Lusas Warning And Error Messages

Transcription

1 LUSAS Warning and Error Messages Lusas Warning And Error Messages General During a LUSAS analysis, Warning and/or Error messages 1 may appear in the LUSAS output file which may be classified as follows Negative Jacobian Diagonal Decay Small Pivot Negative Pivot Zero Pivot System Error Run-time Errors Analysis Specific Errors This document explains the meaning of these messages and also gives suggested remedial action where possible. Negative Jacobian The typical message will be as follows Element Number U Illegal Jacobian Determinant Of V. Check Node Order Or a related one for explicit dynamics elements Current Area Of Element U Is V A Jacobian determinant is a measure used within LUSAS to give an accurate value of the current length, area or volume of an element. A magnitude of less than or equal to zero will automatically invoke this message and may be a result of a) Incorrect definition of the two/three dimensional continuum and plate elements. By design, LUSAS requires these element types to have an anti-clockwise node numbering sequence. The order is controlled from the underlying surface feature in which the element resides. If this message is output, the solution is to reverse the ordering of the surfaces for the elements having these warning messages output (Features => Surface => Reverse). 1 An Error message will terminate the solution immediately. A Warning message will attempt to continue the analysis.

2 Note that the local axis system of the surface may be viewed prior to tabulation - the XY axis system displayed on each surface represents a right handed axis system, from which the anti-clockwise (or positive θ z definition may be checked). b) Too large a loading increment causing massive deformation of one or more elements, i.e., the elements are inverting. Note that this would only occur in nonlinear analyses. Diagonal Decay The typical message(s) will be as follows Element Number U Node V Variable W Has Illegal Diagonal Decay = X Which Exceeds Limit Set At Y. Pivot = Z. Structure Is Inadequately Earthed, Poorly Idealised Element U, Node V, Variable W Has Small Pivot = X Or Diagonal Decay = Y (GT Z) The stiffness matrix is a crucial component in a finite element analysis, but it can be well or poorly conditioned. Poor conditioning may result in round-off error, which is a loss of accuracy in the evaluation of the terms during the reduction process of the solution. This in turn leads to inaccuracies in the predicted displacements and stresses. LUSAS monitors the round-off error by evaluating the amount of diagonal decay present during the Gaussian reduction process. This criterion is based on the assumption that initially large diagonal terms accumulate errors proportional to their size. As reduction progresses, the diagonal term is reduced, amplifying the errors until they become a maximum when the diagonal term is the pivot. An indication of probable errors may be obtained by examining the change in magnitude of the diagonal term. The tolerance threshold above which a diagonal decay warning is output (0.1E5) is actually quite conservative. Although a check would always be recommended for any warning of this description, significant effects would not generally be expected until the decay reaches a value of 0.1E8 or greater. In general, poor conditioning of the stiffness matrix occurs because of large variations in the magnitude of diagonal stiffness terms. This usually occurs because of 1. Large stiff elements being connected to small less stiff elements. An example may be where a stiff beam element is being used to transfer load into the structure. The stiffness of the beam would need to be reduced - typically, the beam would only need to be 1000 times the stiffness of the local elements. 2. Elements with highly disparate stiffnesses, e.g. a beam element may have a bending stiffness that is orders of magnitude less than it's axial stiffness. For instance, the cantilever beam problem is notoriously problematic with respect to ill-conditioning because of the potential for large differences between the axial and shear/rotational stiffness components. A typical stiffness matrix might be EA/L 0 0 (u) F = 0 12EI/L 3 6EI/L 2 (v) 0 6EI/L 2 12EI/L 3 (θ) - 2 -

