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Презентация была опубликована 2 года назад пользователемСветлана Фефилова

1 S8-1NAS105, Section 8, May 2005 SECTION 8 NONLINEAR ANALYSIS

2 S8-2NAS105, Section 8, May 2005

3 S8-3NAS105, Section 8, May 2005 TABLE OF CONTENTS SectionPage NONLINEAR ANALYSIS…………………………………………………………………………8-7 IS THE PROBLEM NONLINEAR?………………………………………………………………8-8 LINEAR VERSUS NONLINEAR STRUCTURAL ANALYSIS………………………………..8-9 TYPES OF NONLINEAR ANALYSIS………………………………………………………… USER INTERFACE FOR NONLINEAR ANALYSIS………………………………………… SUMMARY OF NONLINEAR ANALYSIS………………………………………………………8-22 OVERVIEW OF TRANSIENT ANALYSIS………………………………………………………8-23 CAN THE PROBLEM BE SOLVED IN A LINEAR SOLUTION?…………………………….8-25 GAP CONSTRAINTS IN SOL 101…………………………………………………………… NONLINEAR LOADS IN DYNAMICS………………………………………………………….8-37 EXAMPLE PROBLEM USING NOLIN…………………………………………………………8-44 HINTS WHEN USING NOLINs…………………………………………………………………8-52 NONLINs IN A MODAL TRANSIENT ANALYSIS……………………………………………8-53 TRANSFER FUNCTION – ADDS TERMS DIRECTLY INTO THE MATRICES………… BASICS OF NONLINEAR ANALYSIS…………………………………………………………8-57 TYPES OF NONLINEAR ELEMENTS…………………………………………………………8-58

4 S8-4NAS105, Section 8, May 2005 TABLE OF CONTENTS (CONT) SectionPage GAP ELEMENT………………………………………………………………………………… NLPARM BULK DATA ENTRY…………………………………………………………………8-72 ADVANCING SCHEMES IN MSC.NASTRAN……………………………………………… GAPS IN SOL 106……………………………………………………………………………….8-74 NONLINEAR TRANSIENT ANALYSIS USING SOL 129……………………………………8-78 HINTS AND RECOMMENDATIONS WHEN USING SOL 129…………………………… NONLINEAR TRANSIENT USER INTERFACE………………………………………………8-82 TYPICAL INPUT FILE SETUP FOR SOL 129……………………………………………… NONLINEAR TRANSIENT SOLUTION STRATEGY…………………………………………8-86 EXAMPLE PROBLEM USING GAP ELEMENTS…………………………………………….8-91 EXAMPLE PROBLEM USING GAP ELEMENTS…………………………………………… D SLIDELINE CONTACT…………………………………………………………………… BCONP BULK DATA ENTRY………………………………………………………………… BLSEG BULK DATA ENTRY……………………………………………………………………8-106 BFRIC BULK DATA ENTRY…………………………………………………………………… BWIDTH BULK DATA ENTRY………………………………………………………………… BOUTPUT BULK DATA ENTRY……………………………………………………………… BOUTPUT CASE CONTROL COMMAND…………………………………………………….8-112

5 S8-5NAS105, Section 8, May 2005 TABLE OF CONTENTS (CONT) SectionPage PARAM ADPCON……………………………………………………………………………… PRINTOUT FOR SOLUTION STRATEGY……………………………………………………8-114 EXAMPLE PROBLEM……………………………………………………………………………8-115 RESTARTS FOR NONLINEAR TRANSIENT ANALYSIS……………………………………8-121 NONLINEAR TRANSIENT ANALYSIS USING SUPERELEMENTS……………………… EXAMPLE PEOBLEM USING SUPERELEMENTS………………………………………… MSC.NASTRAN IMPLICIT NONLINEAR (SOL 600) ANALYSIS …………………………

6 S8-6NAS105, Section 8, May 2005

7 S8-7NAS105, Section 8, May 2005 NONLINEAR ANALYSIS With the advent of both hardware and software, nonlinear analysis has become an integral part of structural analysis u If linear analysis is used to simulate a nonlinear structural behavior, the results may be meaningless. However, there are many times when a linear approximation will suffice u Since the nonlinear analysis is an iterative process, the time it takes to perform a nonlinear analysis is in general substantially longer than that required for a linear analysis u Before starting a nonlinear analysis, you should ask yourself the following questions: l Is my structure truly nonlinear? l Can I idealize the nonlinear behavior in a linear solution? l Can I take advantage of superelements to isolate the nonlinear regions?

8 S8-8NAS105, Section 8, May 2005 IS THE PROBLEM NONLINEAR? The following rules of thumb help decide: u Before the analysis look for l Gaps that might close l Areas where the separation or sliding might occur l Is the problem a snap-through buckling problem? l Does the problem depend on large displacements? (Examples: cables out-of-plane loads on membranes) l Is the material nonlinear? Always run a linear analysis first u After the analysis check for l Stresses (strains) exceeding yield (can use PARAM, BIGER) l Areas with large displacements (ex. > (t / 15) for plates l Gaps that might have opened (closed)

9 S8-9NAS105, Section 8, May 2005 LINEAR VERSUS NONLINEAR STRUCTURAL ANALYSIS What Constitutes a Nonlinear Analysis? u Geometric nonlinear analysis: The kinematic relationship is nonlinear. The displacements and rotations are large. Equilibrium is satisfied in deformed configuration. u Follower forces: Loads are a function of displacements. u Large strain analysis: The element strains are a nonlinear function of the element deformations. u Material nonlinear analysis: Element constitutive relationship is nonlinear. Elements may yield. Element forces are no longer equal to stiffness times displacements (K ee · U e )

10 S8-10NAS105, Section 8, May 2005 LINEAR VERSUS NONLINEAR STRUCTURAL ANALYSIS (CONT) What Constitutes a Nonlinear Analysis? (Cont.) u Buckling analysis: Force transformation matrix is not the transpose of displacement transformation matrix. The equilibrium is satisfied in the perturbed configuration. u Contact (interface) analysis: Gap closure and opening, and relative sliding of different components. u Boundary conditions may change during the solution. u It follows that: l Displacements are not directly proportional to loads. l Results for different loads cannot be superimposed. l The solution is a function of the loading path.

11 S8-11NAS105, Section 8, May 2005 TYPES OF NONLINEAR ANALYSIS Geometric Nonlinearity n Large displacements and large rotations u Element deformations are a nonlinear function of the grid point displacements (nonlinear displacement transformation matrix). u Large displacements l Deflection of highly-loaded thin flat plates (geometric stiffening).

12 S8-12NAS105, Section 8, May 2005 TYPES OF NONLINEAR ANALYSIS Geometric Nonlinearity (Cont.) u Large rotations n Both compatibility and equilibrium are satisfied in a deformed configuration. n Effects of initial stress (geometric or differential stiffness) are included. n The follower force effect can be included. n Examples: cable net, thin shells, tires, water hose, etc.

13 S8-13NAS105, Section 8, May 2005 TYPES OF NONLINEAR ANALYSIS (CONT) Material Nonlinearity n Element stiffness matrix is not constant. n Two reasons for variable stiffness matrix: 1.Stress-strain relationship is nonlinear (I.e., matrix D changes), but strains are small (I.e., matrix B is linear). Example: Yielding structure (nonlinear elastic or plastic), creep User Interface: MATS1 and CREEP Bulk Data entries u Nonlinear elastic l Isotropic (MATS1, MAT1)

14 S8-14NAS105, Section 8, May 2005 TYPES OF NONLINEAR ANALYSIS (CONT) Material Nonlinearity (cont) u Elastic-plastic l Isotropic (MATS1, MAT1) l Anisotropic (MATS1 with MAT2 or MAT9) u Viscoelastic l Isotropic (CREEP, MAT1)

15 S8-15NAS105, Section 8, May 2005 TYPES OF NONLINEAR ANALSYSIS (CONT) Material Nonlinearity (cont) u Visco-elastic-plastic l Isotropic (CREEP, MATS1, MAT1) 2. Strains are large (I.e., strain deformation matrix B is nonlinear). In general, stress-strain relationships and displacement transformation relationships are also nonlinear. Example: Rubber materials User Interface: MATHP, PLPLANE, and PLSOLID Bulk Data entries u Large Strains l Element strains are nonlinear functions of element deformations.

