On the Theory of Anisotropic Flat Elasticity

Journal Article · Sat Dec 15 04:00:00 EST 2018 · Journal of Mathematical Sciences

DOI:https://doi.org/10.1007/S10958-018-4083-7· OSTI ID:22773676

For the Lamé system from the flat anisotropic theory of elasticity, we introduce generalized double-layer potentials in connection with the function-theory approach. These potentials are built both for the translation vector (the solution of the Lamé system) and for the adjoint vector functions describing the stress tensor. The integral representation of these solutions is obtained using the potentials. As a corollary, the first and the second boundary-value problems in various spaces (Hölder, Hardy, and the class of functions just continuous in a closed domain) are reduced to the equivalent system of the Fredholm boundary equations in corresponding spaces. Note that such an approach was developed in [19, 20] for common second-order elliptic systems with constant (higher-order only) coefficients. However, due to important applications, it makes sense to consider this approach in detail directly for the Lamé system. To illustrate these results, in the last two sections we consider the Dirichlet problem with piecewise-constant Lamé coefficients when contact conditions are given on the boundary between two media. This problem is reduced to the equivalent system of the Fredholm boundary equations. The smoothness of kernels of the obtained integral operators is investigated in detail depending on the smoothness of the boundary contours.

• OSTI ID: 22773676
• Journal Information: Journal of Mathematical Sciences, Journal Name: Journal of Mathematical Sciences Journal Issue: 4 Vol. 235; ISSN JMTSEW; ISSN 1072-3374
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ANISOTROPY
DIRICHLET PROBLEM
ELASTICITY
FREDHOLM EQUATION
INTEGRALS
KERNELS
LAYERS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
SMOOTH MANIFOLDS
STRESSES
VECTORS