3 The longer the beam, the greater the difference between EA/L and 12EI/L 3. Poor conditioning may be a result of a deliberate modelling strategy but is, more usually, an error in one or more of the following data input areas (each of which are of interest because they make a contribution to the stiffness matrix) Mesh description a) The aspect ratio of some elements are greater than the recommended limits (see the section in the finite element library appendix for further information). An ideal value would be 1:1. This is usually not required, however, and values up to 1:10 would be reasonable. Depending on the results required and the stress field sustained by the elements, this value may be increased still further (a test run would be recommended first however). This problem is indicated by the WARNING message Unreasonably Distorted Element U The only exception is the explicit dynamic elements which really do require aspect ratios of 1:1. b) Some element shapes are too distorted. This refers particularly to the curvature of element sides and the central positioning of the mid-side nodes for higher order elements (see the section in the finite element library appendix for further information) c) For flexible structures, the mesh definition may not be sufficiently refined to account for significant stiffness changes across elements Geometric properties a) Omission of values for any shear area parameters in the geometric properties for beams b) Omission of values for other important properties, such as the torsional constant or thickness c) Defining incompatible 1 st and 2 nd moment section properties for beams Material properties a) Different units used to define the nodal coordinates and the material properties b) Inconsistent units throughout the model. This would be of particular concern for dynamic analyses, where SI units are recommended c) Incorrect nonlinear material parameters (yield stress and hardening values particularly) d) The plastic strain hardening definition requires that the first set of points corresponds to the initial uniaxial yield stress and the elastic strain at which this stress occurs - 3 -

4 e) Incorrect definition of orthotropic properties. The inequalities given in the appropriate element section of the theory manual need to be adhered to. Numerical instabilities may result when the material characterisation approaches their limits (see appendix A for a list of these inequalities) f) Ill-conditioning may occur in large strain analyses using the rubber material model in which the bulk modulus is defined to enable incompressibility approaching 100%. Reducing this modulus will alleviate such problems and permit greater strains to be attained. Note that this does not apply for membrane and plane stress analyses, since the bulk modulus is ignored in such cases g) Slideline stiffness coefficients or joint element stiffness magnitudes too high relative to the structural stiffness Support nodes a) Are supports defined and assigned? The structure must be restrained against free body translation and rotation (except for dynamic analyses) b) Check that there are adequate supports in all translational directions. For beams, be aware that the problem could be with unrestrained torsional motion which is not easy to view Modelling Integrity A further possibility is that the integrity of the MYSTRO model geometry is questionable. This would lead to an element mesh containing gaps within it or having discontinuities in the connection of the elements - thereby permitting some of the elements in, or near, the vicinity of the gap to deform with significantly reduced restraint. Such a lack of integrity may be found by a) Viewing only the outline of the mesh (Meshview => Options => Outline). The view will draw lines wherever a discontinuity occurs b) Drawing the node numbers onto the mesh (Meshview => Node details => Labels) to see if any node numbering is overwriting at any point (indicating two nodes at the same point). Correction would normally require either a merging or an equivalencing operation This message is closely related to the small pivot WARNING message (see below). See also the additional notes in the theory manual regarding the Gaussian solution method. Small Pivot The typical message will be as follows Element U Node V Variable W Has Small Pivot = X Or Diagonal Decay = Y (GT Z) See the preceding section on diagonal decay - the two are closely related

5 Negative Pivot The typical message(s) will be as follows Element U Node V Variable W Has Negative Pivot = X Number Of Negative Pivots (nsch) = X Is Greater Than 1 On Factoring At Start Of A New Increment (May Be Overridden Using Option 62) A negative pivot could be the result of poor conditioning and the remarks in the section on diagonal decay should be checked. However, a well conditioned stiffness matrix can produce a negative pivot if the system is unstable, that is, it is passing through a bifurcation or limit point, e.g., load load Cstiff>0 Pivmin>0 limit point Cstiff<0 Pivmin<0 Cstiff>0 Pivmin>0 bifurcation point Cstiff>0 Pivmin<0 displacement displacement Such a point in the analysis could permit another, non-physical, solution path to be followed because, numerically, it requires less energy. It could be seen as the stiffness matrix expressing a preference for a different path than it is currently on. For example, an axially loaded, straight strut will generate one negative pivot if loaded in a geometrically nonlinear analysis to just beyond the first buckling load. Two negative pivots will occur if the load increases to the second buckling load, and so on. Every negative pivot warning occurring in the LUSAS output file represents such a point in the analysis. A negative CSTIF value, together with a negative PIVMIN value corresponds to a limit point but a positive CSTIF and a negative PIVMIN correspond to a bifurcation point (although this is only the first one located in each case since limit points are detected by a CHANGE in sign). Negative pivots sometimes occur during the iterative solution (indicating that the load step may be too big) but disappear when the solution has converged. If negative pivots occur and the solution will not converge then first try reducing the load step. If the solution still does not converge, a limit or bifurcation point may have been encountered and the solution procedure may need to be changed. Running the problem under arc length control gives the best chance of negotiating a limit or bifurcation point. A load limit point can also be overcome by using prescribed displacement loading. A count of the number of negative pivots is given in the LUSAS log file (parameter NSCH). Initially NSCH = 0 since, initially, a stable path is assumed. When NSCH = 1, an unstable point (limit or bifurcation) has been reached; PIVMN will give the value of the minimum pivot at this point

