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C. Adam:
"Modal analysis of elastic-viscoplastic Timoshenko beam vibrations";
Acta Mechanica, 126 (1998), S. 213 - 229.

A semi-analytic inelastic Timoshenko beam theory based on a modal solution is developed. Inelastic strains are equivalent to eigenstrains in an identical but entirely elastic background structure. Proper resultants of these eigenstrains, i.e. inelastic curvatures and averaged inelastic shear angles, are defined. Deformations and cross sectional stress resultants due to these eigenstrain resultants are obtained by means of proper dynamic Green's functions. Since the deformation of the background structure is elastic, linear dynamic solution methods become applicable in a time incremental procedure. In order to enhance the efficiency of this time domain algorithm, an analytic quasistatic portion is separated from the solution. Rate dependence of plastic deformation is considered and ductile damage in a model of void growth is taken into account. The intensity and distribution of the á priori unknown eigenstrains and imposed shear angles are determined by the constitutive law and calculated in an iterative procedure.

A semi-analytic inelastic Timoshenko beam theory based on a modal solution is developed. Inelastic strains are equivalent to eigenstrains in an identical but entirely elastic background structure. Proper resultants of these eigenstrains, i.e. inelastic curvatures and averaged inelastic shear angles, are defined. Deformations and cross sectional stress resultants due to these eigenstrain resultants are obtained by means of proper dynamic Green's functions. Since the deformation of the background structure is elastic, linear dynamic solution methods become applicable in a time incremental procedure. In order to enhance the efficiency of this time domain algorithm, an analytic quasistatic portion is separated from the solution. Rate dependence of plastic deformation is considered and ductile damage in a model of void growth is taken into account. The intensity and distribution of the á priori unknown eigenstrains and imposed shear angles are determined by the constitutive law and calculated in an iterative procedure.