On The Optimal Forms Finding of Shallow Foundations Made Up of Four Foothills with Explicit Considerations of Structural Perturbations

Abstract

In the absence of the exact footing form of shallow foundations, we develop a procedure to determine the optimal footing form made up of four foothills from the knowledge of the inexact footing forms. The structural perturbations that are the major cause of the inexact forms are approximated in linear elastic model whose the solution is used to formulate the evolutionary structural optimization problem. To stabilize the solution, a serial of decisions is made to minimize structural perturbations in finite element modeling, initial volume and design constraints. By using the evolutionary structural optimization technique, we examine if the material of efficient and inefficient perturbations is needed or not on the points of inexact forms. Our analysis shows that the loading forces can be transferred to structural perturbations when they are efficient and used to reinforce the design material. This transfer can modify geometric elements of footing in finite element analysis and the optimal solution. The results of the numerical experiment provide the optimal footing form of shallow foundation, the sizes of associated foothills and the form of inefficient perturbations. This approach allows to redesign the structures from the inexact forms and detects the errors of dimensioning.