Solutions for flange contact modelling in structural dynamics

Flange support around fasteners is a commonly overlooked topic in industrial structural dynamics applications. It is due to implementation complexity and the difficulty of finding relevant values for input parameters. It is however a very sensitive aspect that can prevent from validating a model when ignored.

We frequently need to add these features treating our clients’ case studies.

Implementation of flange support does not need to be complicated. Zero thickness elements are a practical way of modelling surface bounding features. They are implemented in SDT as flat bricks (hexa) or wedges (penta) elements and use 2D anisotropic shell constitutive properties.

This topology is a good basis to model glue or debonding, and to implement practical contact effects in dynamics.

As the pre-loaded contact conditions vary, the relevant constitutive parameters are generally unknown from design. Robust design and digital twin building must therefore assess their variability and provide critical configurations. In other approaches, model updating from test correlation will also be likely to highlight operational values for the model.

Having a distributed contact stiffness density is thus meaningful in many vibrations use cases:

ūüĎČ When flanges into contact have stiffness differences of several orders so that asperities compression and associated mean surface interpenetration must be accounted for. This is the case when liners or seals are present, or with coarse roughness.

ūüĎČ When the contacting surface is not clearly defined so that the apparent stiffness accounts for unloaded areas. That is the case for fasteners, and is thus critical for assembled housing behavior and for vibration transmission to various equipment (PCB, battery packs…)

ūüĎČ When the dynamic response induces local contact surface changes so that an equivalent stiffness can be defined for a linear equivalent model.

Varying equivalent elastic contact properties is thus essential for model validation [4]. The example below based on [2] illustrates how the natural frequencies of an engine cradle vary when considering a support stiffness on potential contacting areas around weld spots. The variation is over 10 % and must be considered as a first order parameter.

The challenge resides in the need for the defined contact parameters to remain easily accessible and portable to other codes. Solutions based on contact, surface constraint definition or direct matrix coupling have many drawbacks. When letting the code interpret contact or surface constraints, matching is required, and each code use frequently undocumented smoothing/weighting tweaks for convergence. In many cases, implementation variation in complex models significantly alters the expected result after export, and elastic behavior is seldom available. Exporting constraint matrices is impractical, generates heavy files, and is mesh dependent, making it an undesirable solution despite providing equivalent results.

Zero thickness elements match the requirements. They use classical topologies making it easy to recover stiffness matrix contributions and to parameterize.

Exports to other codes can be based on cohesive elements. These elements are widely available and suitable to our needs. We successfully implemented it for ABAQUS using COH3D8 and COH3D6 elements with COHESIVE SECTION and TRACTION type of ELASTIC. INTER-elements in ANSYS, CIFHEX and CIFPENT for Nastran, CHEXCZ and CPENTCZ in Simcenter Nastran should provide equivalent solutions for the need. It corresponds to a bilinear formulation with no (or very high) debonding thresholds, shear effects are available for tangential adherence.

SDT-Contact provides conversion functionalities to generate zero thickness implementations from contact formulations or constraint-based surface coupling. As we commonly import models from external codes or from existing industrial processes, these features are critical to provide an effortless integration.

The limitation of zero thickness elements resides in the need for a compatible mesh between surfaces. Such feature can be obtained in meshing software, or by splitting preliminary meshed solids (as our Unjoin functionality When the mesh is not compatible, it is always possible to use the master surface for the zero thickness elements support and use Multiple Point Constraints (MPC) between the zero thickness and the slave surface. For target use cases, locking risks and implementation variations induced by the MPC will be mitigated by the fact that a softer material is present.


[1] Understanding friction induced damping in bolted assemblies through explicit transient simulation.
G. Vermot des Roches, E. Balmes, ISMA 2014. 

[2] Error localization and updating of junction properties for an engine cradle model.
G. Vermot des Roches, E. Balmes, S. Nacivet. ISMA 2016.

[3] Updating and design sensitivity processes applied to drum brake squeal analysis.
Martin, E. Balmes, G. Vermot des Roches, T. Chancelier. Eurobrake 2016.

[4] Numerical design and test on an assembled structure of a bolted joint with viscoelastic damping.
C. Hammami, E. Balmes, M. Guskov. MSSP 2015.