16 S8-16NAS105, Section 8, May 2005 TYPES OF NONLINEAR ANALYSIS (CONT) Material Nonlinearity (cont) u Hyperelastic (large strain) l Isotropic (MATHP) Rubber Bearing (Hyperelastic Material)

17 S8-17NAS105, Section 8, May 2005 TYPES OF NONLINEAR ANALYSIS (CONT) Material Nonlinearity (cont) Temperature-Dependant Material Properties n Linear elastic materials (MATT1, MATT2, and MATT9). n Elastic u Isotropic (MAT1, MATT1) u Orthotropic (MAT2, MATT2) u Anisotropic (MAT2, MATT2, MAT9, MATT9)

18 S8-18NAS105, Section 8, May 2005 TYPES OF NONLINEAR ANALYSIS (CONT) Material Nonlinearity (cont) n Nonlinear elastic materials (MATS1, TABLES1, TABLEST). n Nonlinear Elastic u Isotropic (MAT1, MATS1, MATT1) Note: Nonlinear elastic composite materials cannot be temperature dependant.

19 S8-19NAS105, Section 8, May 2005 TYPES OF NONLINEAR ANALYSIS (CONT) Contact (Interface) Analysis n Treated by gap and 3-D slideline contact. n Example: O-rings, rubber springs in the auto and aerospace industry, auto or bicycle brakes, and rubber seals in disc brakes, etc.

20 S8-20NAS105, Section 8, May 2005 USER INTERFACE FOR NONLINEAR ANALYSIS n Compatible with linear analysis n Analysis types u Nonlinear static analysis: SOL 106 u Quasi-static (creep) analysis: SOL 106 u Linear buckling analysis: SOL 105 u Nonlinear buckling analysis: SOL106 (PARAM, BUCKLE) u Nonlinear transient response analysis: SOL 129 n Subcase structure u Allows changes in loads, boundary conditions (SOL 106), and methods. u Allows changes in output requests.

21 S8-21NAS105, Section 8, May 2005 USER INTERFACE FOR NONLINEAR ANALYSIS (CONT) n Bulk Data classification u Geometric data u Element data u Material data u Boundary conditions u Loads and enforced motion Selectable in Subcases u Solution Strategy

22 S8-22NAS105, Section 8, May 2005 SUMMARY OF NONLINEAR ANALYSIS n In nonlinear analysis: u Any one or more of the following relationships may be nonlinear: l Kinematics l Element compatibility l Constitutive relationship l Equilibrium u Loads may be functions of displacements. u Opening and closing of different components. u Boundary conditions may change. n Nonlinear Solution Sequences: u SOL 106:Nonlinear static analysis (geometric, material, large strain, buckling, surface contact, and constraint changes). u SOL 129:Nonlinear transient analysis (geometric, material, large strain, and surface contact). No constraint changes are allowed.

23 S8-23NAS105, Section 8, May 2005 OVERVIEW OF TRANSIENT ANALYSIS n Static analysis: u Compute a solution U that satisfies the equilibrium equation: F(U) = P n Transient analysis: u Compute a solution u that satisfies the equilibrium equation: n For a linear system n For a general nonlinear system u Mass of the system may change Inertia Forces Damping Forces Element Forces External Load

24 S8-24NAS105, Section 8, May 2005 OVERVIEW OF TRANSIENT ANALYSIS (CONT) u Damping may change u Stiffness may change u Load may be function of system response u In MSC.NASTRAN mass and damping (except for CBUSH and CBUSH1D) cannot change. Therefore, the equilibrium equation is n Nonlinear Transient Analysis u Nonlinear transient analysis proceeds by dividing the time into a number of small time steps.

25 S8-25NAS105, Section 8, May 2005 CAN THE PROBLEM BE SOLVED IN A LINEAR SOLUTION? n Certain class of nonlinear problems can be solved with a linear solution (e.g. SOL 101 or 109). n The following criteria must be satisfied. u The structure must not yield. u The displacements and the rotations of the structure are small. u Boundary condition does not change. u The nonlinearity is localized (recommended). u Ideal for modeling nonlinear springs and dampers. n In Statics, SOL 101 has the ability to model gaps (added in V70.5). Using PARAM, CDITER and SUPORT entries. n In transient solutions, MSC.NASTRAN has a series of nonlinear loads which can be applied to any transient solution to simulate this type of nonlinear problem. u These types of nonlinear loads can be used to simulate nonlinear springs and dampers. u These nonlinear loads are applied on the right hand side of the equation as follows: u N(t) can also be a function of displacement and/or velocity.

26 S8-26NAS105, Section 8, May 2005 GAP CONSTRAINTS ON SOL 101 n The sssalter cda.v70 has been implemented as part of SOL 101 n This feature allows you to model GAPs in SOL 101, rather than having to use SOL 106 with GAP elements. n The feature is actually a GAP constraint. It constrains the displacement of selected dof to be >=0.0 (or the reaction force may not be negative). n This works well for points which may come into contact with the ground. n The initial opening is set to 0.0 and you determine whether the gap is assumed to open or closed. n The constraints are satisfied by an iterative procedure which is built into SOL 101. The process starts with a random vector, which assumes certain GRIDs to be in contact and others to be open. n A solution is obtained when all of the GAP constraints are satisfied (there are no negative reaction forces at the selected dof). n Multiple SUBCASEs are allowed, each is solved separately.

27 S8-27NAS105, Section 8, May 2005 GAP CONSTRAINTS ON SOL 101 (CONT) n User Interface: Input u You need to use the SUPORT Bulk Data entry, some new parameters and a special DMIG entry named CDSHUT. u SUPORT (required) Selects constrained degrees-of-freedom. These points must be in the a-set of the residual structure. This means they must not be dependent in an MPC equation, constrained by SPC, partitioned by OMIT, or in an upstream superelement. u PARAM CDITER,I (required) Constraints will be applied if CDITER is greater than zero. The value is the maximum number of iterations allowed. (Default=0). u PARAM CDPRT Controls the printing of constraint violations during iterations. The sparse matrix printer prints UR (negative displacements) and QR (negative forces of constraint) for constrained degrees-of-freedom. (Default=YES) u PARAM CDPCH Controls the PUNCH output of DMIG CDSHUT records for the final state of the constrained degrees-of-freedom. (Default=NO) u DMIG CDSHUT Optional input of the vector defining the state of the constrained degrees-of-freedom. A one indicates closed and a zero means open. See PARAM CDPCH for a method to have MSC.NASTRAN create these records. (Default=all closed)

28 S8-28NAS105, Section 8, May 2005 GAP CONSTRAINTS ON SOL 101 (CONT) n Output u The output is standard for SOL 101, and all existing postprocessors will work. Forces for closed degrees-of-freedom are in the SPCFORCE output. In addition there is information in the.f06 file which shows diagnostic information for the iterations. A final state vector may be output in the.pch file. n Guidelines u The finite element model input looks just like input to SOL 101 with the addition of input records shown above. It is recommended that the.f06 file be examined to ensure that the iterations have converged, since the results of the last iteration will be output. The last iteration should have zero changes. u If the constraint is between a finite element model and a fixed boundary, then arrange to have one of the degrees-of-freedom at the boundary grid points represent motion perpendicular to the boundary. A positive displacement represents motion away from the boundary. If, on the other hand, the constraint represents relative motion between two bodies, MPC equations are needed to define a relative motion degree-of-freedom, which is then constrained to have a non-negative displacement.

