Optimization of Elevated Concrete Foundations for Vibrating Machines

Abstract

The objective of this study is to describe a problem formulation and an optimization procedure for the design of elevated reinforced concrete foundations for vibrating machines. Special emphasis is placed on structures composed of footings, beams, and columns. The dimensions of the structure and its reinforcement are the design variables for the optimization problem. The objective function consists of costs of the concrete, the steel, the form, and the propping form. Constraints related to material and soil failure, as well as geometrical limits and human comfort are imposed. A new failure surface for columns and beams subjected to biaxial bending and axial loads is defined and used in the formulation. The main motivation of using the new failure surface is to save a large amount of computational effort in the solution of this dynamic response optimization problem. The problem of minimizing the structural cost while satisfying the operating and safety requirements is solved using an augmented Lagrangian method. A large number of constraints (time dependent and time independent) is treated without any difficulty in the method. The numerical methods used in the solution process are described. Optimal solutions for an example problem are obtained and discussed.