Modeling of Dynamic Elastic-Plastic Behavior of Beams of Irregular Layered-Fibrous Structures

In approaching the Karman the initial-boundary value problem is formulated for the dynamic elastic-plastic deformation of flexible composite beams of irregular layered-fibrous structures with account of their weakened resistance to the transverse shear. Beams consist of walls and load-bearing layers (shelves). Walls can be reinforced longitudinally or crosswise in its plane, and the shelves are reinforced in the longitudinal direction. The mechanical behavior of the component materials of the composition is described by the equations of the theory of plasticity with isotropic hardening. The explicit “cross” scheme was constructed for numerical integration of the formulated initial-boundary value problem coordinated with the step-by-step scheme and used for the simulation of elasticplastic deformation of composite material of each layer of the beam. The calculations of dynamic and quasistatic bending behavior are carried out for homogeneous and reinforced beams of I-beam cross-section. It is found that the classical theory of bending may not be acceptable to carry out such calculations for some types of metal compositions for relatively long beams. For the adequate calculation of elastoplastic deformation of composite beams of laminated-fibrous irregular structures it is necessary to use the Timoshenko theory, which takes in account the weakened resistance of the walls to the transverse shears. It is shown that in the case of dynamic loading of composite beams, the final deflections are much larger by absolute value than in the case of quasi-static loading with the same load level