000013270 001__ 13270
000013270 005__ 20161114160334.0
000013270 04107 $$aeng
000013270 046__ $$k2009-06-22
000013270 100__ $$aVan Genechten, B.
000013270 24500 $$aAn efficient wave based modelling approach for the steady-state dynamic analysis of two-dimensional solids with holes

000013270 24630 $$n2.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013270 260__ $$bNational Technical University of Athens, 2009
000013270 506__ $$arestricted
000013270 520__ $$2eng$$aThe 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.

000013270 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013270 653__ $$aElastodynamics, Navier, Mid-frequency, Trefftz method, Wave Based Method Abstract. 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. 1

000013270 7112_ $$aCOMPDYN 2009 - 2nd International Thematic Conference$$cIsland of Rhodes (GR)$$d2009-06-22 / 2009-06-24$$gCOMPDYN2009
000013270 720__ $$aVan Genechten, B.$$iVergote, K.$$iVandepitte, D.$$iDesmet, W.
000013270 8560_ $$ffischerc@itam.cas.cz
000013270 8564_ $$s1992467$$uhttps://invenio.itam.cas.cz/record/13270/files/CD406.pdf$$yOriginal version of the author's contribution as presented on CD, section: Computational methods for waves - i (MS).
000013270 962__ $$r13074
000013270 980__ $$aPAPER