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Essentials of stress analysis and implementation in approximation techniques

In spite of the advanced state to which theoretical and numerical techniques of stress analysis have developed, they are not yet capable of describing the behaviour of real engineering systems in every particular. Consequently, an essential element in the process of designing such systems is the generation of conceptual models of proposed situations to which one’s current stock of analytic techniques may be applied. Depending on the requirements of the problem under consideration and the current state of one’s capability for solution (including financial resources), models at various levels of sophistication may be comtemplated and calculations based on these models will yield predictions at various levels of precision. Although one naturally hopes that such calculations will be adequate for the purpose at hand, the ultimate test is embodied in the accord found between the predictions and any observed test or in-service behaviour: the closer the correlation one seeks between the predicted and actual behaviour, the more sophisticated does the modelling need to be. Unfortunately, increased sophistication almost always incurs increased complexity in analysis and whilst the powers of various computing devices considerably alleviate the technical capability factor, the cost may be very great indeedt. An important factor is therefore the consideration of an analysis which is ‘good enough for the purpose at hand‘, which in turn requires experience in order that adequate judgements may be made. The formulation and solution of problems in stress analysis are concerned with manipulating three essential ingredients: conditions of equilibrium, conditions of geometric fit or compatibility, and some force-deformation or stress-strain characteristic for the elements of the system. The discussion may proceed along one of two broad paths: in the vector or direct approach, the three ingredients are manipulated in an explicit fashion whilst in the variational approaches, one or more may be observed only implicitly. Either approach is valid, but the application of variational principles, perhaps culminating in the finite-element method, becomes increasingly attractive as the problems of interest become more and more complex. In a formal approximation technique, one or other of the first two ingredients may be satisfied only in some weighted or average way and this must be clearly understood by the practitioner if the results are to be usefully interpreted.