Adaptive meshing for two-dimensional thermoelastic problems using Hermite boundary elements

Abstract

In the present work, error indicators for the potential and elastostatic problems are used in a combined fashion to implement an adaptive meshing scheme for the solution of two-dimensional steady-state thermoelastic problems using the Boundary Element Method. These error indicators exploit in their formulation the possibility of generating two different numerical solutions from just one analysis using Hermite elements. The first solution is the standard one obtained from an analysis using Hermite elements. The second is a "reduced" solution obtained representing the field variables inside an element using some of the degrees of freedom of the Hermite element together with Lagrangian shape functions. The basic idea behind the computation of the error indicator is to compare these two solutions, on an element by element basis, to obtain an estimate of the magnitude of the error in the numerical solution corresponding to the Hermite elements. In this sense, it is assumed that the bigger the difference between these two solutions, the bigger the error in the original solution with Hermite elements. Since the thermoelastic problem in its uncoupled fashion is considered, the former approach is applied to both problems, heat conduction and thermoelastic. Since both numerical solutions for each one of these problems are obtained from just one analysis, the computational cost of the proposed error indicators is very low. ᭧

Adaptive Integration Method Based on Sub-Division Technique for Nearly Singular Integrals in Near-Field Acoustics Boundary Element Analysis

“…So the simple method to eliminate nearly singular integrals is adaptive integration technique based on element sub-division. So far, adaptive tactics have been widely used in tackling nearly singular integrals arising in many boundary element analyses of engineering problems, such as potential problems [34,35], contact problems [36], plate bending [37], thermoelastic problems [38], elastoplastic problems [39,40], etc. E. Kita and N. Kamiya [41] gave a comprehensive review on adaptive mesh refinement schemes for the BEM.…”

Use of the tangent derivative boundary integral equations for the efficient computation of stresses and error indicators

“…All the examples presented in this work were performed using this scheme. If the reader is interested in reviewing some results obtained through the summation approach, Muci-K uchler et al [19], Muci-K uchler and Miranda-Valenzuela [20] and Miranda-Valenzuela et al [21] present some examples for the potential, elastostatic, and thermoelastic problems in two dimensions, respectively.…”

“…Muci-K uchler et al [19], Muci-K uchler and Miranda-Valenzuela [20], and MirandaValenzuela et al [21] presented formulations for the computation of simple error indicators for Hermite elements in potential, elastostatic, and thermoelastostatic problems in two dimensions. These error indicators were based on the possibility of obtaining two di erent numerical solutions for the tangential derivatives of the ÿeld variables from just one analysis with Hermite elements.…”

Adaptive integration technique for nearly singular integrals in near-field acoustics boundary element analysis

“…More recently, this variable transformation method is extended to three-dimensional boundary element method [15]. Apart from the above methods, adaptive tactics have been widely used in tackling nearly singular integrals arising in many boundary element analyses of engineering problems, such as potential problem [16,17], contact problems [18], plate bending [19], thermoelastic problems [20], elasto-plastic problems [21,22], etc. Kita and Kamiya [23] gave a comprehensive review on adaptive mesh refinement schemes for boundary element methods.…”