abaqus经典声学分析例题l4-dynamic

1、Buckling, Postbuckling, and Collapse Analysis with ABAQUSLecture 4Damped Static Postbuckling AnalysisCopyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.2OverviewMotivationAutomatic Stabilization and Dashpots Postbuckling and Loss of Contact ExamplesSummaryCopyrigh

2、t 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSMotivationCopyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.4Motivation To obtain an accurate assessment of the postbuckling behavior of structures, static analysis methods are preferred

3、because they provide insight into the postbuckling characteristics of the structure. However, it is not always possible to carry out such an analysis: in situations where loss of contact occurs or where the deformation localizes, the static postbuckling method may fail to yield a solution.In such ca

4、ses a transient analysis can be done, either dynamically or statically with viscous forces.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.5Motivation The addition of inertial forces provides a solution to the physical postbuckling behavior. However, it is not

5、always required or even desired that the actual dynamic solution be obtained. In many cases the objective of the analysis is not to simulate the actual dynamic response but to obtain the static equilibrium state after buckling. In some cases, such as in automotive roof crush or side intrusion calcul

6、ations, elastic buckling is only an initial effect that is followed by extensive bending and plastic deformation.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.6Motivation In such cases a more effective and less “noisy” solution may be obtained through the add

7、ition of suitable “damping” forces in a static analysis. There are two ways in which damping can be introduced in a static analysis:Damping can be introduced using automatic viscous damping with the ABAQUS static procedure options.Alternatively, discrete dashpots can be added to the model. Element t

8、ype DASHPOT1 can be used to damp absolute motions. Element type DASHPOT2 can be used to damp relative motions.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.7Motivation If damping is used in static analysis, the velocity is assumed to be equal to the displacem

9、ent increment divided by the time increment. Assume that the cumulative effect of all damping added to the static model is described by the damping matrix C. The equilibrium equations can then be written in the formCu + I = CDu / Dt + I = P. In linearized form this becomesK + 1 C c= P - I - CDu / Dt

10、.uDt It is clear that the damping matrix becomes more important when the time increment decreases.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSAutomatic Stabilization and DashpotsCopyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQ

11、USL4.9Automatic Stabilization and Dashpots When damping is applied through the automatic stabilization procedure, ABAQUS builds a volume proportional damping matrix:C = cM1,whereM1 = mass matrix with unit density andc= damping factor. ABAQUS automatically determines the damping factor, c, based on t

12、he following premises: The models response in the first increment of a step to which stabilizing damping is applied is stable. Under stable circumstances the amount of dissipated energy should be very small.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.10Auto

13、matic Stabilization and Dashpots This is accomplished as follows:During the first increment of the step, calculations are made of the strain and dissipation energies.These energies are extrapolated to the time scale of the step, as if the solution were to be scaled linearly in time.The damping facto

14、r, c, is determined in such a way that if the solution were linear, the viscous dissipation energy would be a small fraction of the models strain energy at the end of the step.This small fraction, called the dissipation intensity, a, is controlled by the user. It has a default value of2 10-4.Copyrig

15、ht 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.11Automatic Stabilization and Dashpots Alternatively, the user may specify the damping factor directly. Since c is related to the model size and material stiffness in nonobvious ways, it may be difficult to choose a prop

16、er value.Initiate a run without explicit declaration of a damping factor.ABAQUS prints out the value of the damping factor, which can then be used as a guideline for selecting appropriate values.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.12Automatic Stabil

17、ization and Dashpots There are cases where the first increment is either unstable or singular (e.g., due to a rigid body mode).In such cases it is not possible to obtain a solution in the first increment without damping.ABAQUS precomputes the damping factor based on a sampling of the average element

18、 stiffness.If the calculated strain energy in the first increment indicates the solution without damping is stable, the damping factor is recalculated as described earlier; otherwise, the initially calculated factor is maintained. Warning: The damping factor may be stronger than desired; critically

19、review the solution.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.13Automatic Stabilization and DashpotsABAQUS usage: Automatic stabilization Automatic stabilization can be added in the following quasi-static procedures in ABAQUS:*STATIC*VISCO*COUPLED TEMPERA

20、TURE-DISPLACEMENT*SOILS, CONSOLIDATION It is specified by including the STABILIZE parameter on the procedure option. In addition, the FACTOR parameter can also be included on the procedure option.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.14Automatic Stabi

