An immersed enriched finite element method is proposed for the analysis of phononic crystals (PnCs) with finite element (FE) meshes that are completely decoupled from geometry. Particularly, a technique is proposed to prescribe Bloch–Floquet periodic boundary conditions strongly on non-matching edges of the periodic unit cell (PUC). The enriched finite element formulation effectively transforms a periodic non-confirming discretization into an enriched node-to-node periodic discretizations where periodicity is enforced by any standard procedure. The enriched formulation is also used to describe the interior material interface. This completely eliminates the tedious process of generating matching or fitted meshes during the design process, as it allows changing the inclusion’s geometry as well as the PnC’s lattice type without changing the FE mesh. The proposed approach, which is used to analyze phononic crystals in 1-D, 2-D, and 3-D using structured meshes, exhibits the same performance as the standard finite element analysis on fitted meshes.

提出了一种浸入式富集有限元方法，用于分析具有与几何完全分离的有限元（FE）网格的声子晶体（PnCs）。特别是，提出了一种强力规定Bloch-Floquet周期边界条件的技术在周期性单位单元（PUC）的不匹配边缘上。富集的有限元公式有效地将周期性的非确认离散化转换为富集的节点到节点的周期性离散化，其中周期性可以通过任何标准过程来强制执行。丰富的配方还用于描述内部材料界面。这完全消除了在设计过程中生成匹配或拟合的网格的繁琐过程，因为它允许在不更改FE网格的情况下更改夹杂物的几何形状以及PnC的晶格类型。所提出的方法用于使用结构化网格来分析1-D，2-D和3-D中的声子晶体，其性能与拟合网格上的标准有限元分析相同。