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1 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick Date 31/07/2015 Page 1/22 FORMA12 Practical works of the formation introduction to the linear & non-linear dynamic analysis Summary This case east is an introduction to the use of for the dynamic transitory analysis (linear and nonlinear). It deals with thick plate of steel, prone to a sinewave excitation on a mobile plate. The plate is modelled in elements 3D. One compares the transitory analysis on modal basis with a direct transitory analysis. In the last part one takes into account the plasticity of steel by a non-linear law. Various modelings approached are modeling a analyzes modal; direct modeling b transitory; modeling C transient on modal basis; modeling D T transitory on modal basis with static correction; modeling E non-linear transient. The first chapter presents the geometry and the data common to all modelings. Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

2 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick 1 Introduction 1.1 Geometry Date 31/07/2015 Page 2/22 The study relates to a thick steel plate. Its geometry is simple. It is about a simple flattened cube length 2,0 mètres, width 2,0 mètres and thickness 0,003 mètre [Figure 1.1-1]. The plate firmly is embedded on one on its sides (ENCAS) and is fixed on a mobile plate. One wishes to calculate the displacement of a point located on the higher face in a corner of plate, contrary to embedding (not P) [Figure 1.1-2]. 2m 2m 0.03 m z y x Figure P E N C A S y x Figure Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

3 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick 1.2 Date 31/07/2015 Page 3/22 Materials Steel, for the linear analyses, is regarded as an isotropic, elastic material linear S Young modulus E = Pa, coefficient of Fish =0,3, density =8 000 kg /m3 1.3 Boundary conditions and loading The plate is embedded on one on its sides. An engineer inattentive (or somewhat facetious) made an error in the parameters of the mobile plate. Instead of the request envisaged (a synthetic accélérogramme), he sent a simple sinusoidal signal but of very strong amplitude. The plate was not designed for such a jolt and one seeks to determine the movement which the plate could undergo during this unfortunate test. The entry signal is a simple sine of frequency 15 Hertz. The amplitude is 30g horizontally and 30g vertically to the bottom ( The duration of the signal is g =10 m/s 2 ). 0.5 s. Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

4 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick 2 Modeling A modal Analysis 2.1 Objectives Date 31/07/2015 Page 4/22 To have an idea of the dynamic properties of the system, one starts with a modal analysis. The geometry is drawn then with a grid under SALOME-MECA. The first modes of the plate are then calculated with Geometry in SALOMÉ One models the system in SALOMÉ. In the module Geometry, the menu is used New Entity > Primitive > Box to build a box with the dimension of the problem. To specify in the boundary conditions and to identify the nodes useful for postprocessings, one needs to name some elements of the geometry and some nodes. It is done thanks to New Entity > Group > Create. The plate is fixed on one on the sides. One makes use of a point of the higher face, in an opposite angle at the embedded edge, like node of postprocessing. To be able to specify the smoothness of the grid in the thickness of the plate, it can be useful to create a group corresponding to stops vertical of one of the corners of the plate. Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick 2.1.2 Date 31/07/2015 Page 6/22 Grid in SALOMÉ The following stage is the creation of the grid by the module Mesh.

6 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick Date 31/07/2015 Page 6/22 Grid in SALOMÉ The following stage is the creation of the grid by the module Mesh. Many mailleurs are available in the software. To obtain a regulated and prédictible grid, a choice possible is Hexahedron (I, J, K) /Quadrangle (Mapping) /Wire discretization Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

7 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick Date 31/07/2015 Page 7/22 To avoid a too fine grid in the thickness of the plate, one advises to create a under-grid on one of stop corner. N.B. one should not forget to propagate the discretization of stops corner chosen on the others by specifying it in Add. Hypothesis. Like compromise meanwhile of calculation and precision, one will be able to create 40 elements in the width from the plate and 2 in the thickness. A coarse grid then is obtained but this defect can be to compensate by quadratic elements. To pass from linear elements to quadratic elements one uses the following option in the menu meshing Modification > Convert to/from quadratic. At the end of the procedure, the grid understands 4725 nodes and 800 elements 3D. Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