21、lization and Dashpots For example,*STATIC, STABILIZEor*STATIC, STABILIZE=dissipated energy fractionor*STATIC, STABILIZE,damping factorFACTOR=Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.15Automatic Stabilization and Dashpots Volume proportional damping can b

22、e activated during any step of an analysis.The values of the damping coefficient are not carried from one step to the next.They are deactivated if the STABILIZE parameter is not re-declared and recalculated if this parameter is re-declared.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Colla

23、pse Analysis with ABAQUSL4.16Automatic Stabilization and DashpotsOutput variables: Automatic stabilization The total amount of viscous energy dissipated by volume proportional damping is reported separately from other viscous dissipation energies by means of the element output variables ELSD and ESD

24、DEN and the global energy variable ALLSD.Use the *ENERGY OUTPUT or*ENERGY PRINT option to request this output.The reported energy can be limited to a group of elements.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.17Automatic Stabilization and Dashpots The no

25、dal viscous forces and moments are available as nodal output variable VF (VFn and VMn). The damping factor calculated by ABAQUS is reported in the message (.msg) file.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.18Automatic Stabilization and DashpotsNot outp

26、ut by default to.odb file!Copyright 2004 ABAQUS, Inc.ELSDElement stabilization dissipation energyELSDDNElement stabilization dissipation energy densityALLSDElement set or model stabilization dissipation energyVFNodal viscous forcescDamping factor (message file)Buckling, Postbuckling, and Collapse An

27、alysis with ABAQUSL4.19Automatic Stabilization and DashpotsIf you want to know how much you altered a problem by adding stabilization, look at:1Energy dissipation due to stabilizationLook at whole model energies.Here, the total energy dissipated due to stabilization is very small compared to the tot

28、al energies involved in deformation.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.20Automatic Stabilization and Dashpots2Viscous forces during deformationThe figures at right show the load and viscous forces at the load application point as functions of displ

29、acementVF varies significantly in time; its order-of-magnitude is very small compared to the global load, however.Can conclude the presence of stabilization has not changed the problem significantly.Copyright 2004 ABAQUS, Inc.1.510000Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.21Auto

30、matic Stabilization and DashpotsAutomatic stabilization usage hints The automatic calculation of the damping factor, c, is done based on information obtained during the first increment of a step. Thus, the first increment should be representative of the deformation pattern that follows. If the chara

31、cter of the deformation changes during the step, split the step to force a reevaluation of damping. If the first part of the step can be completed without stabilization, it is betterto split the step and introduce stabilization in the latter steps. This ensures that a stable response is the basis fo

32、r computing the damping factor.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.22Automatic Stabilization and DashpotsDashpot usage hints To select the damping coefficients in the dashpots, the following procedure can be used:Estimate the magnitude of the displa

33、cements that will occur after buckling.Divide the estimated displacement magnitude by the step time to get an estimate for the velocity that would occur if the response were stable.Determine typical nodal forces in the model prior to buckling.Choose the damping coefficients such that, for the estima

34、ted velocity, the damping forces will be one to two orders of magnitude less than the static forces.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.23Automatic Stabilization and DashpotsDashpot output variables The total viscous energy dissipated by dashpots is

35、 included in the global energy variable ALLVD. The viscous forces in the dashpots are reported as element variable S11.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.24Automatic Stabilization and DashpotsSummary The methods described on the previous pages will

36、 have the result that, prior to buckling, the damping has almost no effect on the solution. However, as soon as instability in the structure develops, the velocities increase rapidly and damping starts to become effective. For the solution procedure to converge, the time increment will usually decre

37、ase as the velocities increase, leading to a controlled postbuckling behavior. Damping in a static analysis should not be combined with the Riksprocedure. The Riks procedure will calculate the velocities as displacement increments divided by the arc length; hence, these pseudo-velocities will not in

38、crease sufficiently for the dashpots to become effective.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.25Automatic Stabilization and DashpotsExample 1: Damped static postbuckling analysis As an example of dynamic postbuckling, consider this frame structure. T

39、his structure can also be analyzed with the quasi-static method. The structure is expected to buckleat a load of about 57,500 lbs.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.26Automatic Stabilization and Dashpots To investigate the postbuckling behavior, we

