Numerical shakedown analysis of axisymmetric sandwich shells: An upper bound formulation

Abstract

SUMMARYShakedown analysis of axisymmetric elastic-perfectly plastic sandwich shells is performed here using a new upper bound formulation based on a special form of Koiter's theorem concerning piecewise linearized yield surfaces. Starting from finite element techniques and the Tresca sandwich yield condition, shakedown analysis is reduced to a linear programming problem which is solved by a powerful simplex algorithm. Numerical results are given for a number of examples and a comparison is made with a previously computed lower bound formulation.

Shakedown analysis of defective pressure vessels by a kinematic approach

“…In previous kinematic shakedown analyses, linear programming techniques were developed by using piece-wise linear (Tresca) or linearized yield criterion, e.g. [11,23]. The application of von Mises criterion leads to a nonlinear mathematical programming problem, the solution of which in practical engineering applications with complex structures and loading still represents a challenge.…”

Kinematical shakedown analysis with temperature-dependent yield stress

“…The left scheme was suggested by K onig and Kleiber [36] and has been applied in a simple step-by-step shakedown analysis [1]. The right one was adopted by Morelle et al [38][39][40] and is used in the present work. Based on the modiÿed kinematical theorem in Section 2, we can give an e ective implementation in a general displacement ÿnite element formulation.…”

A general approximate technique for the finite element shakedown and limit analysis of axisymmetrical shells. Part 2: Numerical applications

“…Type of formulation p/ W [14] Lower bound 0·050432 [14] Upper bound 0·05324 [15] Lower bound 0·049624 [15] Upper bound 0·054064 [13] Upper bound 0·048168 [16] Upper bound 0·0518 Present Techn.…”