This paper introduces a mathematical framework for explicit structural dynamics, employing approximate dual functionals and rowsum mass lumping. We demonstrate that the approach may be interpreted as a Petrov-Galerkin method that utilizes rowsum mass lumping or as a Galerkin method with a customized higher-order accurate mass matrix. Unlike prior work, our method correctly incorporates Dirichlet boundary conditions while preserving higher order accuracy. The mathematical analysis is substantiated by spectral analysis and a two-dimensional linear benchmark that involves a non-linear geometric mapping. Our results reveal that our approach achieves accuracy and robustness comparable to a traditional Galerkin method employing the consistent mass formulation, while retaining the explicit nature of the lumped mass formulation.

翻译：本文提出了一种用于显式结构动力学的数学框架，采用近似对偶泛函与行和型质量集中技术。我们证明该方法可被解释为利用行和型质量集中的彼得罗夫-伽辽金方法，或采用定制化高阶精确质量矩阵的伽辽金方法。与现有工作不同，我们的方法在保持高阶精度的同时正确引入了狄利克雷边界条件。通过谱分析及涉及非线性几何映射的二维线性基准算例验证了数学分析的可靠性。结果表明，本方法在保持集中质量公式显式特性的同时，达到了与传统使用一致质量公式的伽辽金方法相当的精度和鲁棒性。