Geometrically nonlinear finite element implementation based on highly accurate 1st and 2nd numerical derivative scheme using hyper-dual numbers

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  • Hyper-dual numbersを用いた高精度一階・二階数値微分法に基づく幾何学非線形有限要素法の定式化

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This paper proposes a novel implementation scheme of geometrically nonlinear finite element programs, which automatically compute exact internal force vectors and element stiffness matrices by numerically differentiating a strain energy function at each element. This method can significantly simplify the complex implementation procedure which is often observed in conventional finite element implementations, since it never requires B matrices, stress tensors, and elastic tensors by hand. The proposed method is based on a highly accurate numerical derivatives which use hyper-dual numbers and never suffer from any round-off and truncation errors. Several numerical examples are performed to demonstrate the effectiveness and robustness of the proposed method.

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