Decomposition method in linear elastic problems with eigenstrain.

*(English)*Zbl 1070.74006Summary: The general theory of linearized elasticity with eigenstrain is considered with applications to continuous, discrete and discretized structures. It is shown that any eigenstrain can be uniquely decomposed into impotent and nilpotent constituents. The proven theorem on decomposition is based on the concepts of functional analysis, in particular, on Hilbert functional spaces. This unique decomposition allows for the individual and independent control of stresses, strains and displacements (e.g. shape control). The associated algorithm avoids the cumbersome solution of boundary value problems with eigenstrain in connection with these control problems. Decomposition of eigenstrain opens the practically important opportunity to fully separate the control of strains and stresses produced by force loading.

##### MSC:

74B15 | Equations linearized about a deformed state (small deformations superposed on large) |

74M05 | Control, switches and devices (“smart materials”) in solid mechanics |

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\textit{Y. Nyashin} et al., ZAMM, Z. Angew. Math. Mech. 85, No. 8, 557--570 (2005; Zbl 1070.74006)

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