29 S8-29NAS105, Section 8, May 2005 GAP CONSTRAINTS ON SOL 101 (CONT) n Limitations u The only nonlinearity allowed is the constrained displacements. u There is no gap stiffness and no sliding friction. u Free bodies can not be analyzed using SUPORT to define rigid body modes and have constrained degrees-of-freedom in the same model. Parameters INREL and CDITER are mutually exclusive. A fatal message is issued if both parameters are not present. u No constraint changes are allowed between subcases. u There is no guarantee that the solution will converge or that all systems will follow the same path.

30 S8-30NAS105, Section 8, May 2005 GAP CONSTRAINTS ON SOL 101 (CONT) n Example: A cantilever beam with a GAP along the span n Since the GAP constraint only checks to see if a displacement is >=0., we define a dof (by GRID points, 60 and 61) to measure the opening. n Point 60 will measure the gap. n Point 61 will have the initial opening as a constraint. n The following equation will be used (as an MPC) to accomplish this: n If the displacement of GRID 60 becomes less than 0.0, the GAP will be closed and the displacement will be zero (0.0).

31 S8-31NAS105, Section 8, May 2005 GAP CONSTRAINTS ON SOL 101 (CONT) n Example: Input file gap101. dat – ID CBAR, TEST GAP IN SOL 101 SOL 101 CEND TITLE = LINEAR STATICS WITH A GAP LABEL = CANTILEVER BEAM WITH GAP SPC = 1 LOAD = 12 MPC = 100 set 999 = 1 spcforce = ALL MPCFORCE = ALL GPFORCE = ALL $ SUBCASE 1 LABEL = TIP LOAD DISP = ALL BEGIN BULK PARAM,POST,0 GRID,1,,0.,0.,0. =,*(1),=,*(10.),== =(8) GRID,11,,0.,1.,0.,, CBAR,1,1,1,2,11 =,*(1),=,*(1),*(1),== =(7) $ PBAR,1,1,1.,10.,10.,10. PARAM,AUTOSPC,YES MAT1,1,30.+6,,,.283 SPC1,1,123456,1 FORCE,12,10,,2.,0.,–1.,0. $ $ MODEL.05 GAP AT POINT 6 $ $ GRID 60 = GAP MEASUREMENT $ GRID 61 = INITIAL GAP $ U60 = U61+U6 $ GRID,60 GRID,61 MPC,100,6,2,–1.0,60,2,+1.0,,61,2,–1.0 SUPORT,60,2 SPC,1,61,2,.05 PARAM,CDITER,10 ENDDATA

32 S8-32NAS105, Section 8, May 2005 OUTPUT FROM GAP 101

33 S8-33NAS105, Section 8, May 2005 OUTPUT FROM GAP 101

34 S8-34NAS105, Section 8, May 2005 GAP CONSTRAINTS ON SOL 101 (CONT) n Example: gap101. dat – results n From the output, we see that the GAP has not closed under this loading. n For the first iteration, the gaps are assumed closed. n Matrix QRI indicates that we have a negative force in GRID 60 from the gap in the initial iteration, so the gap is opened for the second iteration, which converges. n Example: gap101close.dat – change the loading to – more than enough to close the gap.

35 S8-35NAS105, Section 8, May 2005 OUTPUT FROM GAP101CLOSE

36 S8-36NAS105, Section 8, May 2005 OUTPUT FROM GAP101CLOSE

37 S8-37NAS105, Section 8, May 2005 NONLINEAR LOADS IN DYNAMICS n These nonlinear loads are applied on the right hand side of the equation as follows: where: N(t) is function of displacement and/or velocity. n Allows for the specification of load at a particular degree of freedom to be the function of displacement and velocity at another degree of freedom. Example: Load at grid point 1, displacement component 2 as a function of the displacement component 1 at grid point 3. n Useful for specifying nonlinear springs and nonlinear damping. n Nonlinear loads are specified using NONLINi entries.

38 S8-38NAS105, Section 8, May 2005 NONLINEAR LOADS IN DYNAMICS (CONT) n Nonlinear loads are selected via the NONLINEAR Case Control command. n Nonlinear loads cannot be selected via the DLOAD Case Control command. n All degrees of freedom referenced on NOLINi entry must be members of the solution set. n Velocity for an independent degree of freedom (for the purpose of loads) is calculated as Note: This may be different from that calculated in the integration scheme. But it is acceptable. n In all NOLINi entries a degree of freedom is specified by the grid number and its component number. n All loads generated with NOLINi entries lag behind by one time step t in the linear solutions, they are updated at each time step in SOL 129.

39 S8-39NAS105, Section 8, May 2005 NONLINEAR LOADS IN DYNAMICS (CONT) NOLIN1 Bulk Data Entry Description: Defines nonlinear transient functions of the form. Function of displacement:(1) Function of velocity : (2) where and are the displacement and velocity at point GJ in the direction of CJ. Format: Example: Field Contents SIDNonlinear load set identification number (Integer > 0) GIGrid, scalar, or extra point identification number at which nonlinear load is to be applied. (Integer > 0) CIComponent number for GI. (0 < Integer < 6; blank or zero if GI is a scalar or extra point) SScale factor (Real)

40 S8-40NAS105, Section 8, May 2005 NONLINEAR LOADS IN DYNAMICS (CONT) NOLIN1 Bulk Data Entry (CONT) GJ Grid, Scalar, or extra point identification number (Integer > 0) CJComponent number for GJ according to the following table: TIDIdentification number of a TABLEDi entry. (Integer > 0)

41 S8-41NAS105, Section 8, May 2005 NONLINEAR LOADS IN DYNAMICS (CONT) NOLIN2 Bulk Data Entry Description: Defines nonlinear transient forcing functions of the form: where X j (t) and X k (t) can be either displacement or velocity at points GJ and GK in the directions of CJ and CK. Format: Example:

42 S8-42NAS105, Section 8, May 2005 NONLINEAR LOADS IN DYNAMICS (CONT) NONLIN3 Bulk Data Entry Description: Defines nonlinear transient forcing functions of the form: where X j (t) may be a displacement or a velocity at point GJ in the direction of CJ. Format: Example:

43 S8-43NAS105, Section 8, May 2005 NONLINEAR LOADS IN DYNAMICS (CONT) NONLIN4 Bulk Data Entry Description: Defines nonlinear transient forcing functions of the form: where X j (t) may be a displacement or a velocity at point GJ in the direction of CJ. Format: Example:

44 S8-44NAS105, Section 8, May 2005 EXAMPLE PROBLEM USING NOLIN n The following nonlinear problem can be solved using a linear solution (e.g., SOL 109) n Detailed behavior of the nonlinear spring stopper A = in 2 I = in 4 = 0.3 lb/in 3 20 Beam Elements Forcing Function

45 S8-45NAS105, Section 8, May 2005 EXAMPLE PROBLEM USING NOLIN (CONT)

46 S8-46NAS105, Section 8, May 2005 EXAMPLE PROBLEM USING NOLIN (CONT)

47 S8-47NAS105, Section 8, May 2005 EXAMPLE PROBLEM USING NOLIN (CONT)

48 S8-48NAS105, Section 8, May 2005 EXAMPLE PROBLEM USING NOLIN (CONT) n Input Loading:

49 S8-49NAS105, Section 8, May 2005 EXAMPLE PROBLEM USING NOLIN (CONT) n Response at GRID 10005

50 S8-50NAS105, Section 8, May 2005 EXAMPLE PROBLEM USING NOLIN (CONT) n Response at GRID 10010

51 S8-51NAS105, Section 8, May 2005 EXAMPLE PROBLEM USING NOLIN (CONT) n Nonlinear load:

52 S8-52NAS105, Section 8, May 2005 HINTS WHEN USING NOLINs n Use smaller time steps than normal linear transient analysis. n Start with initial stiffness or damping value and use NOLIN to add or subtract stiffness or damping value rather than defining the whole range on the NOLINs directly. n Verify the nonlinear loads (using NLLOAD). n Easier to use in a direct solution.

