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首页> 外文期刊>Applied Mathematical Modelling >An efficient numerical method to solve 2-D interval bi-modular problems via orthogonal polynomial expansion
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An efficient numerical method to solve 2-D interval bi-modular problems via orthogonal polynomial expansion

机译：通过正交多项式扩展解决2-D间隔双模块化问题的有效数值方法

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摘要

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.
机译：通过解决确定性解决方案的效率和非线性FE迭代的计算成本的效率来提出了不确定的双模问题的间隔分析。首先，通过简明的数学图示指出了2-D常规双模型基质的奇异性，并且通过与同轴条件一致的剪切模量的互补来除去。开发了一种具有完整等级构成矩阵的新FE模型以解决确定性的双模块化问题，该问题在数值测试中进行了很好的执行，特别是在收敛期间。其次，构建了基于正交的多项式膨胀的代理，以减轻在界限估计中的优化过程中重复的非线性Fe解决方案引起的重计算负担。给出了数值例子来说明所提出的方法的准确性和效率，并且在通过所提出的方法和参考解决方案获得的结果之间可以观察到徽益。

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