Application of the Complex Variable Step Method and the Boundary Element Method for Sensitivity Analysis of Steady Heat Conduction Problems

2021 ◽  
Vol 412 ◽  
pp. 83-96
Author(s):  
Grzegorz Dziatkiewicz ◽  
Ewa Majchrzak ◽  
Bohdan Mochnacki
Keyword(s):  
Sensitivity Analysis ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Complex Variable ◽  
Volume Flow Rate ◽  
Physical Parameters ◽  
Shape Sensitivity ◽  
Step Method ◽  
Variable Step ◽  
Element Method

The paper concerns the problems related to applying the complex variable step method for the sensitivity analysis of the steady temperature field in the solid body domain due to the perturbations of the geometrical and physical parameters. The optimization problem using the approach proposed is also discussed. At the stage of numerical modelling, the boundary element method is used. The first part of the paper is devoted to the shape sensitivity. The results obtained are compared with the solution resulting from the implicit approach of sensitivity analysis. In the second part, the practical problem concerning optimizing the geometry of continuous casting mould cross-section is considered. The project variable vector contains the cooling pipes' radius and the volume flow rate of the cooling water. The numerical results and the conclusions are presented in the final part of the paper.

scholarly journals The Boundary Element Method and Path-independent Integrals in Sensitivity Analysis of Structures with Stress Concentration

2007 ◽  
Vol 1 (2) ◽  
Author(s):  
T. Burczynski ◽  
M. Habarta
Keyword(s):  
Sensitivity Analysis ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Stress Concentrator ◽  
The Body ◽  
Numerical Verification ◽  
Shape Sensitivity ◽  
Stress Concentrations ◽  
Stress Concentrators ◽  
Element Method

This paper presents the implementation of the boundary element method to shape sensitivity analysis of elastic structures with stress concentrators. An elastic body which contains a number of voids (internal boundaries), playing the role of stress concentrators, is considered. We are interested in calculating the first order sensitivity of shape–dependent functionals with respect to the shape variation of the body domain. This task is accomplished using the adjoint variable method. As it has been shown by Dems and Mróz [10], for a basic transformation (i.e. a translation, a rotation or a scale change) of the body, the sensitivity of the considered functional takes the form of a path-independent integral (PII) whose integrand depends on the primary and adjoint state fields, along an arbitrary path (curve in 2D, surface in 3D), enclosing the transformed stress concentrator (void). It is very important for numerical computations, because we can compute this integral along the path placed far from the stress concentrator to eliminate the negative influence of stress concentrations on the accuracy of calculations. The boundary element method (BEM) is used to solve both primary and adjoint problems. Some important cases of adjoint problems related to functionals are analyzed in the paper. A thorough numerical verification of the proposed method is performed in this work. The presented method of sensitivity analysis is utilised in gradient-based optimization and identification problems. Numerical examples of optimization and identification are shown in this paper.

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