10 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick 2.2 Date 31/07/2015 Page 10/22 Modal analysis with To calculate the first modes in simple cases with, the simplest tool is probably the assistant available in SALOME-MECA. Once activated the module Aster, one uses Wizards aster > Modal Analysis and one can let oneself guide by the few dialog boxes. If the calculation of 4 modes is asked for, one should obtain the modes until a frequency of It is a careful choice since the frequency of excitation rises only with 15 Hz. 50 Hz. N.B. thanks to the editor of orders Eficas, one can modify the command file and directly choose the option of calculation on a tape frequencies. It is simply enough to specify, in CALC_MODES, the following option OPTION=' BANDE', CALC_FREQ=_F (FREQ= (0., 50.),) 2.3 Postprocessing in PARAVIS Postprocessing in SALOME/PARAVIS is rather intuitive. However some stages should be known initially to charge the module PARAVIS To explore a result with format MED, one imports the file of results thanks to WireE > Open Paraview Slips by. One creates the vectors of visualization of displacements by reading the modes by the action of the button apply (not to forget to notch the option GenerateVectors ) The filter warp makes it possible to obtain the deformation of the mode. By a menu of the bar top, One can also choose to color the deformation. Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

Illustration 1 First mode (6.3 Hz) Illustration 2 Second mode (13.4 Hz) Illustration 3 Third mode (38.

0 Hz) To check the quality of the grid, one can, of course, make a study of convergence according to the smoothness of

But on such a simple geometry, it is possible to find a good approximation by an analytical formula (for example in

11 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick Date 31/07/2015 Page 11/22 Here, by way of an example some modal deformations Illustration 1 First mode (6.3 Hz) Illustration 2 Second mode (13.4 Hz) Illustration 3 Third mode (38.6 Hz) Illustration 4 Fourth Mode (49.0 Hz) To check the quality of the grid, one can, of course, make a study of convergence according to the smoothness of the grid. But on such a simple geometry, it is possible to find a good approximation by an analytical formula (for example in Formulated for Stress, Structural Strain, and Matrices, Walter D. Pikey éd. John Wiley & Sounds, Inc. 1994). In the studied case, one finds f1=6.23 Hz f3=38.16 Hz The results given by are thus rather precise, in spite of the coarseness of the grid. With a linear grid, the results would not have been also good. Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

12 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick Date 31/07/2015 Page 12/22 Modeling B direct transitory Analysis Problem and draft of calculation One now wishes to calculate the movement of the plate on his mobile plate. One starts with the most natural calculation, direct calculation on physical basis. Platform SALOME-MECA does not propose yet of assistant. But one can help oneself of the graphic and syntactic assistance to the drafting of the command files, EFICAS The principal stages of the command file are; beginning BEGINNING reading of the grid LIRE_MAILLAGE construction of the model AFFE_MODELE definition of materials DEFI_MATERIAU affection of materials to the various groups of the grid AFFE_MATERIAU boundary conditions AFFE_CHAR_MECA definition of the loading AFFE_CHAR_MECA (PESANTEUR=_F (GRAVITE=300., DIRECTION= (- 1,0,1)) construction of the matrices of mass and stiffness and of the vector of second memberassembly definition of a list of moments (One can take a list of moments on 0.5 s with a step of time of s ) DEFI_LIST_REEL definition of the modulation in time (sine of period 15 2 π seconds) FORMULA transitory analysis DYNA_VIBRA (TYPE_CALCUL=' TRAN', BASE_CALCUL=' PHYS') recovery of displacement in a point RECU_FONCTION impression of the curve IMPR_FONCTION Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

13 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick 3.2 Date 31/07/2015 Page 13/22 Results Let us see the curve of the results One observes a sinusoidal answer to the frequency of excitation. This sinusoidal answer nevertheless is strongly modulated by the answer of the first clean mode of the plate. Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

