Guaranteed and computable bounds of the limit load for variational problems with linear growth energy functionals
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- Haslinger, J., Repin, S. & Sysala, S. Appl Math (2016) 61: 527. doi:10.1007/s10492-016-0146-6
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The paper is concerned with guaranteed and computable bounds of the limit (or safety) load, which is one of the most important quantitative characteristics of mathematical models associated with linear growth functionals. We suggest a new method for getting such bounds and illustrate its performance. First, the main ideas are demonstrated with the paradigm of a simple variational problem with a linear growth functional defined on a set of scalar valued functions. Then, the method is extended to classical plasticity models governed by vonMises and Drucker-Prager yield laws. The efficiency of the proposed approach is confirmed by several numerical experiments.