Improved calculation of field variables in the domain based on BEM

• Published in: Engineering analysis with boundary elements Vol. 11; no. 3; pp. 257 - 264
• Main Authors: Gaul, L., Fiedler, C.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 1993; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Frequency domain method; Vibration; Elastic wave; Weight function; Boundary element method
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/0955-7997(93)90027-I

BEM-based formulations for calculating field variables at internal points are well established and are effective, especially when only certain regions of the domain are of interest. Numerical integration problems exist while evaluating interior displacements and stresses near the boundary. The aim of this paper is to derive kernel functions, which allow the calculation of displacements and stresses in the frequency domain of elastodynamics. An easy way to improve the accuracy of the calculation of displacements in the boundary layer is also presented. The derived functions approximate the static solution, when the frequency tends to zero. The results obtained with the new kernel functions are compared with analytical 1-D and 3-D solutions of vibrating rods. The analytical solution is based on the Pochhammer equation for cylindrical bars adapted to given boundary conditions. The results presented indicate the effectiveness of the proposed kernel functions.