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BIE solutions for applied thermoplasticity by collocation. (English) Zbl 0708.73085

Discretization methods in structural mechanics, Proc. IUTAM/IACM Symp., Vienna/Aust. 1989, 29-38 (1990).
Summary: [For the entire collection see Zbl 0707.00025.]
The design application of BIE methods to the stress analysis of advanced turbomachinery components involves four domain integral problems: transient thermal strains, temperature dependent material properties, steep thermal gradients due to thermal shock, and plastic strains caused by thermal shock. Application of the BIE method to such problems has been significantly hindered by the need to provide domain elements to model each of these effects. The goal of the current study is to include each of these effects through the use of collocation methods, using particular solutions corresponding to properly selected global interpolation functions.
The application of a collocation system for particular integral formulation to thermoplasticity problems in boundary element methods is presented. The particular solution is used to evaluate dual-boundary integral equations (BIE) for this inhomogeneous problem formulation. The dual-BIE replaces the usual domain integral formulations. Issues regarding numerical performance and the nature of the solution algorithm are discussed in the framework of progressively more complex application problems.

MSC:

74S15 Boundary element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs

Citations:

Zbl 0707.00025