Displacement Variation Methods Of Half Space Foundation Beams

The analysis of the foundation beam is a classic subject, with the appearance of new foundation models ,new analysis methods and new operation methods, this subject is still under development. Actually, the theory analysis and calculation methods of elastic foundation beams as the important issue in architectural engineering, still need to further improvement.First this paper introduces the existing foundation models, and give detail analysis on defects of the Winkler foundation models, compare Winkler foundation models with Boussinesq models systematically and comprehensively, then analyzes various methods of elastic foundation models. On this basis,the main research contents including the following four aspects:take semi-infinite elastic foundation and foundation beam as a separate stress system to study it, take the distribution of the forces between the foundation and foundation beam as external force, infer the stored elastic potential energy under the deformation process of Boussinesq foundation models and foundation beams respectively. Second, using the superposition principle and equivalence principle of Elasticity, take elastic foundation and foundation beams as a whole to study it,based on the principle of potential energy conservation of Elasticity, deduced the Potential energy functional equation of the system, use the principle of minimum energy solve out the distribution force and displacement of the elastic half space and the foundation beams. Third, combine with general issues and then establish the solving equations,adopt Mathematic language write corresponding programs and calculate it. Fourth, Using the algorithm which derived from this paper,giving several examples calculate the Winkler foundation and Boussinesq foundation respectively,the results well reflects the superiority of this algorithm.The main research results is that derive out the potential energy equation of Boussinesq foundation and elastic foundation beams,and presents a new algorithm based on Boussinesq Foundation models, this algorithm is simple, accurate, and can be more widely used in various types of engineering calculations.