14 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick Date 31/07/2015 Page 14/22 4 Modeling C analyzes transitory on modal basis 4.1 Problem and indices The transitory analysis can also be done more effectively by projecting the problem on a modal basis. One proposes to compare this method with direct transitory calculation. The procedure is close to that of modeling B. One must simply pay attention to be projected (PROJ_BASE) S equations on the modes, which one already calculated with modeling A. to save time, if one took the precaution to save the modal base in a base ASTER, one can avoid taking again modal calculation and directly beginning the command file with CONTINUATION. recovery of the results of modeling a CONTINUATION definition of the loading of gravity AFFE_CHAR_MECA (PESANTEUR=_F (GRAVITE=300., DIRECTION= (- 1,0,1)) elementary calculation of the second member CALC_VECT_ELEM assembly of the vector of loading to the second member ASSE_VECTEUR projection of the matrices of mass, stiffness and the vector of loading PROJ_BASE data of the multiplicative function in time (sine of period 15 2 π s) FORMULA definition of a list of moments (One can take a list of moments on 0.5 s with a step of time of s ) DEFI_LIST_REEL transitory calculation on modal basis DYNA_VIBRA (TYPE_CALCUL=' TRANS', BASE_CALCUL=' GENE') recovery of the displacement of the point P RECU_FONCTION (RESU_GENE) impression of curved P/temps displacementimpr_fonction Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

15 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick 4.2 Date 31/07/2015 Page 15/22 Results For vertical displacement one gets results very close to direct transitory calculation. But if one examines displacements in the horizontal direction, they are rather different!!! Though the modal base was calculated beyond 45 Hz and that the usual rule was complied with recommending to twice cover the maximum frequency of the excitation, in the horizontal direction, the method by modal projection moves away from the direct result. Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

16 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick Date 31/07/2015 Page 16/22 What did it occur? The plate is in fact very stiff in its plan (horizontal direction). The clean modes thus represent only imperfectly this movement. To restore it correctly, it would be necessary to take much more clean modes. A method is shown however much more powerful. It is the method of the static correction, which makes it possible to take into account the static contribution of the structure the movement. Following modeling is an example of its use. Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

17 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick 5 Model D static correction a posteriori 5.1 Procedure of calculation Date 31/07/2015 Page 17/22 The stages are rather close to the method without static correction. But one adds some stages to take into account the deformations due to the static effects of the loading. Caution! One should not forget to include the correction at the time of the return towards the physical base. taken again modal basecontinuation definition of the loading of gravity AFFE_CHAR_MECA (PESANTEUR=_F (GRAVITE=300., DIRECTION= (- 1,0,1)) elementary calculation of the second member CALC_VECT_ELEM assembly of the vector of loading to the second member ASSE_VECTEUR calculation of the static correction MACRO_ELAST_MULT projection of the matrices of mass, stiffness and the vector of loading PROJ_BASE data of the multiplicative function in time (sine of period 15 2 s) FORMULA definition of a list of moments (One can take a list of moments on 0.5 s with a step of time of s ) DEFI_LIST_REEL One needs also the derivative first and seconds for the multiplicative function in time formula (if one knows their analytical form or CALC_FONCTION for a digital approximation) transitory calculation on modal basis DYNA_VIBRA (TYPE_CALCUL=' TRANS', BASE_CALCUL=' GENE') to give behind MODE_CORR static deformation and to specify behind D_FONC_DT and D_FONC_DT2 the derivative first and seconds recovery of the displacement of the point P RECU_FONCTION (RESU_GENE). Not to forget CORR_STAT=' OUI' impression of curved P/temps displacementimpr_fonction Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

18 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick 5.2 Date 31/07/2015 Page 18/22 Results Thanks to the static correction, the results are much better. Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

19 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick 6 Modeling E dynamics non-linear 6.1 Objective Date 31/07/2015 Page 19/22 One now seeks to determine the damage of the plate caused by the excessive amplitude of the instruction in acceleration. One uses a law of plasticity to consider the deformation residual, following the unfortunate test. 6.2 Procedure of calculation To calculate the dynamic non-linear behavior, one uses the operator of use general DYNA_NON_LINE. It is close to STAT_NON_LINE and its use as a close relation. The principal difference is due to the diagram of integration in time and the influence of inertia (matrix of mass). To compare the linear and non-linear results, one can leave modeling B. The first orders (reading of the grid, definition of the model, materials ) are the same ones. The principal stages are beginning BEGINNING reading of the grid LIRE_MAILLAGE construction of the model _AFFE_MODELE definition of the properties nonlinear materials DEFI_MATERIAU assignment of materials AFFE_MATERIAU boundary conditions AFFE_CHAR_MECA loadings AFFE_CHAR_MECA definition of a list of moments (one can calculate on 0.5 s with a step of DEFI_LIST_REEL then DEFI_LIST_INST modulation in time (sine of pulsation 15 2 ) FORMULA transitory calculation DYNA_NON_LINE (one can use the diagram of NEWMARK) recovery of displacement at the point P RECU_FONCTION impression of the curveimpr_fonction s ) Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

