An object-oriented finite element formulation for construction simulation

A new method, simulation analysis, is developed which analyzes the structural effects of the sequence of adding members and loads during construction or repair. Also, a new scheme for equation solving based on interaction between objects is presented. A computer program which performs simulation analysis using this equation solving scheme is implemented through an object oriented model encoded in C++. Simulation analysis is an incremental method based on the stiffness formulation of finite element analysis. By including the construction sequence of a structure, simulation analysis provides more realistic results. The structural effects of different construction practices can be included in this analysis. A rational analysis of the 'sequential dead load application problem' can be done using this approach. The object oriented model performs equation solving by interaction between objects. In this equation solving scheme, the global stiffness, force, and displacement matrices are replaced with objects which encapsulate the relationships described by these arrays. Only non-zero relationships between degrees-of-freedom are modeled in a network-like data structure. Equation solving is performed by propagating changes to connected objects along the network. This model can easily re-solve a structure when small changes take place and so is ideally suited for incremental formulations. The construction of a three story, two bay, braced steel frame is solved as an example problem. A construction sequence is chosen based on typical construction practices. Comparison of the results with conventional analysis shows differences in displaced shapes, moment distributions in beams, and loads in bracing members. The conventional analysis feature of the program yields results which are practically identical to results from commercial finite element packages. This validates the new equation solving scheme. Simulation analysis can be used for comparing possible construction sequences, evaluating incomplete structures, analyzing effects of construction loads, estimating deflections during construction etc. The equation solving scheme can be applied to other problems which require solving real, positive definite, symmetric, sparse matrices. The object oriented model developed in this research can be used as an analysis engine in other software such as optimization and structural design.