Boundary integral equation analysis in linear viscoelasticity: Variational and saddle point formulations
This interesting paper extends a formulation previously produced by the third author (for elasticity and inviscid plasticity problems) [e.g. Mech., Res. Commun. 10, 45-52 (1983; Zbl 0511.73090); with \textit{C. Polizzotto}, Comput. Methods Appl. Mech. Eng. 60, 175-194 (1987; Zbl 0602.73081); with \textit{G. Novati} and \textit{S. Sirtori}, Discretization methods in structural mechanics, Proc. IUTAM/IACM Symp., Vienna/Aust. 1989, 191-200 (1990; Zbl 0728.73086)] to viscoelasticity applications. In this context, the approach presented includes some advantageous aspects in comparison to the classical boundary element formulation for the title problem, such as symmetry of the final system of equations. The formulation, however, requires double integration as early Galerkin type formulations, but the complete Green's functions for the fundamental problem included in the appendix indicate the same order of singularities as the early elasticity implementation. The paper still lacks examples and comparisons with previous procedures, but represents a further step in the highly original line of action of this strong team of researchers.
symmetric, double integration boundary integral equation
algebraic equations with symmetric coefficient matrix
variational characterizations of the boundary solutions
scientific article; zbMATH DE number 4215512