40、 apply a load of 150,000 lbs. The load-displacement curve obtained with the Riks quasi-static method and the deformed shape at approximately 250,000 lbs are shown below:Buckling occurs hereunstablestableCopyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.27Automati

41、c Stabilization and Dashpots To analyze the problem as a damped static problem, we add DASHPOT1 elements to every single node in degree of freedom 1 and 2. To calculate a damping value for the dashpots, we estimate typical nodal forces on the order of 10,000 lbs. Considering that the load is applied

42、 over a period of 10 sec and the total deflection is on the order of 100 in, a typical constant velocity to attain the total deformation would be about 10 in/sec. With these assumptions the damping coefficient corresponding to thevelocity would be 1000 lb sec/in. We choose 1% of this value as the ac

43、tual damping coefficient. The partial input for this problem follows; the load-deflection and energy- deflection curves are shown on the subsequent pages.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.28Automatic Stabilization and DashpotsDamped static postbuc

44、kling analysis: partial input*HeadingFrame - damped static postbuckling analysis:*Imperfection, file=framEigen, 1, -0.12*Boundarystep=1ends, 1,*Element,:*Dashpot,:*Dashpot,:2type=dashpot1elset=dashpotxelset=dashpoty*Step, nlgeom, inc=400*Static0.1, 10., , 0.25*Cloadcorner, 2, -200000.*End stepCopyri

45、ght 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.29Automatic Stabilization and DashpotsDamped static postbuckling analysis: resultsSnap-throughInstability starts hereLoad-displacement curveEnergy-displacement curveCopyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and

46、 Collapse Analysis with ABAQUSL4.30Automatic Stabilization and Dashpots As can be seen from the load-displacement curve, the load increases until the instability develops. When the instability develops, the load remains almost constant while the structure snaps through to a stable state. The final d

47、eformed shape of the frame is in static equilibrium without significant forces in the dashpots and agrees with the solution obtained with the Riks method. The energy curves show how the strain energy stored in the structure isreleased in the form of dissipated energy when the snap-through occurs.Cop

48、yright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.31Automatic Stabilization and DashpotsExample 2: Stabilized static postbuckling analysis The same problem is repeated with the dashpots replaced by volume proportional damping. The problem is run with a dissipation i

49、ntensity two orders of magnitude smaller than the default.The default value is too high, because the first increment of the analysis captures essentially axial deformation of the vertical member of the structure.Later on, the snap-through behavior is dominated by bending of thestructure.Since the be

50、nding behavior is much less stiff than the axial behavior, a small fraction of the axial strain energy is still relatively high when compared with the bending strain energy.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.32Automatic Stabilization and DashpotsSt

51、abilized static postbuckling analysis: partial input*HeadingFrame - stabilized static postbuckling:analysis*Imperfection, file=framEigen, 1, -0.12*Boundary ends, 1, 2*Step, nlgeom, inc=400*Static, stabilize=2.e-60.1, 10., , 0.25*Cloadcorner, 2, -200000.*End stepstep=1Copyright 2004 ABAQUS, Inc.Buckl

52、ing, Postbuckling, and Collapse Analysis with ABAQUSL4.33Automatic Stabilization and DashpotsStabilized static postbuckling analysis: resultsSnap-throughLoad-displacement curveEnergy-displacement curveCopyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.34Automatic

53、Stabilization and Dashpots Both the load-displacement curves and the energy curves are very similar to those in the static analysis damped with dashpots.The amount of damping was somewhat less than in the dashpot case and can be controlled with the dissipation intensity.Copyright 2004 ABAQUS, Inc.Bu

54、ckling, Postbuckling, and Collapse Analysis with ABAQUSPostbuckling and Loss of ContactCopyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.36Postbuckling and Loss of Contact Often buckling and postbuckling problems are driven by moving contact surfaces, and the str

55、ucture buckles away from the contact surface. As discussed in Lecture 3, the Riks method is not able to analyze this kind of problem. This kind of discontinuity does not present problems for damped static analysis. At the load level at which contact is lost, the structure deforms without being moved by the boundary conditions, and the inertia and viscous forces ensure that the solution does not diverge.Copyright 2004 ABAQUS, Inc.Buckling, Postbuckling, and Collapse Analysis with ABAQUSL4.37Postbuckling and Loss of ContactExample 3: Stabilization static snap