Stress-free displacement control of structures

Summary.

The theorem on the unique decomposition of eigenstrain provides the tool to construct prescribed displacements inside and (or) at the surface of a linear elastic body in two novel ways (e.g., in connection with shape control). The first approach applies Maysel’s formula and renders the linear relationship between nodal displacements and impotent eigenstrain in discrete or discretized systems. The second, alternative approach can be applied to continuous systems as well, and allows controlling the shape of the body. Both approaches do not require the solution of the associated boundary value problem with prescribed eigenstrain, thus circumventing the possibly cumbersome (numerical) solution, which can present some difficulties with respect to its convergence.