contact in small swipes with X- FEM [:external:ref:`R5.03.55 `] Method LAC — Local Average Contact Large deformations and large displacements ------------------------------------------- [:external:ref:`R3.03.04 `] External pressure efforts during major movements [:external:ref:`R3.03.07 `] Follower pressure for volume shell elements [:external:ref:`R5.03.21 `] Elasto (visco) plastic modeling with isotropic work hardening in large deformations [:external:ref:`R5.03.22 `] Law of behavior in large rotations and small deformations [:external:ref:`R5.03.24 `] Large deformation models GDEF_LOG [:external:ref:`R5.03.40 `] Static and dynamic modeling of beams in large rotations Buckling ---------- [:external:ref:`R7.05.01 `] Structural stability criteria Thermal --------- [:external:ref:`R3.06.07 `] Diagonalization of the thermal mass matrix [:external:ref:`R5.02.01 `] Transient linear thermal algorithm [:external:ref:`R5.02.02 `] Nonlinear thermal [:external:ref:`R5.02.04 `] Nonlinear thermal in a moving coordinate system Fluid-structure interaction ---------------------------- [:external:ref:`R4.07.02 `] Modelling turbulent excitations [:external:ref:`R4.07.03 `] Mass matrix calculation added on a modal basis [:external:ref:`R4.07.04 `] Fluid-structure coupling for tubular structures and coaxial shells [:external:ref:`R4.07.05 `] Homogenization of a network of beams immersed in a fluid [:external:ref:`R4.07.07 `] Identification of fluid forces Boundary analysis -------------- [:external:ref:`R7.07.01 `] Limit load calculation using the Norton-Hoff-Friaâ method, behavior NORTON_HOFF Error estimators -------------------- [:external:ref:`R4.10.01 `] ZHU - ZIENKIEWICZ error estimator [:external:ref:`R4.10.02 `] Residual error estimator [:external:ref:`R4.10.03 `] Residual spatial error indicator for transient thermal [:external:ref:`R4.10.04 `] Detecting singularities and calculating an element size map [:external:ref:`R4.10.05 `] Residual error indicator for HM models [:external:ref:`R4.10.06 `] Error estimators in quantities of interest [:external:ref:`R4.10.07 `] Calculation of the error in relation of behavior in dynamics under a frequency formulation Post-treatments ---------------- [:external:ref:`R3.06.03 `] Calculation of node stresses by local smoothing [:external:ref:`R4.09.01 `] Thermo-mechanical energy balance [:external:ref:`R4.20.01 `] Indicators of discharge and loss of proportionality of elastoplasticity loading [:external:ref:`R7.04.03 `] Post-treatment according to RCC -M [:external:ref:`R7.04.05 `] Algorithm for calculating reinforcement densities [:external:ref:`R7.04.10 `] Wear calculation operator [:external:ref:`R7.10.02 `] Post-processing of modal calculations with shock [:external:ref:`R7.10.03 `] Post-processing of tree line calculations: Campbell diagram [:external:ref:`R7.20.01 `] Projecting a field onto a mesh Business tools ------------- [:external:ref:`R7.06.01 `] Modeling the deformation of fuel assemblies with the MAC3 tool