53 S8-53NAS105, Section 8, May 2005 NOLINs IN MODAL TRANSIENT ANALYSIS

54 S8-54NAS105, Section 8, May 2005 NOLINs IN MODAL TRANSIENT ANALYSIS (CONT)

55 S8-55NAS105, Section 8, May 2005 NOLINs IN MODAL TRANSIENT ANALYSIS (CONT)

56 S8-56NAS105, Section 8, May 2005 TRANSFER FUNCTION – ADDS TERMS DIRECTLY IN THE MATRICES n Transfer functions are used to add terms directly into the dynamic matrices. The form of these is: where u d =dof determining the row in the matrices b i =term to be added to the diagonal terms in the mass (b 2 ), damping (b 1 ), or stiffness (b 0 ) matrices a i =term to be added in the mass, damping, or stiffness column associated with the u i dof n Equivalent to P-type DMIG matrices (M2PP, B2PP, K2PP) n Defined by the TF Bulk Data entry and selected by the TFL Case Control command (residual structure only)

57 S8-57NAS105, Section 8, May 2005 BASICS OF NONLINEAR ANALYSIS n Basic User Interface: u Solution strategy: l Solution strategy nonlinear static analysisNLPARM l Arc length increments for nonlinear static analysisNLPCI l Solution strategy for nonlinear transient analysisTSTEPNL l Displacement-increment analysisSPCD, SPC u Nonlinear materials: l Nonlinear elastic and plasticMATS1 l Creep materials CREEP l Hyperelastic (rubber-like) materials MATHP l Temperature-dependant elastic materialsMATT1, MATT2, MATT9 l Temperature-dependant nonlinear elastic materials TABLEST, TABLES1 u Geometric nonlinear PARAM, LGDISP u Follower forces FORCE1, FORCE2, MOMENT1, MOMENT2, PLOAD, PLOAD2, PLOADX1, and RFORCE u Nonlinear buckling analysis: PARAM, BUCKLE, in SOL106 u Contact (interface): gap and 3-D slideline contact u Boundary changes: SPC, SPCD, and MPC (in static nonlinear)

58 S8-58NAS105, Section 8, May 2005 TYPES OF NONLINEAR ELEMENTS n Physical elements which support geometric and material nonlinear (selected elements from table 1 from Section 5.1 in the Reference Manual)

59 S8-59NAS105, Section 8, May 2005 TYPES OF NONLINEAR ELEMENTS (CONT) u Small strain – less than 10% (ROD, CONROD, BEAM, QUAD4, TRIA3, HEXA, PENTA, TETRA). u Large strain – hyperelastic elements (QUAD4, QUAD8, QUAD, QUADX, TRIA3, TRIA6, TRIA6, TRIAX, HEXA, PENTA, TETRA) n Contact (interface) elements u GAP u 3-D slideline

60 S8-60NAS105, Section 8, May 2005 GAP ELEMENT n Connects two grid points with the orientation (gap direction). n Opening or closing (contact) is determined in the gap direction. n Uses hard surface contact, I.e., no penetration of grid points is allowed in the gap direction. n Can specify friction between the two points n Uses the penalty method for both contact and friction. n Can have a large opening between the two points. n No large relative slipping between the two points is permitted. n No large rotation for the two points (relative or rigid). NoPGAPCGAP Geometric Nonlinearity MaterialPropertyConnectivity

61 S8-61NAS105, Section 8, May 2005 GAP ELEMENT (CONT) CGAP Bulk Data Entry Defines a gap or frictional element for nonlinear analysis. Format: Example: Alternate Format and Example: n If CID is present, then CID identifies the element coordinate system n T1, T2, and T3 of the CID are the element x-, y-, and z- axis, respectively. n If CID field is blank and GA and GB are not coincident (distance from A to B > ), then the GAP element coordinate system is defined as follows: u GA – GB defines the x-axis. u Orientation vector is given by x 1, x 2, and x 3, (like beam element) or GA – GO defines the x-y plane.

62 S8-62NAS105, Section 8, May 2005 GAP ELEMENT (CONT) n For coincident grid points GA and GB, u If CID is blank, the job is terminated with a fatal message CGAP Element Coordinate System Note: KA and KB is this figure are from the PGAP entry.

63 S8-63NAS105, Section 8, May 2005 GAP ELEMENT (CONT) PGAP Bulk Data Entry Defines the properties of the gap element (CGAP entry) Format: Example:

64 S8-64NAS105, Section 8, May 2005 GAP ELEMENT (CONT) GAP Element Force-Deflection Curve for Nonlinear Analysis. Shear Force for GAP Element.

65 S8-65NAS105, Section 8, May 2005 GAP ELEMENT (CONT) n There are 2 kinds of GAP element: u New and adaptive (TMAX > 0., preferred choice). New GAP can force bisection and stiffness updates. u Old and non-adaptive (TMAX = -1.0) n New adaptive GAP element is recommended. n Initial GAP opening is defined by U 0, not by the distance between GA and GB. n Preload is defined by F 0 (not recommended). n Closed stiffness K a is used when U a – U b > U 0 n The default for open stiffness K b = K a

66 S8-66NAS105, Section 8, May 2005 GAP ELEMENT (CONT) n The transverse shear stiffness K T becomes active upon contact. (The default = 1 * K a ) n The continuation line is applicable for adaptive features of the new GAP element only. n Adaptive features are specified by TMAX > 0. n If the penetration is greater than TMAX, the penalty value is increased by an order of magnitude. n If the penetration is less that TRMIN * TMAX, the penalty value is decreased by an order of magnitude. n MAR defines the lower and upper bounds for the penalty value adjustment ratio Static Friction Kinetic Friction 1 2 DefaultNew

67 S8-67NAS105, Section 8, May 2005 GAP ELEMENT (CONT) n Proper Estimation of Gap Stiffness n The stiffness of the beam at points 1 and 2 n The recommended GAP stiffness: n The recommended stiffness acts rigid when closed, and free when open with an error of 0.1%. n Factors (10 3 or ) may be reduced to facilitate convergence at the expense of accuracy. n Recommended stiffness is based on the decoupled stiffnesses.

68 S8-68NAS105, Section 8, May 2005 GAP ELEMENT (CONT) n Friction Features n Friction effect is turned off with K t = 0 n Static and kinetic frictions are allowed. n Frictional gap problem is path dependent. n Sticking with elastic stiffness K t before slipping n Slipping is similar to plasticity. n Subincremental process similar to plasticity is used for the new gap. n No subincremental process for the old gap. n Accuracy deteriorates if the increment produces large changes in the displacements with friction. n The slip locus is generalized by an ellipse: Closed and Sticking Closed and Slipping

69 S8-69NAS105, Section 8, May 2005 GAP ELEMENT (CONT) n Caution for Using GAP Element n Large displacement or rotation capability is not implemented. n When used for linear analysis, GAP stays linear with the initial stiffness. n The penalty values (K a and K t ) should be as small as possible for solution efficiency, but large enough for acceptable accuracy. n Penalty values are constants while the structural stiffness in the adjacent structure changes continuously during loading. n Avoid friction unless its effect is significant. n Use smaller increments if friction is involved. n Avoid complications by using isotropic friction (for old gap). n Typical coefficients of friction: u Steel on steel (dry) 0.4 to 0.6 u Steel on steel (greasy) 0.05 to 0.1 u Brake lining on cast iron 0.3 to 0.4 u Tire on pavement (dry) 0.8 to 0.9

70 S8-70NAS105, Section 8, May 2005 GAP ELEMENT (CONT)

71 S8-71NAS105, Section 8, May 2005 GAP ELEMENT (CONT) n Output is obtained by a STRESS output request in the Case Control Section. n Output quantities are in the element coordinates. n Output shows GAP status: open, slide, stick, slip. n Positive F x is a compression force. n Total displacement is from the original position. n Slip displacement for the sticking or slipping condition is the slip from the current contact position or slip center. n Slip displacement for the open or sliding condition is the same as the total displacement.