6 It is, however, equally possible that a negative pivot may occur as a result of an illconditioned stiffness matrix. The following are some of the more frequent examples. a) The system is not adequately restrained using a 3D beam in a 2D analysis Omission of supports causing significant structural flexibility b) A further possibility in the case of the semiloof shell is that a mechanism has been excited. This may occur in the case of very thin, curved surface analyses. The use of OPTION 18, however, will normally solve this problem. If the problem persists, continue with the use of the option but refine the mesh further. c) Using inconsistent units when defining a model. For example using millimetres to specify the coordinates and metres within the material and geometric properties d) For beam elements, the second moments of area should correspond to the first moments of area (only for non-symmetrical sections) e) For well constrained structures, a zero shear area may cause this problem f) The specification of an axisymmetric analysis without any axial support conditions. Note also that centreline supports are not defined automatically by MYSTRO g) Bifurcations may be excited due to a cracked model (improperly merged and/or equivalenced) h) The magnitude of the bulk modulus is too large when using the rubber material model i) A zero yield stress has been specified j) Large aspect ratios in elements which are sustaining a significant amount of plastic strain Note that the use of LUSAS option 62 (ignore negative pivots) is not recommended until all other checks have been carried out to ensure model integrity. Before modifying the solution procedure to arc length, the checklist given in the section above on small pivots should be checked. Zero Pivot The typical message will be as follows Pivot On Leading Diagonal Is Zero. Matrix Is Singular. Is There A Restraint At Nodal Point Number X For Nodal Variable Number Y LUSAS uses a Gaussian reduction solution technique to solve the finite element equations. This technique requires the structure stiffness matrix to be non-singular. This means that the structure or any components of the structure must not permit any rigid body displacements or rotations. Failure to comply with this criterion will result in a zero pivot message. The error message includes the node and variable number that may be affected by the poor conditioning - these variables should be investigated in the model

7 Reasons for this message include a) Omission of a support condition in one or more of the structural degrees of freedom for the structure causing a rigid body motion b) Omission of values for any shear area or torsional stiffness parameters in the geometric properties for beam or grill elements c) Insufficient additional restraint when connecting a beam/shell element to a continuum element. In this case a rigid body torsional spin about the axis of the beam would occur d) Six degrees of freedom have been specified for a thick shell element, but the drilling rotation has not been correspondingly restrained. Version 12 has an additional option (278) which eliminates this problem e) Insufficiently large slideline interface stiffness coefficients allowing the two bodies to pass through each other as rigid bodies. The load increment may also be too large f) Incorrect nonlinear material parameters, such as a zero yield stress or significant softening behaviour g) Joint elements may require investigation as the stiffnesses operate in local directions and can be easily defined incorrectly - as a result, the joint stiffnesses will not be resisting in the required directions h) There may be totally or partially unconnected elements within the structure as a result of incomplete merging or equivalencing of the model. Note that torsional rigid body motion of beams is a typical problem which is not possible to view in Mystro post processing i) BAR elements used on there own without the use of a geometrically nonlinear analysis to generate stress stiffening are prone to zero pivots. Bars have no transverse (shear) stiffness and are typically used to model reinforcement bars or "tie" linkages where there is no moment connectivity. These elements will not present any difficulties when used in conjunction with other plane elements (shells, plates, etc.) since the transverse stiffness required to prevent a numerical mechanism will be contributed from the surface elements. Mechanisms will, however, result if they are used independently to model, for example, a simple cantilever j) Frictional contact using slidelines uses a force methodology for tangential sliding and does not invoke additional stiffness components. This means that friction cannot be relied on solely to prevent rigid body motion in the plane of the sliding. If there is no other physical support then a small spring stiffness may be used to artificially impose a tangential restraint to eliminate pivot problems but not to affect the results k) Assigning nonlinear material properties to an element type which does not support that particular facility System Errors During a LUSAS analysis checks are continually made on the integrity of data. There are two principal types of check - 7 -