SDT 7.5 posted

For download, demos, … see here

SDT 7.5 is compatible with MATLAB 9.4 (2018b) to 24.1 (2024a). In the base and FEMLink modules, key changes of this release are

  • To answer customer requests on making numerical and test processes accessible through GUI, revision and extension work has continued. In particular
    • for the tabs Ident identification of modal tests, MAC shape correlation, MDRE expansion, Report automated report generation.
    • This is enabled by the continued rewrite of the SDT handle and sdtm allowed implementation of generic utilities transversely used in SDT. urn resolutions for object search urnObj. Callback and string formatting urn_fmt are now more explicitly documented. User readability of parameters is better supported using vhandle.uo objects. Integration of graphical tables is now uniformly supported by
    • code was made compatible with the deployment of GUI using the MATLAB Compiler and Runtime license.
  • Parametric superelement/reduced model handling continues to be a key capability that differentiates SDT from other software. The latest developments are
    • uniformisation efforts to render SDT a FEM code neutral import form the major software (NASTRAN, ANSYS, Abaqus, …). This has driven recent FEMLink developments of nasread, ans2sdt, abaqus, and documentation efforts SeImport.
    • to answer the need to efficiently animate models in tens of million of DOF and deal with confidentiality issues, new level-set based model selections for display as plane cuts combinations for feplot, see selcut.
    • GUI interactions between state-space building fe2ss  frequency response computations qbode, and state-animation have been notably extended.
    • ability to use superelements in test-analysis correlation processes
    • parametric superelements deal with reduced models with stiffness, complex modulus, mass, thickness, … aggregated in element groups zCoef or distributed in non-linearities NLdata.
    • Integration of parameter inputs in abaqus for SDT compatible types.
    • for large FEM, DOE, JobH applications, out-of-core functionalities have been thoroughly revised and extended. Revision of sdthdfmethods for HDF5 support with optimized read/write capabilities and improved robustness. Implementation of omat object for out-of-core numerical data handling, supporting several underlying file strategies (extended v6, low level HDF5 or high level MATLAB builtin commands HDF5).
    • job generation and monitoring for abaqus, combined with module SDT/JobH
    • cases reduced using nominal periodicity and extendend to variable properties  [2, 3, 4, 5]
  • In relation to the experimental vibration applications
    • ufread and fe_sens support better channel label translation
    • on the experimental modal analysis side, the handling of parametric tests (dependence on temperature, loading, amplitude, …)
  • To support of the development of efficient custom solvers
    • low level optimization associated with time integration continued with performance optimization in vhandle.matrix, viscoelastic transient models, …
    • Contact support for ans2sdt and abaqus, combined with SDT/Contact, or translated as MPC.
    • Moving contact of surfaces was notably extended for the simulation of rail-wheel contact problems.
  • Piezo capabilities for active control and SHM applications, were continued and the associated documentation ( will be updated soon.

CSMA 2024 : Hybrid FEM/test twin building, an electric engine case history

SDTools will be present at the CSMA 2024 conference

The talk [1] to be given will address challenges associated to the generation of a Hybrid FEM/test twin model of an automotive electric car engine in partnership with Stellantis:

  • Describing test outputs
    The electric engine case study being detailed combines strong dominance of harmonic responses and un-measured inputs. The harmonic balance vector signal model chosen gives a space/time/frequency approximation of the response.
  • Choosing model parameters
    Geometry, contacts in bolted joints and laminated stacks, non-linear viscoelastic bushings have here a notable impact.
  • Building a reduced parametric model
    This provides a 2 to 3 orders of magnitude speedup that is necessary for any practical application.
  • Building a Hybrid FEM/test twin model
    Test and FEM are combined using an expansion-based state/parameter estimation process.


SDT 7.3 posted

The major revision 7.2 was only made available as a beta version, with the stable version skipped due COVID related constraints.