72 S8-72NAS105, Section 8, May 2005 NLPARM BULK DATA ENTRY NLPARM with all its field is shown below Parameters for Nonlinear Static Analysis Control Defines parameters for nonlinear static analysis iteration strategy. Format: Example:

73 S8-73NAS105, Section 8, May 2005 ADVANCING SCHEMES IN MSC.NASTRAN u Constant load increments u Constant displacement increments u Arc-length increments Constant Load Increment FieldContents IDIdentification number (Integer > 0) NINCNumber if increments (0 < Integer < 1000) Example:

74 S8-74NAS105, Section 8, May 2005 GAPS IN SOL 106 n Example: Cantilever beam with a GAP (the same problem as was shown in earlier using SOL 101) n Stiffness of the beam at point 6: n The recommended GAP stiffness:

75 S8-75NAS105, Section 8, May 2005 GAPS IN SOL 106 (CONT) ID CBAR, TEST GAP IN SOL 106 SOL 106 CEND TITLE = LINEAR STATICS WITH A GAP SUBCASE 1 LABEL = TIP LOAD DISP = ALL SPC = 1 LOAD = 12 nlparm = 9 set 999 = 100 stress = 999 force = 999 set 998 = 6,60 spcforce = all GPFORCE = all BEGIN BULK nlparm,9,1 GRID,1,,0.,0.,0. =,*(1),=,*(10.),== =(8) GRID,11,,0.,1.,0.,, CBAR,1,1,1,2,11 =,*(1),=,*(1),*(1),== =(7) PBAR,1,1,1.,10.,10.,10. PARAM,AUTOSPC,YES MAT1,1,30.+6,,,.283 SPC1,1,123456,1 FORCE,12,10,,2000.,0.,–1.,0. $ $ MODEL.05 GAP AT POINT 6 grid,60,,50.,–.5,0.,, CGAP,100,100,6,60,1.,0.,0. PGAP,100,.05,,7.2+9,7.2 ENDDATA

76 S8-76NAS105, Section 8, May 2005 GAP ELEMENTS (CONT)

77 S8-77NAS105, Section 8, May 2005 GAP ELEMENTS (CONT)

78 S8-78NAS105, Section 8, May 2005 NONLINEAR TRANSIENT ANALYSIS USING SOL 129 GENERAL FEATURES n Transient, material nonlinear, geometric nonlinear, combined geometric and material nonlinear, and contact problems can be solved using this solution sequence. n Linear superelements can be used to simplify the nonlinear solution. n Modal reduction (SEQSET, EIGRL) and generalized dynamic reduction (DYNRED) are available for the linear superelements. n Parameter-controlled Restarts are available from the end of any SOL129 subcase, or from SOL 106.

79 S8-79NAS105, Section 8, May 2005 NONLINEAR TRANSIENT ANALYSIS USING SOL 129 (CONT) GENERAL LIMITATIONS n No constraint changes after first subcase – including restart. n No time–varying thermal loads (except using LOADSET–LSEQ) or enforced displacements. n Reduction (GDR, Guyan reduction, component modes) only for superelements. n PARAM G damping only applies to linear elements (requires PARAM,W3 also). n Nonlinear element damping provided by GE on MAT Bulk Data entries (PARAM W4 must also be used) only for initial K. n Damping stays linear (except for damping via CBUSH1D). n No element force output for nonlinear elements. n Upstream loads are ignored in the superelement data recovery. n No grid point stresses for nonlinear elements. n Mass is assumed to remain constant.

80 S8-80NAS105, Section 8, May 2005 HINTS AND RECOMMENDATIONS WHEN USING SOL 129 (CONT) n Care should be taken as to ensure that loading history is properly traced with the adaptive time stepping. n Some damping is desirable for numerical stability There is no such thing as an undamped structure. n Avoid massless degrees of freedom. n Put linear regions in upstream superelement(s). n Use the adaptive time stepping algorithm. n Adaptive time stepping is based on the response of the model, not the dynamic loading. Consequently, if sudden change in loading occurs, the adaptive time step may miss it.

81 S8-81NAS105, Section 8, May 2005 NONLINEAR TRANSIENT USER INTERFACE n Solution sequence u SOL 129. n Solution strategy u TSTEPNL Bulk Data entry. u TSTEPNL Case Control command (always required). u PARAM,LGDISP,1 – enable large displacement nonlinearities (default is –1 = no large displacement effects included) n Mass specification u RHO field in MATi Bulk Data entries. u CMASSi Bulk Data entries for scalar mass elements. u CONMi Bulk Data entries for concentrated mass elements. u PARAM,COUPMASS, to specify the generation of coupled rather than lumped mass matrices for elements with coupled mass capability. u PARAM,WTMASS.

82 S8-82NAS105, Section 8, May 2005 NONLINEAR USER INTERFACE (CONT) n Damping specification u CVISC Bulk Data entry for the viscous damper element u Field GE in MATi Bulk Data entries for nonlinear element damping u PARAM, G for overall structural damping u PARAM, W3 to convert structural damping to equivalent viscous damping u PARAM, W4 to convert element damping to equivalent viscous damping u PARAM, NDAMP to specify numerical damping n Initial conditions specification (same as linear transient) u TIC Bulk Data entry u IC Case Control command

83 S8-83NAS105, Section 8, May 2005 NONLINEAR USER INTERFACE (CONT) n Additional entries for nonlinear analysis u Similar to nonlinear static analysis u Material nonlinear l MATS1 u Geometric nonlinear l PARAM, LGDISP, +1 u Contact (interface) l CGAP/PGAP l BCONP, BLSEG, BWIDTH, BFRIC, BOUTPUT u Combined material and geometric nonlinear l MATS1 l PARAM, LGDISP, +1

84 S8-84NAS105, Section 8, May 2005 TYPICAL INPUT FILE SETUP FOR SOL 129

85 S8-85NAS105, Section 8, May 2005 INTEGRATION SCHEMES n Two-Point Integration Scheme u Use the following equilibrium equation: u Assume that the acceleration for a time step is equal to the average of the beginning and end of the step. u Velocity and displacement are obtained by integration.

86 S8-86NAS105, Section 8, May 2005 INTEGRATION SCHEMES u Rearrange the equilibrium equation in terms of incremental values. Dynamic Stiffness Dynamic Load Factor

87 S8-87NAS105, Section 8, May 2005 INTEGRATION SCHEMES n Two-point integration scheme is the same as the trapezoidal rule or average acceleration method except for the calculation of acceleration in postprocessing. n For linear problems, this scheme is second-order accurate, is unconditionally stable, and has no numerical damping. n Easy starting, restarting, ending. n Residual error carried over effectively.