8 a) Those resulting in warning and error messages due to a clearly definable problem source in either the data processing or the data itself b) Those resulting in a System Error. These error types are typically non-specific and may be a result of Machine dependent software problems Database corruption due to software/hardware problems Descriptive warning and/or error messages are not possible because of the non-specific nature of the trapped problem since, in general, a theoretically impossible software path has been traversed. On occurrence of such a system error, LUSAS will immediately set switches to terminate the solution at the earliest moment. The system error message format is as follows Where ***SYSTEM ERROR*** (<Name> Processor) Nerror = N 1, N 2, N 3 Name N 1 N 2 N 3 Name of the subroutine in which the problem was found An error number to identify which system error reported the problem (there may be a number of these in any subroutine) Value of an important parameter at the moment of termination Value of an important parameter at the moment of termination If such a system error is experienced, customer support should be contacted and informed of the system error parameters. They will be able to ascertain the general problem area and suggest remedial action or send an updated version of the software with any errors rectified. Run-Time Errors LUSAS may crash with the following error messages Denormalised operand Subscript out of range These type of error messages are output from the Fortran run-time Programs (Run77.exe and DBOS.exe) for PC machines or the error messaging system of the operating system for workstations. Because of this, the messages are not LUSAS-specific and are not typically useful in interpreting the problem. In the first instance the LUSAS output file should be examined for any warning or error messages - particularly the first occurrence

9 Without a corresponding system error (see above) this may indicate the presence of very large displacements or stresses in the solution as a result of a significant weakness in the structure. If this is the case, a pivot warning would also usually be present and the corrective suggestions investigated in the appropriate pivot section above should be investigated. If these errors occur in conjunction with a system error, however, it will simply be a result of the compiler also trapping a serious software problem. Both the system error message and the traceback associated with the above errors should be relayed to customer support at FEA who will be able to advise on the probable source of error. Analysis Specific Warning/Error Messages The following notes relate to facility-specific messages and may help if you are experiencing difficulty in their interpretation. General Nonlinear Analyses General incrementation failure messages are as follows Current Increment Has Failed To Converge Step Reduction In Progress Current Increment Has Failed To Converge, Run Terminated The key question is "How did it fail?". Apart from an incorrect specification in the nonlinear control commands, consider the following possibilities a) There are either a significant number of pivot warnings in the LUSAS output file during the iterative process or the values of diagonal decay exceed 1E8. In this case, see the relevant pivot section above b) There are warning messages which indicate specific problems within the iterative procedure. These should be examined closely and acted upon c) If any of the convergence norms (particularly the residual norm) oscillate between two values during the iterative procedure, consider the following possible sources of error A section of the structure assigned with the concrete model particularly (or any nonlinear material model generally) is close to complete collapse and requires smaller load increments The slideline extension parameter is not specified for non-planar slideline geometries The slideline stiffness scale factors specified are too large and causing chatter at the interface An insufficient number of contact nodes has been defined. The concentration of contact force in few nodes causing chatter at the interface Large values of friction coefficient in a slideline analysis may produce instability with large load increments Significantly different material properties defined across a slideline can cause chatter at the interface unless the stiffness scale factors are reduced or the automatic averaging procedure is invoked - 9 -

