Useful solutions to standard problems （有用的解决标准问题）.pdf

Usefulsolutions to standard problems Introduction and synopsis Modelling is a key part of design. In the early stage, approximate modelling establishes whether the concept will work at all, and identifies the combination of material properties which maximize performance. At the embodiment stage, more accurate modelling brackets values for the forces, the displacements, the velocities, the heat fluxes and the dimensions of the components. And in the final stage, modelling gives precise values for stresses, strains and failure probability in key components; power, speed, efficiency and so forth. Many components with simple geometries and loads have been modelled already. Many more complex components can be modelled approximately by idealizing them as one of these. There is no need to reinvent the beam or the column or the pressure vessel; their behaviour under all common types of loading has already been analysed. The important thing is to know that the results exist and where to find them. This appendix summarizes the results of modelling a number of standard problems. Their useful- ness cannot be overstated. Many problems of conceptual design can be treated, with adequate precision, by patching together the solutions given here; and even the detailed analysis of non- critical components can often be tackled in the same way. Even when this approximate approach is not sufficiently accurate, the insight it gives is valuable. The appendix contains 15 double page sections which list, with a short commentary, results for constitutive equations; for the loading