20 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick 6.3 Date 31/07/2015 Page 20/22 To enter a non-linear behavior One considers, for the behavior of the plate, a behaviour elastoplasic with a kinematic damping. The elastic limit is 200 MPa. And one takes E /100 like rate of work hardening. The properties of steel thus entered as follows E = 2.E11 BA_PLAS=DEFI_MATERIAU (ELAS=_F (E=E, NU=.3, RHO=8000.,), ECRO_LINE=_F (D_SIGM_EPSI = E/100, SY = 200.0E6),) In DYNA_NON_LINE one specifies an incremental behavior with a field of elasticity delimited by a criterion of Von Mises COMPORTEMENT=_F (RELATION = VMIS_CINE_LINE, DEFORMATION=' PETIT', TOUT=' OUI',), To facilitate convergence, one can exploit the iteration count before the procedure of linearization of Newton-Raphson is declared in failure CONVERGENCE=_F (ITER_GLOB_MAXI=30,), If the algorithm still does not converge, the step of time will be reduced. With this intention, one must create heuristics of choice of step of time using DEFI_LIST_INST. If the convergence criteria are not reached with a step of time, it will be subdivided in 5 pas de smaller times. LIS=DEFI_LISTE_INST (DEFI_LIST=_F (METHODE=' MANUEL', LIST_INST=LIR,), ECHEC=_F ( SUBD_NIVEAU=5, SUBD_PAS_MINI=1e-5, SUBD_METHODE=' MANUEL',),); Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

21 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick 6.4 Analysis of the results Course of calculation Date 31/07/2015 Page 21/22 With the reading of the file of message.mess, one observes that the iteration count increases when the material enters a non-linéairre field, a contrario linear elastic steps, where convergence is done in a single iteration. For example of time t=0.264 s at time s MOMENT OF CALCULATION E ITERATIONS RESIDUE RESIDUE OPTION NEWTON RELATIVE ABSOLUTE ASSEMBLY RESI_GLOB_RELA RESI_GLOB_MAXI E E-10 TANGENT MOMENT OF CALCULATION E ITERATIONS RESIDUE RESIDUE OPTION NEWTON RELATIVE ABSOLUTE ASSEMBLY RESI_GLOB_RELA RESI_GLOB_MAXI X E-03 X E+02 TANGENT 1 X E-04 X E+01 2 X E-05 X E+00 3 X E-06 X E E E-02 In certain cases, the algorithm can not converge before the 30 allowed iterations. That causes a subdivision of the step of time. Total time CPU increases. One can compare the computing times required by DYNA_LINE_TRAN and DYNA_NON_LINE in the file.resu. For example one finds 7 s for DYNA_VIBRA (TYPE_CALCUL=' TRAN', BASE_CALCUL=' PHYS') and 692 s for DYNA_NON_LINE. Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

22 Titre FORMA12 - Travaux pratiques de la formation «Anal[...] Responsable TAMPANGO Yannick Date 31/07/2015 Page 22/22 Analysis of the curve of displacement It is observed that, compared to elastic design plasticity deadens the amplitude of the answer; the apparent frequency of the structure decreases slightly. These observation are a sign of the easing of the structure under the effect of plasticity. Copyright 2019 EDF R&D - Licensed under the terms of the GNU FDL (http//

FORMA02 - Practical works of the formation Initiation : pipe bent under thermomechanical and dynamic request

Titre : FORMA02 - Travaux pratiques de la formation «Init[...] Date : 02/05/2018 Page : 1/16 FORMA02 - Practical works of the formation Initiation : pipe bent under thermomechanical and dynamic request