10 The slideline geometry has nodes that are in contact initially. By default, these will be automatically brought back normally to their opposing surface. However, if option 185 has been specified to suppress this automatic facility, the initial penetration can cause significant initial straining of the model Incorrect application of the pre-contact detection facility can cause significant initial straining of the structure Insufficient close contact factor d) Increasing Residual Norms are a sign of severe nonlinearity within an iteration from which recovery is not possible. This may be a result of A crack present in the model Too large a load increment Inconsistent units specified in the model The convergence tolerance on previous increments being too slack to follow the nonlinearity sufficiently closely It can be helpful to specify LUSAS options 16 and 17 if convergence difficulties are being experienced. This will force LUSAS to continue the solution without convergence being achieved and will also generate a MYSTRO results file if requested. Investigation of the unconverged results in MYSTRO post processing can give understanding of the reasons for the convergence difficulties. Materially Nonlinear Analyses Common warning and error messages related to nonlinear material definition are as follows Stress-Return Has Failed To Converge In X Iterations For Element Number Y. Step Reduction In Progress 50 Iterations Have Been Made In An Attempt To Evaluate Plastic Lagrange Multiplier For Element X Gauss Point Y Value Of Yield Function Exceeds 10.0 After X Iterations For Element Y Gauss Point Z 40 Iterations Have Been Made In An Attempt To Scale The Stresses For Element ',I10,' Gauss Point ',I2, 50 Iterations Have Been Made In An Attempt To Evaluate Plastic Lagrange Multiplier For Element X Gauss Point Y Evaluation Of Creep And Plastic Strain For Element X Gauss Point Y Failed To Converge After Z Iterations Element X Gauss Point Y Creep And Plastic Strain Iterations Converged Onto Negative Root Value Of Yield Function Exceeds After X Iterations For Element Y Gauss Point Z 100 Iterations Have Been Made In An Attempt To Scale The Stresses For Element X Gauss Point Y These messages indicate significant numerical difficulties in bringing the current iterative stress point back to the yield surface and may be a result of

11 a) Inconsistent units used to specify the problem. For instance the coordinates of the structure may have been specified in millimetres, but the material properties given in metres b) Elasto-plastic models must have at least three assigned datasets; elastic, plastic and hardening. Check by drawing the features and the assigned material labels c) Check the three nonlinear control datasets are assigned to at least the first load case. d) Incorrect post yield material property values. A zero hardening slope (elasto-perfectly plastic) will give large plastic strains and corresponding deformations. This will cause more convergence difficulties than a non-zero specification. Where possible use realistic hardening slopes e) Too large a load increment either initially or during the analysis. Check that the initial increment causes little or no yielding to enable the structure to settle down initially under the loading. The nonlinear log file parameter MXSTP will be non-zero when plasticity has occurred on any Gauss point. Reduce the starting reference load factor if yielding does occur initially For analyses which exhibit such problems after the first increment and which use the automatic loading procedures, the parameters Desired Number of Iterations/Load Increment and Maximum Change in Load Factor/Increment described in the incrementation section of the nonlinear control command would provide the most effective preventative control (reduction in both) f) Depending on the post yield characteristics of the material, too high a load increment may cause complete yielding of a complete section of the structure. For perfectly plastic characteristics (e.g. Von Mises with zero hardening gradient, the concrete material or the stress resultant plasticity model), this will permit rigid body motion ('mechanisms') and typically make convergence impossible g) With the concrete model, a very small load increment may be required, together with a slacker convergence tolerance (DPNRM = 1, RDNRM = 5). Also, additional stability may be required from reinforcement bar (or an overlaid linear isotropic mesh with small stiffness) in order to arrest the crack development in critical stages that may occur during the analysis h) Numerical difficulties are encountered when a stress point lies at a singular point on a yield surface since the direction of plastic straining is indeterminate. This occurs for the Mohr-Coulomb criterion as the lode angle approaches 30 and also at the apex. Therefore, the stress integration algorithms are modified for these two cases. When a value of > 29 is encountered, the Drucker-Prager criterion is used to form the flow vector, for both evaluating the modulus matrix and integrating the stresses. When a stress point passes beyond the apex, it is returned directly to the apex, and the tangent modulus matrix is zeroed for this stress point. The error message invoked in these cases is as follows Stress Point Lies Beyond Apex Of Yield Criterion For Element X Gauss Point Y Increasing the value of the cohesion will help in such situations, having the effect of shifting the stress point further along the positive hydrostatic compression axis

