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C. Adam, F. Ziegler:
"Forced flexural vibrations of elastic-plastic composite beams with thick layers";
Composites - Part B: Engineering, 28B (1997), 201 - 213.

A theory for predicting the elastic-plastic dynamic response of symmetrically designed thick composite laminates is presented. Piecewise continuous and linear in-plane displacement fields through the layer thickness are assumed. Core and faces are perfectly bonded. By definition of an effective cross-sectional rotation the complex problem reduces to the simpler case of an equivalent homogeneous shear-deformable beam with effective stiffness, effective mass density and with corresponding boundary conditions. Inelastic defects of the material are equivalent to eigenstrains in an identical but elastic background structure of the homogenized beam with effective virgin stiffness. Mathematically, a multiple field approach of the elastic background results. Proper resultants of these eigenstrains are defined. Since the incremental response is linear within a given time step, solution methods of the linear theory of flexural vibrations can be applied both to the given external and the "updated" eigenstrain resultants. Modal expansion is performed on the complementary dynamic part of the solution that contains the inertia effects, whereas the quasistatic portion is determined separately and in closed form. Application for dynamically excited simply supported three-layered beams with different ratios of length to thickness demonstrate the validity, merit and range of applicability of the theory.

A theory for predicting the elastic-plastic dynamic response of symmetrically designed thick composite laminates is presented. Piecewise continuous and linear in-plane displacement fields through the layer thickness are assumed. Core and faces are perfectly bonded. By definition of an effective cross-sectional rotation the complex problem reduces to the simpler case of an equivalent homogeneous shear-deformable beam with effective stiffness, effective mass density and with corresponding boundary conditions. Inelastic defects of the material are equivalent to eigenstrains in an identical but elastic background structure of the homogenized beam with effective virgin stiffness. Mathematically, a multiple field approach of the elastic background results. Proper resultants of these eigenstrains are defined. Since the incremental response is linear within a given time step, solution methods of the linear theory of flexural vibrations can be applied both to the given external and the "updated" eigenstrain resultants. Modal expansion is performed on the complementary dynamic part of the solution that contains the inertia effects, whereas the quasistatic portion is determined separately and in closed form. Application for dynamically excited simply supported three-layered beams with different ratios of length to thickness demonstrate the validity, merit and range of applicability of the theory.