Symbolic computational modelling and solution of problems in applied dynamics: keynote address

Matthew Cartmell, David Forehand, Raya Khanin

Research output: Contribution to conferencePaperpeer-review


The traditional approach to modelling and solving small-scale flexural and rigid body problems in engineering dynamics has been to use Newtonian free bodies, or Lagrangian energy representations, and then to resort to finite element models for bigger, or more complicated, systems. In the main such approaches are acceptable in the sense that reduced-order nonlinear analytical models of relatively simple physical systems are frequently suitable for the study of complicated response motions, or, alternatively, where accurate responses are required for very big complicated systems which cannot be easily modelled by hand. In the first case the nonlinear analytical model, despite being of low order, tends to provide deep insight, particularly if numerical solutions are also sought for that model and then used for the calculation of bifurcatory and phase space parameters. In the second case the large finite element models that are used to solve big systems generally provide high levels of industrially bench-marked accuracy, but do not give an easily understood portrayal of the internal dynamics of the system. This means that there can be a merging of phenomena and an attendant difficulty in 'seeing the wood for the trees' when using finite elements for this sort of problem. The research to be summarised within this presentation is this research group's attempt to scale up the use of analytical models for the dynamics of engineering systems so that systems which would normally tend to be considered 'big' are in fact treatable analytically, through from model to solution. The advantage of doing this is that the dynamics should be fully captured, and, importantly, should also be visible in terms of the analytical structure of the response equations. Taken in conjunction with computer generated numerical solutions an accurate and complete analytical solution for a 'big' dynamical problem can provide a major increase in understanding and insight. The presentation will explain the remit of the research and will summarise the achievements of a previous research grant in which a symbolic solver was constructed in Mathematica [1], [2], to undertake the computational steps for the method of multiple scales. Current work has concentrated on the problem of reliable and generalised symbolic modelling of rigid body systems containing links, joints, discrete springs and dampers using aspects of graph theory and the systematic approach of Roberson & Schwartassek [3]. The result of this work is a generalised multi-body code in Mathematica, Forehand, Cartmell, and Khanin [4], which is now being linked to the multiple scales solver. This work will be summarised in the presentation and plans for the formulation of a linked schematic modeller will be discussed, written in either Mathematica or OpenCascade. The presentation will end with proposals for further work in the area of flexural system modelling.
Original languageEnglish
Publication statusPublished - 27 Jun 2002
EventRussian Academy of Sciences Summer school on Advanced Problems in Mechanics - Repino, St. Petersburg, Russian Federation
Duration: 27 Jun 20026 Jul 2002


ConferenceRussian Academy of Sciences Summer school on Advanced Problems in Mechanics
Abbreviated titleAPM
Country/TerritoryRussian Federation
CitySt. Petersburg


  • computational modelling
  • applied dynamics
  • finite element models


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