An enhanced numerical procedure for the shakedown analysis in multidimensional loading domains

• Published in: Computers & structures 2017-12, Vol.193, p.155-171
• Main Authors: Spiliopoulos, K.V., Panagiotou, K.D.
• Format: Article
• Language: English
• Subjects: Algorithms; Cyclic loading; Cyclic loads; Direct methods; Finite element analysis; Finite element method; Iterative methods; Load; Materials fatigue; Mathematical programming; Numerical algorithms; Plasticity; Residual stress; Residual stresses; Shakedown; Shakedown analysis
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2017.08.008

•An enhanced direct method for the shakedown analysis of elastoplastic structures.•Approach is twice as fast compared to the original one.•Formulated in a 3D thermomechanical loading domain.•Running time almost the same for 2D and 3D domains.•Automation of the approach in any n-dimensional loading domain. The Residual Stress Decomposition Method for Shakedown (RSDM-S) is a new iterative direct method to estimate the shakedown load in a 2-dimensional (2D) loading domain. It may be implemented to any existing finite element code, without the need to use a mathematical programming algorithm. An improved and enhanced RSDM-S is proposed herein. A new convergence criterion is presented that makes the procedure almost double as fast. At the same time, the procedure is formulated in a 3-dimensional (3D) polyhedral loading domain, consisting of independently varying mechanical and thermal loads. Using a cyclic loading program that follows the outline of this domain, it is shown that there is hardly any increase in the computational time when passing from a 2D to a 3D domain. Finally, keeping the efficiency, using an alternative cyclic loading program, an automation of the approach to any n-dimensional loading domain is presented. Examples of application are included.