Numerical Analysis Method For Collapse Of Frame Structures

The collapse of civil structures during an earthquake is the key reason caused catastrophic loss. Numerical simulation of collapse of structures can provide a basis for exploring the phenomena of structural collapse and provide a tool for seismic design of new structures and evaluation of existing structures. The nonlinear dynamic analysis of structures under earthquake excitations is characterized by huge calculation costs. Hence, a series of numerical analysis software systems, which focus on civil structures, had been developed by researchers in civil engineering community. However, most of these software systems are limited to analyze structures remain continuum through the analysis which results in inaccurate evaluation to structures in severe damage and collapse states. Therefore, the development of analysis method for structural collapse and corresponding numerical analysis software system are of great theoretical significance and practical value. This study takes collapse of frame structures as the research object, and a numerical analysis software system for structural collapse analysis is developed by object-orientation method. In addition, several aspects of theoretical analysis are carried out as follows.1. The method of derivation of beam element based on equilibrium theory is presented. The beam element derived by element equilibrium based idea, which is independent with fixed-shape displacement shape functions, avoids the discrete error by the inaccuracy of displacement shape functions in several cases. The application of equilibrium based beam element is extended to beam with variable sections and with variable material properties.2. The geometrical and material nonlinear analysis methods are presented. The geometrical nonlinear analysis method can be used for beams with large displacement, large rotation but small strain. Because the internal deformations of the presented beam element remain small, the potential problems of inaccurate internal element displacement field by existing methods are avoided. The equilibrium based beam element fails to present a consistent response in the case of section moment-curvature relationship with negative stiffness. To resolve the problem, a modified numerical integration strategy is proposed. 3. The element consistent mass matrix of equilibrium based beam element can not be derived by traditional finite element method because no displacement shape functions are employed. A family of displacement shape functions with adaptive capacity for equilibrium based beam element, which gives accurate representation to variation of displacements in element even with the cases of beam with variable sections or material properties, are constructed. Then, a method for construction of element consistent mass matrix is presented. Based on the presented element consistent mass matrix, a new element lumped mass matrix is also presented. The element consistent and lumped mass matrixes are found that have higher accuracies than traditional element mass matrixes.4. The stabilities of Newmark integration method and an explicit integration method are studied for structures with negative stiffness. The rseults show that the Newmark integration method in the case of negative stiffness is conditionally stable, which is much different with the case of positive stiffness. However, the explicit integration method is unconditionally stable.5. The fracture of structural components is studied. A damage index model, which based on material levels, is presented to detect the section axial and flexural damages and fractures. New structural degrees of freedom will be introduced by the fracture of structural components which leads to difficulty in program implementation and low efficiency in numerical calculation. A method using condensation technique is presented to avoid introducement of the new degrees of freedom.6. The collision between structural components is studied. A two step searching strategy is presented to detect the collision between components. Then, the collision is considered combining with the Herz-damp contact model.