12 Geometrically Nonlinear Analyses Common warning and error messages related to geometrically nonlinear analyses are as follows No Roots To Constraint Equation a) This message is related to the arc-length procedure and indicates that non-physical, numerical behaviour has occurred. There is normally other messages in the output file, including, typically, significant diagonal decay and these should be investigated. Arclength procedures are only required in snap-back or snap-through buckling problems and it may be possible to simplify the solution by eliminating this procedure b) If geometrically nonlinear options are specified (54, 87, 167, 229), are they actually required? These are only needed if large deformation is anticipated. Note that the slideline facility does not require them by default Slideline Analyses A general slideline checklist is as follows a) Line slidelines should be assigned to Lines and Surface slidelines to Surfaces b) The slideline facility is inherently nonlinear and requires use of the Nonlinear Control data command. The only exception to this is when tied slidelines are used in an implicit dynamic or static analysis where the solution may be linear. This is because the tied slideline option computes the contact location point once only for each contact node since its relative position never changes and reduces the problem to one of geometric linearity. The same is true for the sliding only type, but care is required to ensure that rigid body motion is prevented in the sliding direction for static analyses c) The outward normals of constituent slideline surfaces should point towards each other. If this is not the case contact will be assumed in geometric configurations in which the surfaces are in fact apart and will result in surfaces being pulled together Note that, in order to increase the efficiency and maintainability of the software, the definition of two dimensional slave surfaces are automatically reversed in LUSAS. This means that a slideline originally defined in the MYSTRO pre-processor (or by hand) with two surfaces defined in the same direction will be viewed in the MYSTRO post processor (using the command DRAW SLIDELINE DIRECTION) as having the master surface in the original direction but the slave surface will now be viewed in the opposite sense d) Mesh refinement in vicinity of contact regions will generally increase the stability of the problem as well as provide a better variation of contact stress e) Check that all potential contact regions are adequately defined as slidelines f) Slidelines defined around sharp corners should be avoided (<45 degrees). It is always better to use two slidelines in such instances g) A value for the slideline extension parameter is normally recommended, except on perfectly flat contact surfaces. A typical value would be 1/10 of the length of a slideline segment length

13 h) A single slideline cannot form a closed loop but different slidelines can overlap i) The distinction between master and slave surfaces is arbitrary for most slideline types. The only exception is when using tied slidelines in explicit dynamic analyses where the solution is more robust if the mesh with the greatest contact node density is designated the master surface. j) Rigid target surfaces may be modelled by fully restraining one of the slideline surfaces. The use of a large value of Young's modulus to simulate a rigid surface in an explicit dynamic contact analysis is not advisable since this will increase the wave speed in that part of the model and give rise to a reduced time step. This practice significantly increases the computing time required k) The slideline initialisation procedure is performed during a pre-analysis data check (option 51). This would help to ensure that the slidelines were defined correctly l) Setting an exaggeration factor of unity for the deformed mesh plots is essential in viewing contact analyses (or indeed any analysis with relative surface deformations) since any deformation exaggeration applied will also modify the penetration distance. An exaggeration factor of two would, thus, display the penetration as twice that actually occurring m) Shell contact is surface-based and not applicable along the edges n) Slidelines are permissible for use with the following elements Plane Stress Plane Strain Axisymmetric Shell Solid TPM3, QPM4, QPM4M, TPM3E, QPM4E TPN3, QPN4, QPN4M, TPN3E, QPN4E TAX3, QAX4, QAX4M, TAX3E, QAX4E TTS3, QTS4 TH4, PN6, HX8, HX8M, TH4E, PN6E, HX8E The higher order versions of these elements also support slideline analyses. In this case, however, constraint equations are automatic defined to constrain the midside nodes to deform according to the average of the two adjacent corner nodes. In some circumstances this can create an artificially stiff structure and care should be taken o) The slideline type can be redefined at selected stages throughout an analysis and involves respecifying the SLIDELINE ASSIGNMENT data chapter. Note, however, that only the slideline type can be changed and all other input data must remain constant. Previously defined SLIDELINE PROPERTIES can also be redefined but additional data sets cannot be introduced p) The default magnitude of the zonal contact detection parameter is 5/9 (for explicit dynamics analyses) or 10/9 (for static and implicit dynamic analyses). This ensures that all the zones overlap. If it is set to less than 0.5, undetected penetration may occur Common warning and error messages related to slideline analyses are as follows Two Dimensional Slideline Definition Node Number Has Incorrect Number Of Occurrences

