Finite element methods applied to boundary value problems derived from the deflection curve of a beam under the action of a point and a uniformly distributed load

Sammanfattning: In this thesis, we analyze a roller - pinned supported beam of length L subjected to a point load at a distance `1 and a uniformly distributed load over the entire span of the beam. The aim of this study is to determine the slope and the vertical deflection curve of the beam. The analysis is conducted by applying the finite element method, which consists of dividing the whole domain into geometrically simple subdomains, namely elements. The analysis is then performed for each subdomain separately. The approximate solution is obtained by assembling all the elements. The problem is reduced into solving a system of linear algebraic equations. It can be expressed in the matrix form as A = where A is the stiffness matrix, the vector of nodal variables, and the load vector. The finite element method has produced a solution close to the analytical solution.The finite element solution is improved by increasing the number of elements with variablestep sized element. The error based on the L2-norm with respect to the displacement is presented as well as the condition number of the stiffness matrix. The finite element method is implemented in Matlab, and the diagram of the deflected beam is presented.