| Problems of mechanics are governed by three fundamental principles namely: equilibrium (the statically admissible set S), kinematics of deformation (the kinematically admissible set K) and constitution of materials (the constitutively admissible set C). They are modeled by equations or other representations so that a mechanics problem can be formulated and solved by a certain technique. When this representations are in the form of sets in an appropriate space, a methodology for solving a problem becomes a search for the intersection of these three fundamental sets.;Limit analysis is convex analysis and it studies the solutions in the intersections of two of these three sets. The Lower bound solution lies in the set ;For computational purpose, a limit solution may be obtained by minimizing an Upper bound solution or maximizing a Lower bound solution. In this connection, a systematic search from the minimizational approach for the limit solution in a convex set is developed.;A limit solution is likely to be nonlinear such that certain non-differentiable functions are perfectly admissible, this algorithm contains a combined smoothing and successive approximation scheme to overcome these difficulties. The numerical solutions are performed under a wide range of process parameters. The results obtained are compared whatever possible with the classical solutions and are in good agreement. The study presented here can then be used for a design purposes. |