14 This indicates that the start node for the sequence could not be located. This could occur if a slideline is defined completely around an enclosed circular surface. In other words, a continuous slideline surface has been defined. The Length Of The Slideline Segment Between Node (A) And Node (B) On Surface (C) Is (D) The two specified nodes are too close together. Either they are the same node numbers and hence a typing error in the slideline definition command has occurred or the units used in the analysis have caused a machine precision problem and the units should be changed to permit a larger number of significant digits for the node coordinates, e.g. change from metres to millimetres. Contact Node Numbers (A) And (B) Are Coincident. Please Check The Element Topology Of Slideline_Surface Number (C) The two specified nodes are too close together. Either they are the same node numbers and hence a typing error in the slideline definition command has occurred or the units used in the analysis have caused a machine precision problem and the units should be changed to permit a larger number of significant digits for the node coordinates, e.g. change from metres to millimetres. Maximum Permissible Number Of Elements Adjacent To A Slideline Node (Mxslae) = (A) Has Been Exceeded Use System Command To Increase Permissible Number By Increasing Value Of Variable Mxslae This will typically occur when a mesh uses one node in the definition of the element topology of many elements. For example, triangular elements "fanning out" from a centre node. The SYSTEM command is described in the LUSAS User manual. The Master Surface Number (A) Specified For Slideline Number (B) Has Not Been Defined In The Slideline_Surface Definition Card The master (or slave) surface number specified in the slideline_surface definition command does not correspond to that specified in the slideline assignment command. The Specification Of A Friction Coefficient Is Invalid For Slideline Type (A) Friction is only applicable with slideline type two. If a zero coefficient of friction is required with general sliding then slideline type one is recommended. Slideline Property Number (A) Has Been Assigned To General And Tied Slidelines. Default Values For Surface Scale Factors Differ For Each Slideline Type. Default Values For These Factors Will Be Assigned When Processing Each Individual Slideline. The stiffness scale factors for tied slidelines (type 3) should be significantly larger than that for a general slideline (types 1 & 2). It is recommended that different slideline properties are defined for each type and assigned to each type separately. Slideline (A) Has Sliding Properties Which Are Only Permitted In Nonlinear Problems Slideline types 1, 2 & 4 must be used in conjunction with the NONLINEAR CONTROL commands, since these permit changing contact conditions throughout the analysis and hence constitute a geometrically nonlinear analysis

15 A Zero Friction Coefficient Has Been Specified For Slideline Type (A) Friction is applicable with slideline type two. If a zero coefficient of friction is required with general sliding then slideline type one is recommended. No Possible Contact Nodes Found For Node (A) Surface Number (B) Slideline Number (C) Typically this error message will never be seen except in the instance of one of the contacting bodies behaving as a rigid body and passing completely through the other. Because the motion is unrestrained, the body may numerically traverse thousands of kilometres and render the slave search algorithm ineffective. Tied Slideline Node (A) Slideline Number (B) Is Not Contained Within The Zonal Contact Detection Radius (C) Local Node (D) This is simply a geometric warning that the slideline surface definition may be incorrect. The nodes on the slideline, however, will be continue to be processed and will maintain their relative position throughout the analysis. Thus, any gaps will remain as gaps throughout the analysis. This may cause an analysis to be overstiff in the contact area due to the rigid tying of nodes which are not part of the active contact conditions. Tied Slideline Node (A) Slideline Number (B) Is Not Contained Within The Zonal Contact Detection Radius (C) Local Node (D) This is simply a geometric warning that the slideline surface definition may be incorrect. The nodes on the slideline, however, will be continue to be processed and will maintain their relative position throughout the analysis. Thus, any gaps will remain as gaps throughout the analysis. This may cause an analysis to be overstiff in the contact area due to the rigid tying of nodes which are not part of the active contact conditions. The Segment Normal Vector Is Unavailable For The Current Configuration:- Contact Node Number = (A) Local Node Number = (B) Surface Number = (C) This will occur when the normalised vector normal to the segment is zero. This may be a result of badly defined slideline definition or, more likely, an indication of very large deformation of the contact surface. The Contact Location Point Is Undefinable For:- Node Number = (A) Surface Number = (B) Slideline Number = (C) This is due to non-convergence of the Newton iterations. The principal reason for this message would normally be very large displacement in the contact area. Contact Node (A) On Surface (B) Of Slideline (C) Has Penetrated In The Initial Configuration. The Node Coordinates Have Been Changed: From: X 1 Y 1 Z 1 To: X 2 Y 2 Z

