Analysis of a mixed boundary value problem for an orthotropic elasticity using a mapping function

A solution is derived for a mixed boundary orthotropic elastic plane problem using a mapping function to solve arbitrary configurations. No stress function using a mapping function seems to have been derived. The problem is solved as a Riemann-Hilbert problem. The final exact stress functions are represented by an irrational mapping function as a closed form. Stress components are represented by one complex variable. Arbitrarily shaped hole problems can be solved by changing the mapping function. Once the analytical solution has been derived, calculating the stress components is simpler than for an isotropic problem. It is easier to use an irrational mapping function than to form a rational mapping function for an isotropic problem. As an example, an infinite plane with a square hole subjected to uniform tension is analyzed. The stress distributions are shown for Cases I and III problems corresponding to two characteristic roots of the fundamental equation. In a Case III problem, the symmetry of stress distributions is lost. A solution of an external force boundary value problem can be derived from that of the mixed boundary value problem. (C) 2020 Elsevier Ltd. All rights reserved.