The development of a modular finite element program for analysis of soil-structure interaction
Morrison, Clark Stephen
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The development of SAGE, a modular finite element program for analysis of soilstructure interaction, is described. The modular structure of the program makes it easy to validate, easy to understand, easy to modify, and easy to extend. Issues affecting the development of the program are discussed. Newton-Raphson iteration, and its application to finite element analysis is described. Methods for improving the convergence behavior ofNewton-Raphson iteration are discussed. The methods include two global convergence algorithms: the line search and the dogleg search. Use of a consistent tangent stress-strain matrix for formulating the stiffness matrix, and its influence on convergence, is discussed. Approximate methods for calculating the consistent tangent stress-strain matrix are presented. Numerical procedures for simulating point loads, distributed loads, gravity loads, excavation, and fill placement are given. It is shown that Newton-Raphson iteration will correct numerical errors associated with the use of very stiff interface elements adjacent to relatively soft soil elements. The results of the use of Gauss integration and Newton-Cotes integration for interface elements are compared. A modification of the hyperbolic model incorporating Mohr-Coulomb plasticity is described. It is shown that use of this model substantially reduces "overshoot", or instances of elements carrying stresses that exceed the strength of the element. Implementation of the Cam clay model into SAGE is described. Several simple example problems are presented that illustrate the stress-strain behavior calculated using this model. Analyses of a footing subjected to combined vertical and horizontal loads are described. The problem was chosen to illustrate the capacity of SAGE to calculate stresses and deformations in soil-structure systems subjected to unusual loading conditions.
- Doctoral Dissertations