This paper presents an extended/generalized finite element method for bridging scales in linear elastodynamics in the absence of scale separation. More precisely, the GFEM^gl framework is expanded to enable the numerical solution of multiscale problems through the automated construction of specially-tailored shape functions, thereby enabling high-fidelity finite element modeling on simple, fixed finite element meshes. This introduces time-dependencies in the shape functions in that they are subject to continuous adaptation with time. The temporal aspects of the formulation are investigated by considering the Newmark-\(\beta \) time integration scheme, and the efficacy of mass lumping strategies is explored in an explicit time-stepping scheme. This method is demonstrated on representative wave propagation examples as well as a dynamic fracture problem to assess its accuracy and flexibility.

本文提出了一种扩展/广义有限元方法，用于在没有尺度分离的情况下弥合线性弹性动力学中的尺度。更准确地说，GFEM ^gl框架得到了扩展，通过自动构建专门定制的形状函数来实现多尺度问题的数值求解，从而在简单、固定的有限元网格上实现高保真有限元建模。这在形状函数中引入了时间依赖性，因为它们随时间不断适应。通过考虑 Newmark- \(\beta\)时间积分方案，并在显式时间步进方案中探索了质量集总策略的功效。该方法在具有代表性的波传播示例以及动态断裂问题上进行了演示，以评估其准确性和灵活性。