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Theory of linearly elastic residually stressed plates. (English) Zbl 1093.74039

Summary: The equations of a plate for a linearly elastic monoclinic material with residual stress are here derived for the first time. By using techniques of \(\Gamma\)-convergence, we show that also in the case with residual stress the displacements are of Kirchhoff-Love type. An improvement of the result of C.-S. Man and D. E. Carlson [Arch. Ration. Mech. Anal. 128, No. 3, 223–247 (1994; Zbl 0829.73017)] on the existence of a solution for the three-dimensional problem of linear elasticity with residual stress is also obtained.

MSC:

74K20 Plates
74B10 Linear elasticity with initial stresses
74Q05 Homogenization in equilibrium problems of solid mechanics

Citations:

Zbl 0829.73017
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References:

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