Applying Incompatible Meshes for Modeling Structural-Acoustic Domains in Energy Finite Element Analysis

Abstract

The Energy Finite Element Analysis (EFEA) has been developed for modeling coupled structural-acoustic systems at mid-to-high frequencies when conventional finite element methods are no longer computationally efficient because they require very fine meshes. In standard Finite Element Analysis (FEA) approach, governing differential equations are formulated in terms of displacements which vary harmonically with space. This requires larger numbers of elements at higher frequencies when wavelengths become smaller. In the EFEA, governing differential equations are formulated in terms of energy density that is spatially averaged over a wavelength and time averaged over a period. The resulting solutions vary exponentially with space which makes them smooth and allows for using much coarser meshes. However, current EFEA formulations require exact matching between the meshes at the boundaries between structural and acoustic domains. This creates practical inconveniences in applying the method as well as limits its use to only fully compatible meshes. In this paper, a new formulation is presented that allows for using incompatible meshes in EFEA modeling, when shapes and/or sizes of elements at structural-acoustic interfaces do not match. In the main EFEA procedure, joints formulations between structural and acoustic domains have been changed in order to deal with non-matching elements. In addition, the new Pre-EFEA procedure which allows for automatic searching and formation of the new types of joints is developed for models with incompatible meshes. The new method is tested using a spherical shaped structural-acoustic interface. Results for incompatible meshes are validated by comparing to solutions obtained using regular compatible meshes. The effects of mesh incompatibility on the accuracy of results are discussed.