An efficient wave based modelling approach for the steady-state dynamic analysis of two-dimensional solids with holes

Abstract eng:
The Finite Element Method (FEM) is the most commonly used prediction technique for dynamic simulations of mechanical structures. This method expands the dynamic field variables within a fine discretisation of the problem domain in terms of local, non-exact shape functions. Given the resulting increasing model sizes and subsequent high computational loads for increasing frequency, the use of the FEM is limited to low-frequency applications. The Wave Based Method (WBM) [1] is a novel Trefftz-based deterministic prediction technique which aims at relaxing the existing frequency limit. Instead of dividing the problem domain into small elements, the domain is divided in a small number of large, convex subdomains. In each of those subdomains, the field variables are expressed in terms of global wave functions, which exactly satisfy the governing dynamic equations. Compared with the FEM, the WBM exhibits a higher convergence rate, which allows the method to be applied up to higher frequencies. A sufficient condition for convergence of the applied wave function expansion is the convexity of the considered problem domains. As a result, only problems of moderate geometrical complexity can be considered and some commonly applied geometrical features cannot be handled at all. A typical example of this is the study of the dynamic behaviour of a two-dimensional solid which contains one or more circular holes. Since the region between two holes or between a hole and the edge of the problem domain needs to be partitioned into convex subdomains, only an approximate, linearised representation of the circular edge can be used to construct a convergent WBM model. The resulting model is only a crude geometrical approximation of the actual problem and has the additional disadvantage of being inefficient since many convex subdomains are required for an accurate represenation of the circle. Recently, an extension of the WBM for two-dimensional unbounded [2] and bounded [3] steady-state acoustic problems has been developed which allows the method to overcome these geometrical limitations in a very efficient way. This paper presents a numerical strategy for the study of two-dimensional elastodynamic problems with one or more circular holes, which is based on that modelling framework. The feasibility of the approach and the efficiency with respect to the FEM is illustrated by means of the dynamic analysis of a perforated membrane.

• Export as: BibTeX | MARC | MARCXML | DC | EndNote | NLM | RefWorks
• Add to your basket