Analysis and behavior of structures on discrete tensionless foundations

The behavior of a discrete tensionless foundation system is analyzed. Subsequently, seven general theorems regarding the nature of this class of problems are proven. Thirteen pure and mixed strategy algorithms are reviewed and their application to a typical illustrative problem is studied. Nonlinear boundary properties which give rise to multiple solutions are modelled, and a new algorithm is presented. The reliability of this algorithm in obtaining a second equilibrium configuration is discussed. The governing equations for the conventional foundations problem have a unique solution. Modifying the Newton-Raphson algorithm, adding adaptive updating, load stopping, and extrapolation leads to an excellent equation solving algorithm. When more than one solution exists, the reliability of the deflation technique for reducing an alternate root for the system is improved by use of a new adaptive under-relaxation of a Newton-Raphson process.