Matrix factorization method in mixed static problems of an elastic wedge: PMM vol. 40, n≗ 4, 1976, pp. 674–681

Abstract

We study the plane contact static problems of an elastic wedge under the condition that it is rigidly connected with the stamp. The question of solvability of the above problems is investigated and an approximate method of solution involving the matrix factorization method developed in paper [1] and others, is proposed. The plane problems of elasticity for a wedge with discontinuous boundary conditions were investigated by a number of authors. For example, in [2] the author used the method of reduction to an integral Wiener-Hopf equation to investigate the problem of indenting a rigid stamp into a perfectly smooth face of an elastic wedge. In [3] a similar problem was reduced to a certain Fredholm equation of second kind. In [4] and others ( ∗ ∗ Lutchenko, S. A. and Popov, G. Ia. On certain plane contact problems of the theory of elasticity for a wedge. In coll: 3-rd All-Union Convention on Theoretical and Applied Mechanics. Moscow, 1968. Annot dokl., Moscow, “Nauka”, 1968. ), the asymptotic and orthogonal polynomial methods were successfully used.