Development of Euler Bernoulli Simulation Model for Analysis of Thin Curved Plates

Abstract

Analysis of curved plate elements requires a high computational effort to obtain reliable solutions for design purposes. Available commercial programs are expensive and they need thorough knowledge for effective use. There is therefore need to code cheaper and accessible programs. This is also in line with vision 2030 of the government of Kenya, of using sustainable methods of production to drive the economy to the middle class level. To address this issue, a uniquemodel is formulated based on the Euler-Bernoulli beam model. This model is applicable to thin elements which include plate and membrane elements. This thesispresents a finite element theory to calculate the master stiffness of a curved plate. The master stiffness takes into account the stiffness, the geometry and the loading of the element. The determinant of the master stiffness is established from which the buckling load which is unknown in the matrix is evaluated by the principal of bifurcation.The curved element is divided into 2,3,6,9 or 12 elements; this demonstrates the computational effort to a reliable solution. Numerical analysis is carried out by abstracting the procedural development of the theory and programming it to run on a Visual Basic platform. The results obtained show that curved plates resist a higher load when it is directed towards the center of the arcand plates with large curvatures resist higher loads than those with smaller curvatures. A comparison made between the result obtained in this research and those of other methods show that there is a good agreement between the proposed and the existing methods. Thus the proposed method is suitable for analysis of curved plates.The research is useful for the study of curved plate elements as it manipulates the given plate and loading parameters to give optimal output. 1