88 S8-88NAS105, Section 8, May 2005 NONLINEAR TRANSIENT SOLUTION STRATEGY n Specified by TSTEPNL Bulk Data entry n Selected by TSTEPNL Case Control command n TSTEPNL Bulk Data Entry u Description: Defines parametric controls and data for nonlinear transient analysis u Format: u Examples: TSTEPNLIDNDTDTNOKSTEPMAXITIERCONV EPSUEPSPEPSWMAXDIVMAXQNMAXLSFSTRESS MAXBISADJUSTMSTEPRBMAXRUTOLRTOLB TSTEPNL PW 1.00E E

89 S8-89NAS105, Section 8, May 2005 NONLINEAR TRANSIENT SOLUTION STRATEGY Field Contents ID Identification number. (Integer > 0). NDT Number of time steps of value DT. (Integer > 4). DT Time increment. (Real > 0.0). NO Time step interval for output. Every NO-th step will be saved for output. (Integer > 0; Default = 1). KSTEP If METHOD = TSTEP, then KSTEP is the time step interval for stiffness Updates. If METHOD = ADAPT, then KSTEP is the number of converged bisection solutions between stiffness updates. (Integer > 0; Default = 2) MAXITER Limit on number of iterations for each time step. (Integer 0; Default = 10)

90 S8-90NAS105, Section 8, May 2005 NONLINEAR TRANSIENT SOLUTION STRATEGY Field Contents (Cont.) CONVFlags to select convergence criteria. (Character: U, P, W, or any combination; Default = PW) EPSUError tolerance for displacement (U) criterion. (Real > 0.0; Default = 1.0E-2) EPSPError tolerance for load (P) criterion. (Real > 0.0; Default = 1.0E-3) EPSWError tolerance for work (W) criterion. (Real > 0.0; Default = 1.0E-6) MAXDIVLimit on the number of diverging conditions for a time step before the solution is assumed to diverge. (Integer > 0; Default = 2) MAXQNMaximum number of quasi-Newton correction vectors to be saved on the database. (Integer 0; Default = 10) MAXLSMaximum number of line searches allowed per iteration. (Integer 0; Default = 2)

91 S8-91NAS105, Section 8, May 2005 NONLINEAR TRANSIENT SOLUTION STRATEGY Field Contents (Cont.) FSTRESSFraction of effective stress (s) used to limit the subincrement size in the material routines. (0.0 < Real < 1.0; Default = 0.2) MAXBISMaximum number of bisections allowed for each time step. (- 9 Integer 9; Default = 5) ADJUSTTime step skip factor for automatic time step adjustment. (Integer 0; Default = 5) MSTEPNumber of steps to obtain the dominant period response. (10 Integer 200; Default = variable between 20 and 40) RBDefine bounds for maintaining the same time step for the stepping function if METHOD = ADAPT. (0.1 Real 1.0; Default = 0.75) MAXRMaximum ratio for the adjusted incremental time relative to DT allowed for time step adjustment. (1.0 Real 32.0; Default = 16.0)

92 S8-92NAS105, Section 8, May 2005 NONLINEAR TRANSIENT SOLUTION STRATEGY Field Contents (Cont.) UTOLTolerance on displacement increment beneath which there is no time step adjustment. (0.001 > Real 1.0; Default = 0.1) RTOLBMaximum value of incremental rotation (in degrees) allowed per iteration to activate bisection. (Real > 2.0; Default = 20.0)

93 S8-93NAS105, Section 8, May 2005 NONLINEAR TRANSIENT SOLUTION STRATEGY n Automatic Time Step Adjustment (Adaptive Method) u Two-Point Integration Scheme u Time step is automatically adjusted (Use ADJUST = 0, to deactivate) u Stiffness is automatically updated to improve convergence (KSTEP = # of converged bisection solutions between stiffness updates) u Accurate, efficient, and user-friendly u Based on the dominant frequency in the incremental deformation pattern: u Number of steps (MSTEP) for a period is adaptive, based on the stiffness ratio:

94 S8-94NAS105, Section 8, May 2005 NONLINEAR TRANSIENT SOLUTION STRATEGY n Bisection Algorithm u To overcome divergent problems due to nonlinearity. u Activated when divergence occurs. u Activated when MAXITER is reached. u Activated when excessive is detected. u Decomposition at every bisection. u Update [K] at every KSTEP-th converged bisection. u Bisection continues until solution converges or MAXBIS is reached. u If MAXBIS is reached, the reiteration procedure is activated to select the best attainable solution.

95 S8-95NAS105, Section 8, May 2005 RESTARTS FOR NONLINEAR TRANSIENT ANALYSIS n Starting from a previous transient analysis u Restarts are allowed only from the end of subcases. u Set parameters: PARAM,LOOPID,II = loop number on printout PARAM,STIME,T o T o = starting value of time u To should be the last printed value for subcase I. u The database will be modified starting from LOOPID+1, T = T o. n Starting from a previous nonlinear static analysis u Set parameter: PARAM,SLOOPID,II = loop number on SOL 106 run u Initial transient load should be identical to static loads at restart state. (SPC, etc., may change) n Caution:The database will be completely overwritten. Transient analysis will destroy the static analysis database.

96 S8-96NAS105, Section 8, May 2005 HINTS AND RECOMMENDATIONS FOR SOL 129 n Identify the type of nonlinearity. n Localize nonlinear region. n Divide time history by subcases for convenience. n Each subcase should not have more than 200 time steps. n Select default values to start - TSTEPNL. n Pick time step size for highest frequency of interest. Twelve or more steps per cycle and frequent content of input. n Some damping is desirable for numerical stability. No such thing as an undamped structure. n Ensure that loading history is properly traced with the adaptive time stepping. n Avoid massless degrees of freedom.

97 S8-97NAS105, Section 8, May 2005 HINTS AND RECOMMENDATIONS WHEN USING SOL 129 (CONT) n Use the Adaptive Time Stepping Algorithm. n Ensure that loading history is properly traced, especially with the adaptive time stepping. Adaptive time stepping is based on the response of the model. Consequently, if sudden change in loading occurs, it may miss it. n Choose GAP stiffness carefully. n Increase MAXITER if convergence is poor.

98 S8-98NAS105, Section 8, May 2005 EXAMPLE PROBLEM 1 n Description: Transient Analysis of a Simply Supported Beam with a Restrained Motion

99 S8-99NAS105, Section 8, May 2005 EXAMPLE PROBLEM 1 (Contd.) n Displacement at the Loading Point (DT=0.0002)

100 S8-100NAS105, Section 8, May 2005 EXAMPLE PROBLEM 1 (Contd.) n Acceleration at the Loading Point (DT=0.002)

101 S8-101NAS105, Section 8, May 2005 EXAMPLE PROBLEM 1:.dat File ID, chap7e1, NAS103, chap 7, example 1 $ (AR 12/28/03) SOL, 129 CEND TITLE=SS Beam with a Restrained Motion (NOLIN1) SUBTITLE=Direct Transient Response, Nonlinear Force LABEL= NOLIN in SOL 129 SEALL = ALL ECHO=SORTED SPC=1002 SET 1 = SET 2 = SET 3 = 10005,10010 DISP=3 VELO=3 OLOAD=1 NLLOAD=2 SUBCASE 1 DLOAD=30 TSTEPNL=20 NONLINEAR=13 $ Select Nonlinear Force $ BEGIN BULK PARAM, POST, 0 PARAM, GRDPNT, PARAM, WTMASS, $ CBAR, 101, 100, 10000, 10001, 0.0, 0.0, 1. CBAR, 102, 100, 10001, 10002, 0.0, 0.0, 1. CBAR, 103, 100, 10002, 10003, 0.0, 0.0, 1. CBAR, 104, 100, 10003, 10004, 0.0, 0.0, 1. CBAR, 105, 100, 10004, 10005, 0.0, 0.0, 1. CBAR, 106, 100, 10005, 10006, 0.0, 0.0, 1. CBAR, 107, 100, 10006, 10007, 0.0, 0.0, 1. CBAR, 108, 100, 10007, 10008, 0.0, 0.0, 1. CBAR, 109, 100, 10008, 10009, 0.0, 0.0, 1. CBAR, 110, 100, 10009, 10010, 0.0, 0.0, 1. CBAR, 111, 100, 10010, 10011, 0.0, 0.0, 1. CBAR, 112, 100, 10011, 10012, 0.0, 0.0, 1. CBAR, 113, 100, 10012, 10013, 0.0, 0.0, 1. CBAR, 114, 100, 10013, 10014, 0.0, 0.0, 1. CBAR, 115, 100, 10014, 10015, 0.0, 0.0, 1. CBAR, 116, 100, 10015, 10016, 0.0, 0.0, 1. CBAR, 117, 100, 10016, 10017, 0.0, 0.0, 1. CBAR, 118, 100, 10017, 10018, 0.0, 0.0, 1. CBAR, 119, 100, 10018, 10019, 0.0, 0.0, 1. CBAR, 120, 100, 10019, 10020, 0.0, 0.0, 1. $ CONM2, 12, 10010,,.1 $ GRID, 10,, 50., 0.,-1. GRID, 10000,, 0., 0., 0.,, 1246 GRID, 10001,, 5., 0., 0.,, 1246 GRID, 10002,, 10., 0., 0.,, 1246 GRID, 10003,, 15., 0., 0.,, 1246 GRID, 10004,, 20., 0., 0.,, 1246 GRID, 10005,, 25., 0., 0.,, 1246 GRID, 10006,, 30., 0., 0.,, 1246 GRID, 10007,, 35., 0., 0.,, 1246 GRID, 10008,, 40., 0., 0.,, 1246 GRID, 10009,, 45., 0., 0.,, 1246 GRID, 10010,, 50., 0., 0.,, 1246 GRID, 10011,, 55., 0., 0.,, 1246 GRID, 10012,, 60., 0., 0.,, 1246