16 The coordinates of all contact nodes which are determined to have penetrated prior to the commencement of the analysis are reset to the contact location point. OPTION 186 will suppress this facility as required and is a useful method for simulating interference fit problems, since the forces required for the interference fit will come directly from the initial penetrations found by the slideline algorithms. Option 186 should preferably not be used while 'de-bugging' a data file since the suppression of the warning messages could remove some important indicators to data file errors. Note that the resetting of coordinates is not available for tied slidelines. Tied Or Sliding Only Slideline Node (A) Slideline Number (B) Is Not In Contact In The Initial Configuration Local Node Number = (C) Normal Distance From Surface = (D) This is simply a geometric warning that the slideline surface definition may be incorrect. The nodes on the slideline, however, will be continue to be processed and will maintain their relative position throughout the analysis. Thus, any gaps will remain as gaps throughout the analysis. This may cause an analysis to be overstiff in the contact area due to the rigid tying of nodes which are not part of the active contact conditions. A Very Small Volume (A) Has Been Detected Whilst Processing Contact Node (B) This may be due to incorrect element topology, probably also giving an illegal Jacobian determinant message. The units used in the analysis may also be causing machine precision problem and the units should be changed to permit a larger number of significant digits for the node coordinates, e.g. change from metres to millimetres. The Average Interface Stiffness Computed For Surface (A) Of Slideline (B) Is Significantly Different From That Of The Adjacent Surface. The Stiffness Has Been Scaled By: (C) Intractable solutions may occur if two materials of significantly differing properties are utilised for the colliding bodies. In this case the following message will be generated: A scaling procedure on the slideline surface stiffnesses will be automatically invoked at the beginning of each analysis if the ratio of the average stiffness values for each constituent slideline surface differ by a factor greater than a default value of 100. The stiffness modification procedure may be suppressed by using OPTION 185. The nodal constraint method, used only for the tied slideline option in an explicit dynamics analysis does not use the stiffness scale factors

17 Final Notes Option 16 and 17 can be used together to override non-convergence as a result of poor conditioning, where option 16 will allow LUSAS to continue from an unconverged increment and option 17 will prevent LUSAS from performing any step reductions as a result of nonconvergence. The use of these two options in this way may often help locate the source of the problem when investigating these unconverged in the MYSTRO post-processor. Other warnings that may be found in the LUSAS output file include Aspect ratios (WARNING Status) See the appendix of the finite element library manual for more information. Excessive curvature for beams (WARNING Status) See the appendix of the finite element library manual for more information. Appendix A For orthotropic material models, the D matrix must be symmetric and, a number of further relations must also be satisfied Material Properties Orthotropic (e.g., QPM4) To maintain symmetry ν yx = ν xy * E y /E x and to obtain a valid material ν xy < (E x /E y ) 1/2 This applies to Fourier elements as a special case to simulate a bladed structure. Material Properties Orthotropic Plane Strain (e.g. QPN4) To maintain symmetry E y * (ν xy *E z + ν yz *ν xz *E x ) = E x * (ν xy *E z + ν xz *ν yz *E y ) Material Properties Orthotropic Axisymmetric (e.g. QAX4). To maintain symmetry ν yx = ν xy * E y /E x ν zx = ν zx * E z /E x ν zy = ν yz * E z /E y and to obtain a valid material

18 ν xy < (E x /E y )½ ν xz < (E x /E z )½ ν yz < (E y /E z )½ Material Properties Orthotropic Solid (e.g. HX8, QSL8). To maintain symmetry ν yx = ν xy * E y /E x ν zx = ν xz * E x /E z ν zy = ν yz * E z /E y and to obtain a valid material ν xy < (E x /E y )½ ν xz < (E x /E z )½ ν yz < (E y /E z )½ Material Properties Orthotropic Thick (e.g. QSC4): To maintain symmetry ν yx = ν xy * E y /E x and to obtain a valid material ν xy < (E x /E y )½ Appendix B: Pivots and DET(k) A pivot refers to the diagonal element of the upper triangular matrix that is formed after elimination has been completed. Note that in the frontal solution these pivots are computed as soon as all the relevant equations have been assembled. Computation of det(k) as part of a nonlinear solution scheme is not necessary since a count of the number of negative pivots (NSCH in the log file) together with the value of PIVMN gives all the information required. A zero pivot implies that det(k)=0. If NSCH=2 then another unstable point has been reached and implies that det(k)>