Limit Analysis of Plates By Optimization Techniques.

An upper bound functional which attains its minima at collapse of thin laterally loaded plates is formulated. A general collapse pattern for various thin plate problems is constructed in terms of a set of unknown parameters. An appropriate mathematical programming algorithm is applied to search for the correct parameters in the minimization procedure. Three types of plates under uniform load are treated specifically. First, the least upper bound solutions for rectangular plates with various boundary conditions are calculated. The corresponding elastic solutions are also calculated. From these elastic and plastic solutions the reserve strength of the plate beyond its elastic load capacity is predicted. Secondly, a class of plates with three simply supported boundaries and a free edge in an arbitrary orientation is analyzed by the same method. This analysis shows that the strength of plate is sensitive to the orientation angle of the free edge. The third application is to simply supported square plates with a circular hole. An extensive investigation is made for all possible parametric variations on the location and size of the hole. It is shown that the hole does not always weaken the plate. The plastic analysis gives realistic load capacities for the plates in applications.PhDOcean engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/158419/1/8125087.pd