Modal solutions have been used to approximate the dynamic response of rigid-plastic structures that are subjected to impulsive loads. In a modal solution, the spatial distributions (modes) of the velocity and acceleration fields are equal and independent of time. Since the mode of deformation is a function of the structural geometry, large deflections can result in a change in the mode. In this case it is possible to define Instantaneous Modal Solutions (IMS), in which the mode changes with time as a result of the change in the structural geometry. The response is then approximated by a succession of IMS. In this paper, a new uniqueness property for the succession of modes is presented. This leads to the concept of evolutionary modes. Application of evolutionary modes to large deflection analysis of rigid-plastic structures is illustrated. A simple numerical technique that uses evolutionary modes to construct IMS is applied for the analysis of a semi-circular arch that is impulsively loaded at the crown. Both symmetric and asymmetric evolutionary modes of deformation are analyzed and compared with calculations by a finite element code. Accuracy of the IMS calculations is assessed, relative to structural and load parameters.
展开▼
