Abstract
An interval analysis of uncertain bi-modular problems is presented by addressing the efficiency of deterministic solution and reduction of computational cost on the non-linear FE iteration. Firstly, the singularity of 2-D conventional bi-modular constitutive matrix is pointed out via a concise mathematical illustration, and is removed via a complement of shear modulus consistent with the coaxial condition. A new FE model with a full rank constitutive matrix is developed to solve deterministic bi-modular problems, which is well performed in the numerical tests, particularly in term of convergence. Secondly, an orthogonal polynomial expansion based surrogate is constructed to alleviate the heavy computational burden caused by repeated non-linear FE solution in the optimization process for bounds estimation. Numerical examples are given to illustrate the accuracy and efficiency of proposed approach, and a good accordance can be observed between the results obtained by the proposed approach and reference solutions.
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