SDT 7.3 is the only version fully compatible with MATLAB 9.4 (2018b) to 9.8 (2020a) mostly due to changes in the representation of complex numbers in MATLAB. Key changes of this release are

  • a major rewrite of the SDT handle object with major impact on GUI performance and compatibility with expect future changes in MATLAB GUI. sdth.urn provides a general mechanism for Uniform Resource Names which can now be used to designate and select many GUI or model components.
  • the introduction of the +vhandle package of classes to upgrade earlier functionality implemented in v_handle. In particular, vhandle.matrix provides a user readable access point to C libraries linked into the mkl_utils mex file corresponding to matrix like operators, but with possible parallel or initialization/repeated call (called inspector/executor by INTEL) optimization. This has provided speedup factors between 2 and 100 for a range of high performance time computations using both implicit or explicit time schemes. The SDT/nlsim token may be required for calls to the nl_solve diagNewmark solver (non-linear time domain transients in modal coordinates) and to the nl_solve expNewmark (explicit time solver). The vhandle.chandle object is used to provide init/call separation for non matrix like objects.
  • on the experimental modal analysis side, the handling of parametric tests (dependence on temperature, loading, amplitude, …)

For femlink the main changes were related to GUI and superelement import. For MATLAB compatibility see section 1.10.2.

SDT 7.4 posted

SDT 7.4 is the only version fully compatible with MATLAB 9.4 (2018b) to 9.12 (2022a) mostly due to changes in the representation of complex numbers in MATLAB. Key changes of this release are

  • the introduction of the¬†+vhandle¬†package of classes to upgrade earlier functionality implemented in¬†v_handle. In particular,¬†vhandle.matrix¬†provides a user readable access point to C libraries linked into the¬†mkl_utils¬†mex file corresponding to matrix like operators, but with possible parallel or initialization/repeated call (called inspector/executor by INTEL) optimization. This has provided speedup factors between 2 and 100 for a range of high performance time computations using both implicit or explicit time schemes. The¬†SDT/nlsim¬†token may be required for calls to the¬†nl_solve diagNewmark¬†solver (non-linear time domain transients in modal coordinates) and to the¬†nl_solve expNewmark¬†(explicit time solver). The¬†vhandle.chandle¬†object is used to provide init/call separation for non matrix like objects.
  • on the experimental modal analysis side, the handling of parametric tests (dependence on temperature, loading, amplitude, …)
  • full rewrite of fluid structure interaction implementation in¬†fsc. Added Transmission Loss and Rayleigh integral computation capabilities.

Tutorial at SURVISHNO

Error characterization in modal analysis and model updating. An overview of tools and procedures using the Structural Dynamics Toolbox.

will be presented by Etienne Balmès at the SURVISHNO conference in Lyon on July 8, 2019. This tutorial will mix theoretical considerations and applications using SDT (animations , presentation )

Experimental modal analysis seeks to extract shape and resonance properties from test data. While identification algorithms have been well documented for a long time, at least under the assumption linear behavior, significant differences continue to exist in the implementation details. In particular, non-linear optimization of poles and work by sub-bands is an often overlooked necessity to avoid bias. Once modal data available, the next step is to obtain test/analysis correlation. This requires topology correlation which brings its share of errors, which despite being usually small should be addressed. Global correlation criteria, such as the MAC, are introduced next but for efficient use should be complemented by a set of procedures to localize measurement, topology and correlation errors. While the simple evaluation of correlation is often an industrial objective, the best exploitation of test results is achieved using hybrid approaches combining test with a model, which does not need to be exact to usefully complement the measurements. In particular, expansion methods estimating the full Finite Element responses from data measured at sensors are particularly useful. Energy based criteria on the model side (Minimum Dynamic Residual Expansion or the various variants of Error in Constitutive Relation) have been long known to provide excellent solutions but deployment has been scarce due to an important numerical cost. Simple model reduction strategies are shown to give excellent results for industrial models and open the way for model error localization and updating.

The tutorial is illustrated using standard procedures implemented in the Structural Dynamics Toolbox which provides experimental modal analysis, finite element modeling, model reduction and correlation tools in the MATLAB environment. A main brake squeal application serves a red line and is complemented by illustrations from other industries.

SDT 7.1 released

SDT 7.1 is the only version fully compatible with MATLAB 9.4 (2018b) to 9.6 (2019a) mostly due to changes in the representation of complex numbers in MATLAB. Key changes of this release are

    • A continued effort in making the experimental modal analysis part of SDT section 2.2 fully accessible without any script is nearly complete. Functions however obviously remain accessible from the command line to users will to learn how to use them. The associated docks Id (for experimental modal analysis see section 2.2), CoTopo (topology correlation see section 3.1) and CoShape (test/FEM correlation see section 3.2) have been extended and tutorials have been introduced.
    • A major effort was put on the documentation. The new structuration of demos into tutorials helps training. You can for example see tutorials in various files with d_mesh(‘tuto’), gartid(‘tuto’), d_cor(‘tuto’), d_cms(‘tuto’), …. Equations are now shown as SVG files which improves readability, but may pose problems on some older versions of MATLAB where the help browser does not support SVG.
    • We are still working with the MathWorks on improving reliability of the help browser. To bypass some bugs, you may have to change default location where the help is shown using sdtdef(‘browser-SetPref’,‘-helpbrowser’) or sdtdef(‘browser-SetPref’,‘-webbrowser’). For clickable areas of SVG figures, use Ctrl-Click to open in a new window or right-click and select Open in a new tab.

