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Simulation of in-plane vibrations of 2D structural solids with singularities using an efficient wave based prediction technique

Vanmaele C., Vergote K., Vandepitte D., Desmet W.

Computer Assisted Methods in Engineering and Science

2012

Vol. 19, no. 2

135-171

This paper proposes the wave based method for the steady-state dynamic analysis of the in-plane behaviour of 2D structural solids. This novel prediction technique relaxes the frequency limitations of the commonly used finite element method through an improved computational efficiency. This efficiency is obtained by selecting basis functions which satisfy the governing equations a priori, in accordance with the indirect Trefftz approach. Special attention is paid to problems in which singularities appear in the problem solution. For these problems, the conventional set of basis functions is extended with functions which can represent the singularity accurately. The capabilities of this novel method for mid-frequency applications, as compared to the standard finite element method, are demonstrated by means of two numerical examples.

Application of a hybrid finite element --- Trefftz approach for acoustic analysis

Pluymers B., Vanmaele C., Desmet W., Vandepitte D.

Computer Assisted Mechanics and Engineering Sciences

2006

Vol. 13, No. 3

427-444

This paper reviews a wave based prediction technique for steady-state acoustic analysis, which is being developed at the K.U. Leuven Noise and Vibration Research group. The method is a deterministic technique based on an indirect Trefftz approach. Due to its enhanced convergence rate and computational efficiency as compared to conventional element based methods, the practical frequency limitation of the technique can be shifted towards the mid-frequency range. For systems of high geometrical complexity, a hybrid coupling between wave based models and conventional finite element (FE) models is proposed in order to combine the computational efficiency of the wave based method with the high flexibility of FE with respect to geometrical complexity of the considered problem domain. The potential to comply with the mid-frequency modelling challenge through the use of the wave based technique or its hybrid variant, is illustrated for some three-dimensional acoustic validation cases.