A recent development for the numerical modelling of material discontinuities is presented in this thesis. The concepts considered here are founded on the idea that for each physical variable (e.g. temperature, enthalpy, etc.) there exists an associated non-physical variable. The numerical technique presented here that utilises non-physical variables is called the non-physical finite element method (NPFEM). The NPFEM involves the replacement of a discontinuous physical field with a limiting-continuous non-physical field (i.e. abstract mathematical object) which is continuous over the domain but has a source-like behaviour at the place of a discontinuity. Non-physical variables are rigorously defined in the thesis and are related to their physical counterparts by means of transport equations. As a consequence of the coupling of physical and non-physical variables, equivalent forms of transport equations arise. However, as a consequence of limiting continuity the adopted approach permits the representation of non-physical variables by means of a polynomial basis standard to the continuous Galerkin finite element method (CGFEM).The non-physical method was originally devised for the modelling of material discontinuities in solidification problems involving a strong discontinuity in enthalpy and a weak discontinuity in temperature. The work presented here extends previous works by providing a general framework for the non-physical method to facilitate modelling of strong material discontinuities in all the state variables along with velocity arising with material discontinuities. The approach is founded on the integral transport form of the governing conservation laws. The advantage of the non-physical methodology is that it permits the precise annihilation of discontinuous behaviour in the governing finite element equations by means of a distribution like source term at the discontinuity location. Different case studies of single and multiple stationary and transient 1-D shock waves in fluids and solids are undertaken to show the accuracy, flexibility and robustness of the non-physical finite element method. Also presented as part of the work is a newly developed analytical model for the 1-D high velocity crushing of the cellular bars.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:626968 |
| Date | January 2014 |
| Creators | Darvizeh, Roohoolamin |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/nonphysical-finite-element-method-for-modelling-of-material-discontinuities(62b803fa-fb34-425e-8a77-a77822a078ab).html |
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