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International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749


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

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

Koumbe Mbock
Department of Mathematics and Physics, National Advanced School of Engineering, Yaounde, P.O. Box 8390, Cameroon.

Etoua Remy Magloire
Department of Mathematics and Physics, National Advanced School of Engineering, Yaounde, P.O. Box 8390, Cameroon.

Ayissi Raoul Domingo
Department of Mathematics, Faculty of Sciences, University of Yaounde, P.O Box812, Cameroon.

Mamba Mpele
Department of Civil Engineering, National Advanced School of Engineering, Yaounde, P.O. Box 8390, Cameroon.

Okpwe Mbarga Richard
Department of Civil Engineering, National Advanced School of Engineering, Yaounde, P.O. Box 8390, Cameroon.

DOI https://dx.doi.org/10.33889/IJMEMS.2019.4.3-048

Received on October 25, 2018
  ;
Accepted on February 26, 2019

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.

Keywords- Perturbations, Ill-posed problems, Linear elastic model, Eurocode 7, Topology optimization, Foundations.

Citation

Mbock, K., Magloire, E. R., Domingo, A. R., Mpele, M., & Richard, O. M. (2019). On The Optimal Forms Finding of Shallow Foundations Made Up of Four Foothills with Explicit Considerations of Structural Perturbations. International Journal of Mathematical, Engineering and Management Sciences, 4(3), 601-618. https://dx.doi.org/10.33889/IJMEMS.2019.4.3-048.

Conflict of Interest

The authors confirm that there is no conflict of interest to declare for this publication.

Acknowledgements

We thank the Department of Mathematics and Civil Engineering for their cooperation at the National Advanced School of Engineering (NASE/ UYI) in Yaounde, Cameroon. We would also like to show our gratitude to Ayissi Raoul Domingo, Professor of Mathematics at University of Yaoundé I for assistance on the manuscript at the department of mathematics. We thank the African Center of Excellence in Information and Communication technologies at the University of Yaounde I for their collaboration and support.

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