102 S8-102NAS105, Section 8, May 2005 EXAMPLE PROBLEM 1:.dat File (Contd.) GRID, 10013,, 65., 0., 0.,, 1246 GRID, 10014,, 70., 0., 0.,, 1246 GRID, 10015,, 75., 0., 0.,, 1246 GRID, 10016,, 80., 0., 0.,, 1246 GRID, 10017,, 85., 0., 0.,, 1246 GRID, 10018,, 90., 0., 0.,, 1246 GRID, 10019,, 95., 0., 0.,, 1246 GRID, 10020,,100., 0., 0.,, 1246 $ MAT1, 1000, 3.E7,, 0.3, 0.3 $ PBAR, 100, 1000, , , 1., 0. $ SPC, 1002, 10, SPC, 1002, 10020, 3,, 10000, 3 $ Modeling Information for Center Spring CROD, 10, 10, 10, MAT1, 10, 10.,, 0. PROD, 10, 10, 1. $ MATS1, 10,, PLASTIC, 0., 1, 1, 3.E8 $ Loading and Solution Information TLOAD2, 30, 33,,, 0., 0.011, 90.91, -90. DAREA, 33, 10005, 3, 47.2 TSTEPNL, 20, 200, , 1, ADAPT $ Modeling Information for Nonlinear Spring NOLIN1, 13, 10010, 3, 1., 10010, 3, 13 TABLED1, 13,, -2.5E-2, 4.95, -2.0E-2, 0., 0., 0., ENDT ENDDATA

103 S8-103NAS105, Section 8, May D SLIDLINE CONTACT Concept n Allows contact between two deformable bodies in a plane n One of the bodies is called the master and the other the slave. n The master/slave line is the region where contact can occur.

104 S8-104NAS105, Section 8, May D SLIDLINE CONTACT (CONT) n A master/slave segment is the line joining two consecutive nodes. n Master/slave nodes are the grid points in the contact region. n The slideline plane is the plane in which the master and the slave nodes must lie. n The master and slave nodes can have large relative motion within the slideline plane. n Relative motions outside the slideline plane are ignored. Therefore, they must be small. n Contact is determined between the slave nodes and the master line.

105 S8-105NAS105, Section 8, May D SLIDLINE CONTACT (CONT) 3-D Slideline Element n Consists of 3 nodes: slave s, and master m1 and m2. wheres, m 1, m 2 =slave, master node 1, master node 2, respectively a, a 0 =current and previous surface coordinate g n =penetration of slave node into the master segment g t = sliding of the slave node on the master segment n= normal direction for the master segment

106 S8-106NAS105, Section 8, May D SLIDLINE CONTACT (CONT) n The element tangential (x) direction is the direction from master node 1 to master node 2. n The element normal (y) direction is perpendicular to the tangential direction in the slideline plane. n The element z-direction is the slideline plane vector. n Normal direction (y) is obtained by z x x. n The normal direction must point toward the slave node. n The penetration or gap is calculated by measuring how close the slave node is to the master segment in the normal direction. n The slave node slides on the master segment until a tensile force develops. n The surface coordinate is the parametric projection (0 to 1) of the slave node onto the master segment. n A 3-D slideline element is created for each slave node. n The master nodes to which a slave node connects change continually. n The only way an internal element can be identified is by the external grid number of the slave node.

107 S8-107NAS105, Section 8, May D SLIDLINE CONTACT (CONT)

108 S8-108NAS105, Section 8, May D SLIDLINE CONTACT (CONT) General Features n Can have as many slideline contact regions as desired. n Contact is determined only for slave nodes and the master line. n May specify symmetric penetration, i.e., contact is determined for both slave and master nodes into master and slave line, respectively. n Initial penetration of slave nodes into master line is not allowed. n User Warning Message 6315 is issued, if the initial penetration is less than 10% of the master segment length. n Coordinates of the slave node are changed internally to preclude penetration. n User Fatal Message 6314 is issued, if initial penetration for any slave node is greater then 10% of the master segment length.

109 S8-109NAS105, Section 8, May D SLIDLINE CONTACT (CONT) General Features(Cont.) n The master and slave nodes must be in the slideline plane in the initial geometry; otherwise Fatal message 6312 is issued. n During the analysis, no check is made to ensure that the master and slave nodes are in the slideline plane. n The slave or master nodes need not be attached to the physical element (model rigid surface). n Ensure that the contact is properly defined so that there are no erroneous overhangs. n Output can be requested in SORT1 or SORT2.

110 S8-110NAS105, Section 8, May D SLIDLINE CONTACT (CONT) User Interface n Bulk Data entries: BCONPDefines the parameters for a contact region and its properties. BLSEGDefines the grid points on the master/slave line. BFRICDefines the frictional properties. BWIDTHDefines the width/thickness associated with each slave node. BOUTPUTDefines the output requests for slave nodes in a slideline contact region. n Case Control Command: BOUTPUTSelects contact region for output. n DMAP parameter: ADPCONAdjusts penalty values on restart.

111 S8-111NAS105, Section 8, May 2005 BCONP BULK DATA ENTRY Description: Defines the parameters for a contact region and its properties Format: Example: FieldContents IDContact region identification number (Integer > 0) SLAVESlave region identification number (Integer >0) MASTERMaster region identification number (Integer >0) SFACStiffness scaling factor. The factor is used to scale the penalty values automatically calculated by the program (Real >0. or blank; Default = 1.0). FRICIDContact friction identification number (Integer > 0. or blank) PTYPEPenetration type (Integer = 1 or 2; Default =1) 1: Unsymmetrical (slave penetration only by default) 2: Symmetrical CIDCoordinate system ID to define the slide line plane vector and the slide line plane or contact (Integer > 0 or blank; Default = 0 which means the basic coordinate system)

112 S8-112NAS105, Section 8, May 2005 BCONP BULK DATA ENTRY (CONT) n Can have as many contact regions as desired. n Penalty values are automatically selected based on the diagonal terms of grid points. n In symmetrical penetration, both the slave and master nodes are checked for penetration into the master and the slave surface, respectively. n The t 3 direction of CID is the z-direction of all the 3-D slideline elements (one corresponding to each slave node and also to each master node for symmetric penetration) of the contact region.

113 S8-113NAS105, Section 8, May 2005 BLSEG BULK DATA ENTRY Description Defines a curve which consists of a number of line segments via grid numbers that may come in contact with another body. A line segment is defined between every two consecutive grid points. Thus, number of line segments defined is equal to the number of grid points specified minus 1. A corresponding BWIDTH Bulk Data entry may be required to define the width/thickness. Otherwise, the widh/thickness for the corresponding line segment will be assumed to be unity. Format: Examples: FieldContents IDLine segments identification number (Integer > 0) GiGrid number on a curve in continuous topological order so that the normal to the segment points towards the other curve.