Outside improved robustness of the GUI, key changes for FEMLink are

    • ans2sdt extended BDF reading in particular for orthotropic materials and substructure export (to ease superelement import). Job submission integration is now supported as a consulting project feature.
    • nasread compatibility with NX Nastran BGSET and BSURFS cards. Documentation of superelement (see d_cms(‘TutoNasCb’)). Performance of MAT9 and set reading.
    • ¬†abaqus significant .inp reading improvements *distribution,*hyperelastic, set handling, … Performance of large .fil reading. Robustness and performance enhancements of resolve commands. Introduction of a .dat reading framework for customer use, with complex modes output reading support.

You can download SDT 7.1 from

Keynote lecture of Etienne Balmès, CEO of SDTools, at the ISMA conference

Etienne Balmès, CEO of SDTools was invited as a keynote speaker at the ISMA (International Symposium on Modal Analysis) conference in Leuven, Belgium on September 17, 2018.

ISMA 2018 is the 28th international conference in a series of annual courses and biennial conferences on structural dynamics, modal testing and noise and vibration engineering, organised by the Department of Mechanical Engineering of the KU Leuven., and is a reference in the field of structural dynamics and vibro-acoustics.

Shapes & DOF: on the use of modal concepts in the context of parametric non-linear studies

copy of the slides (pdf)

Physical responses tend to lie within restricted subspaces even for parametric problems. For a given subspace, the choice of a basis defines Degree Of Freedom (DOF) and this choice may give interesting meaning to the associated amplitudes. Classical modal analysis builds subspaces combining modeshapes and static responses. Parametric loads for non-linear, damped, variable, … structures are discussed to extend the theory and illustrated for test and simulation cases. Challenges in shape extraction and basis generation techniques are then detailed. Introducing the ability to manipulate models with variable junction properties, component material and geometry, load and operating conditions, … opens new questions on the quantification and tracking of changes and objectives throughout design exploration. The definition of a reference linear system and the use of global and/or local modal DOF are shown to provide an interesting perspective.

SDT 7.0 released

SDT 7.0 is now released.

SDT 7.0 is the only version compatible with MATLAB 9.2 (2017a), 9.3 (2017b) and 9.4 (2018b) mostly due to ongoing improvements of MATLAB graphics. Key changes of this release are

  • A full rewrite and major extension of modal analysis graphical interfaces and documentation detailed in section¬†2.2. Step-by-step tutorials, such as ¬†section¬†2.2.1, include buttons of the form Run which you can use to execute a step. LSCF and stabilization diagrams are now supported.
  • The new notion of docks corresponds to MATLAB docks where multiple figures are combined for a typical use. Currently supported docks are
    • Id : for experimental modal analysis see section¬†2.2
    • TestFEM : topology correlation see section¬†3.1
    • MAC : test/FEM correlation see ii_mac.
  • A major update of SDT GUI with most existing tabs ported to Java mode and necessary in docks. You can set the default tab to Java mode using sdtdef(‘JavaUI’,1) or turn it off with sdtdef(‘JavaUI’,0). User documentation of tabs can be found in¬†section¬†8.2. Developer level documentation of GUI functions is now included in section¬†8.
  • Use sdtweb(‘feplot’,‘webbrowser’) to bypass the not yet fixed MATLAB bug where the links within pages are not called appropriately.

Key changes for FEMLink are

  • ans2sdt improved import of .cdb and support of contacts.
  • nasread Direct import of EXTESOUT output to SDT superelement format. Continued enhancements of bulk and op2 reading. Initial support of .op2 format writing of responses.
  • abaqus continued enhancements of .INP reading in particular for composites and superelements, contact, … Significant writing enhancements.
  • GUI import of models is supported with the FEMLink tab, section¬†8.2.2.

You can download SDT 7.0 from