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Title: On the collapse of ideally elasto-plastic complex structures
Author: Chan, Shiu-Lau
Awarding Body: University of London
Current Institution: Imperial College London
Date of Award: 1969
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A general approach to the plastic collapse (limit) and shakedown analyses of any complex structure is here presented. The approach entails the idealisation of the structure into a number of finite elements, each one is assumed to resist one dominant type of stress. An upper and a lower yield limit can then be associated with each element by postulating a perfectly plastic behaviour for the material. These simplifications effectively linearise the problems of plastic collapse and shakedown which can now be formulated conveniently in matrix form. The governing theorems of plastic collapse are stated and proved in this context. The applications of these theorems, corresponding to the force and displacement methods of analysis, each resulted in a linear programming problem. Their methods of solution and physical implications, as well as their mutual relationship are analysed and discussed. The problem of shakedown, including the effect of thermal strain, is treated by a similar procedure. Computer programmes are developed for each method of solution, and a number of examples are given as illustration. They are chosen to demonstrate the methods of idealisation of typical structures, to show their typical modes of collapse, to compare the results with existing solutions using other methods, and to assess the relative merits of the two methods of analysis. Finally, the possibilities for further investigation in connection with the present problem are discussed. As an example, the limit analysis of a three-dimensional continuum is formulated, using tetrahedral elements. The result is shown to be a non-linear programming problem. Also the possibility of generating orthogonal self-equilibrating systems for the force method of elastic analysis by a linear programming procedure is briefly presented.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available