Inverse mass matrix for isogeometric explicit transient analysis via the method of localized Lagrange multipliers
Inverse mass matrix for isogeometric explicit transient analysis via the method of localized Lagrange multipliers
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DOI：
10.1002/nme.5986
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发表时间：
2018-11
影响因子：
2.9
通讯作者：
J. A. González;J. Kopačka;R. Kolman;S. Cho;Kyung-Duck Park
中科院分区：
文献类型：
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作者：
J. A. González;J. Kopačka;R. Kolman;S. Cho;Kyung-Duck Park
一个变分的框架，生成逆质量矩阵等几何分析（伊加）。由于不同的对偶基不仅影响精度，而且还影响计算开销，因此对几种对偶基进行了广泛研究。具体而言，局部不连续的双正交基函数的详细评估B-样条的高连续性和贝塞尔元素与标准的C 0连续有限元结构。在生成完全自由体的质量逆矩阵后，用局部拉格朗日乘子法施加边界条件。因此，与不采用拉格朗日乘子方法的逆质量矩阵方法不同，不需要修改倒数基函数来考虑边界条件。因此，本方法不需要对现有伊加软件结构进行内部修改。数值算例表明，全局连续的对偶基函数比局部不连续的双正交基函数具有更好的精度，但计算量要大得多。局部不连续的对偶基函数被发现是一个经济的替代集中质量矩阵时，结合质量参数化。所得的逆质量矩阵进行了测试，在几个振动问题，并施加到显式瞬态分析的结构。
A variational framework is employed to generate inverse mass matrices for isogeometric analysis (IGA). As different dual bases impact not only accuracy but also computational overhead, several dual bases are extensively investigated. Specifically, locally discontinuous biorthogonal basis functions are evaluated in detail for B‐splines of high continuity and Bézier elements with a standard C0 continuous finite element structure. The boundary conditions are enforced by the method of localized Lagrangian multipliers after generating the inverse mass matrix for completely free body. Thus, unlike inverse mass matrix methods without employing the method of Lagrange multipliers, no modifications in the reciprocal basis functions are needed to account for the boundary conditions. Hence, the present method does not require internal modifications of existing IGA software structures. Numerical examples show that globally continuous dual basis functions yield better accuracy than locally discontinuous biorthogonal functions, but with much higher computational overhead. Locally discontinuous dual basis functions are found to be an economical alternative to lumped mass matrices when combined with mass parameterization. The resulting inverse mass matrices are tested in several vibration problems and applied to explicit transient analysis of structures.