DETERMINING THE EULER´S BUCKLING LOAD WITH THE FINITE ELEMENT METHOD USING MATLAB
Universidad Politécnica de Valencia (SPAIN)
About this paper:
Appears in: INTED2011 Proceedings
Publication year: 2011
Conference name: 5th International Technology, Education and Development Conference
Dates: 7-9 March, 2011
Location: Valencia, Spain
Abstract:The buckling problem of uniform columns subjected to a compressive load is a common content for undergraduate students. In this work an integrated project that includes numerical and experimental studies is presented to facilitate teaching of buckling of uniform columns with intermediate supports and different boundary conditions, that are not usually reported in the textbooks about mechanics for undergraduate students. The paper shows how the students are able to use their skills in mathematics, strength of materials, and computer applications by means of a single integrated project.
In the present paper, an integrated project is presented, to improve active learning and motivation in students in order to study the concepts related to buckling of slender columns with intermediate supports and different boundary conditions with the Finite Element Method using MATLAB. To achieve this objective, the differential equations that govern the buckling of slender column and the foundations of the Finite Element Method for buckling problems are explained. The application of the Finite Element Method applied to buckling becomes the problem in one of eigenvalues and eigenvectors, which can be easily solved with the aid of symbolic algebra software such as MATLAB, in a personal computer. The numerical results of three columns with different boundary conditions and intermediate supports are presented, and these are compared with the experimental results obtained in the laboratory.
The study of buckling is included in the subject of Strength of Materials for the Degrees of Mechanical and Electrical Industrial Engineering, Design Engineering and Materials Engineering. In the studied subject, the students should have certain previous knowledge. Students must know some concepts of Algebra and Calculus, and have to be familiar with the equations of Statics and Mechanical Properties of Materials.
The first experiments with buckling of centrally compressed prismatic bars were made by Musschenbroek (1729) and Euler (1759). From that time, a considerable amount of literature has been written about the elastic stability problems in structures.
Uniform columns subjected to axial loads are common elements of engineering and architectural structures. In the laboratory is possible to design simple experiments in order to analyze the buckling of slender columns subjected to axial loads. The treatment of this type of problems can be found in most undergraduate textbooks of physics and mechanics of materials which report buckling of simply cases of uniform columns with different boundary conditions. These textbooks don’t contain more complex cases like columns with intermediate supports, non uniform columns, frames...etc. That´s because in the undergraduate textbooks, the buckling is studied using the differential equations of the deflection curve of the column which are difficult to use when dealing with more complex cases.
Keywords: Buckling, Finite Element Method, MATLAB.