114 S8-114NAS105, Section 8, May 2005 BLSEG BULK DATA ENTRY (CONT) n Grid points must be specified in topological order. n Normals to (z x t) of the master segments must face toward the slave line for unsymmetric penetration. n Normals of master and slave segments must face each other for symmetric penetration. n These conditions are accomplished by traversing counterclockwise or clockwise from the master line to the slave line depending on whether the slideline vector forms the right- hand rule or the left hand rule. n The master line must have at least two grid points. n The slave line may have only one grid point for unsymmetrical penetration. n Two grid points in a line cannot be the same or coincident except for the first point and the last point, which signify a close region.

115 S8-115NAS105, Section 8, May 2005 BFRIC BULK DATA ENTRY Description:Defines frictional properties between two bodies in contact. Format: Example(s): FieldContents FIDFriction identification number (Integer > 0) STIFFrictional stiffness in stick (Real > 0.0; Default = auto select by program) MU1Coefficient of static friction (Real > 0) (Note: no distinction made between static and kinetic friction.)

116 S8-116NAS105, Section 8, May 2005 BWIDTH BULK DATA ENTRY Description:Defines width/thickness for line segments in 2-D / 3-D slideline contact defined in the corresponding BLSEG BULK Data entry. This entry may be omitted if the width/thickness of each segment defined in the BLSEG entry is unity. Number of thicknesses to be specified is equal to the number of segments defined in the corresponding BLSEG entry. If there is no corresponding BLSEG entry, the width/thickness specified in the entry are not used by the program. Format: Examples: FieldContents IDWidth/thickness set identification number (Integer > 0) WiWidth/thickness values for the corresponding line segments defined in the BLSEG entry (Real > 0.0)

117 S8-117NAS105, Section 8, May 2005 BWIDTH CULK DATA ENTRY (CONT) n ID is the same as the slave line (BLSEG) ID. n Widths/thicknesses are specified for slave nodes only. Default = unity. n Widths/thicknesses are used for calculating contact stresses. n Each slave node is assigned a contributory area. n The number of widths to be specified is equal to the number of slave nodes minus one. n For only one slave node, specify the area in W1 field.

118 S8-118NAS105, Section 8, May 2005 BOUTPUT BULK DATA ENTRY Description:Defines the slave nodes at which the output is requested. Format: Example: FieldContents ID Boundary identification number for which output is desired (Integer > 0) GiSlave node numbers for which output is desired Note: The ID is the same as the corresponding BCONP ID. This entry can selectively specify the slave grid points for which OUTPUT is desired.

119 S8-119NAS105, Section 8, May 2005 BOUTPUT CASE CONTROL COMMAND Description: Selects slave nodes specified in the Bulk Data entry BOUTPUT for history output. Format: Example: BOUTPUT = ALL BOUTPUT = 5 Field Contents SORT1Output is presented as a tabular listing of slave nodes for each load or time depending on the solution. SORT2Output is presented as a tabular listing of load or time for each slave node. PRINTThe print file (Fortran I/O unit 6) is the output media. PUNCHThe punch file is the output media. PLOTGenerate salve node results history but do not print. ALLHistories of all the slave nodes listed in all the BOUTPUT bulk data entries are output. If no BOUTPUT bulk data entries are specified, histories of all the slave nodes in all the contact regions are output. nSet identification of previously appearing set command. Only contact regions whose identification numbers appear on the set command are selected for output. If there is a BOUTPUT bulk data entry for a contact region selected via the set command, histories for all the slave nodes in that contact region are output. NoneResults histories for the slave nodes are not calculated or output. NOTE:This command selects the contact region for which output is desired

120 S8-120NAS105, Section 8, May 2005 PARAM ADPCON n User interface PARAM, ADPCON, (real value) n On restart, ADPCON can be used to increase or decrease the penalty vales for all the line contact regions. n A negative value of ADPCON implies that penalty values are calculated at the beginning of a subcase only. This is useful for contact between elastic bodies. n Penalty values for a line contact region are given by where k s = number calculated automatically for a slave node by Nastran SFAC = scale factor specified in BCONP

121 S8-121NAS105, Section 8, May 2005 PRINTOUT FOR SOLUTION STRATEGY n This is printed only for the converged iteration n This is printed only for the converged iteration.

122 S8-122NAS105, Section 8, May 2005 EXAMPLE PROBLEM Purpose n To illustrate the use of slideline contact and nonlinear transient analysis in bumper crash applications. Problem Description n A rigid barrier moving at 5 mph impacts a bumper fixed at the bumper brackets. Plot the deformed shape of the bumper after 20 msec of contact.

123 S8-123NAS105, Section 8, May 2005 EXAMPLE PROBLEM (Cont.) Solution n Five separate contact regions are defined with the barrier as the master and the bumper as the slave. n Each master region consists of two master nodes. n Each slave region consists of 23 slave nodes.

124 S8-124NAS105, Section 8, May D SLIDELINE CONTACT (Cont.) Concluding Remarks n Penalty method is used for both contact and friction. n Penalty values automatically calculated. n Multiple slideline contacts can be specified. n Relative motions outside the slideline plane are ignored during the analysis n The master and slave nodes must be in the slideline plane in the initial geometry. n Initial penetration is not allowed and is checked. n Only Coulomb friction (slick and slip) with equal static and kinematic coefficient is available for relative sliding. n Only hard surface contact is available for opening and closing.

125 S8-125NAS105, Section 8, May D SLIDELINE CONTACT (Cont.) Summary of Capabilities n Applicable for 2-D plane strain/stress, axisymmetric, and 3-D models. n Can be used with all element types. n Can be used with geometric and material nonlinearities. n With and without friction n Nonlinear static solution (SOL 106) n Nonlinear transient dynamic solution (SOL 129) n More than 2-D surface contact and less than 3-D surface contact

126 S8-126NAS105, Section 8, May 2005 NONLINEAR TRANSIENT ANALYSIS USING SUPERELEMENTS Why Use Superelement in Nonlinear Transient Analysis? n All the benefits of using superelements in a linear analysis can also be realized. See section on Superelement Analysis. n In many nonlinear problems, the nonlinearity may be localized. u Substantial computational savings can be obtained by putting the linear portion of the structure as superelements. n The portion of the structure that is nonlinear must be placed in the residual structure. n Restrict the iterations to the nonlinear regions of the structure.

127 S8-127NAS105, Section 8, May 2005 NONLINEAR TRANSIENT ANALYSIS USING SUPERELEMENTS (Cont) n Linear assumptions – only the residual structure is allowed to be nonlinear (material or geometric). n Nonlinear superelement analysis can be restarted from linear analysis (databases from SOL 101, and SOL 109). n Restarts – No recalculations are required for upstream superelements if there is no change in superelements. n Load vectors for the upstream elements must be generated before the nonlinear solutions. n Case Control command SUPER is used to partition the proper subcase to a superelement.

128 S8-128NAS105, Section 8, May 2005 NONLINEAR TRANSIENT ANALYSIS USING SUPERELEMENTS (Cont) n All the subcases should include the SUPER command (default, SUPER = 0) except when SUPER = ALL is specified above the subcases. n Component modes information is passed down to the residual structure using SPOINT and SEQSET1 - similar to conventional superelement analysis. n Since PARAM, AUTOSPC does not constrain singular DOF in the residual structure in nonlinear analysis, specify the exact number of generalized coordinates needed. n If feasible, assign load application points to the residual structure.

129 S8-129NAS105, Section 8, May 2005 MSC.NASTRAN SOL600 OVERVIEW n MSC.Nastran SOL 600 = MSC.MARC ALGORITHMS + MSC.NASTRAN INTERFACE n Adaptive Re-Meshing n DDM n ROBUST

130 S8-130NAS105, Section 8, May 2005 WHAT IS MSC.NASTRAN SOL 600? n Integrated Package: u MSC.Nastran Interface u MSC.Marc Algorithms u MSC.Patran GUI n Access to most MSC.Marc Capabilities n Access to all MSC.Marc Structural / Thermal / Coupled Analysis Capabilities n Easy to Use n Intuitive n Powerful

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