Analysis of Curved Plate Elements Using Open Source Software (Review Completed - Accepted)
Analysis of curved plate elements requires a high computational effort to obtain a reliable solution for a buckling load for design purposes. Available programs are expensive to acquire and they need thorough knowledge for effective use. There is therefore need to code cheaper and accessible programs in line with using sustainable methods to better the livelihood of mankind. To address this issue a theory is formulated based on the Euler-Bernoulli beam model. This model is applicable to thin elements which include plate and membrane elements.
This paper illustrates 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 this matrix 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 and 12 elements; this demonstrates the computational effort to a reliable solution. As expected, that as you divide the curve into smaller constituent elements, the solution of the buckling load is tedious as more mathematical operations are involved hence the need to program the operations.
Numerical analysis is carried out by abstracting the procedural development of the theory and programming it to run in a visual basic platform. The results obtained are giving a good agreement with results obtained with classical plate equations. This program is proposed to increase computational efficiency in the analysis of curved plates at a sustainable cost. It can also be used to establish the relationship between buckling load and curvature of plates