Increasing size of wind turbine blades and designing thin-walled structures with a high-degree of freedom in the high-density offshore industry has led to an increasing danger of buckling of structures subjected to high compressive forces. High density complex geometries are computationally challenging to analyse for their modes of failure where efficient handling and post-processing of large structures is often the most computationally intensive aspect of the simulation. The transparent and computationally efficient methodology of structural buckling analysis using native open-source numerical environments is outlined in this paper. A tailor-made Scilab algorithm for building global linear stiffness matrices and geometric stiffness matrices was developed from discretizing a characteristic viscoelastic strut into a discrete element Euler-Bernoulli beam model. To gain the most efficiency, the algorithm implemented storage as sparse matrices to conserve large amounts of memory so that larger, otherwise unsolvable problems may be addressed. Directly solving the generalized eigenvalue problem by Arnoldi-iteration appears to have provided a way to extract the desired buckling load multiplier, along with a graphical display of main failure modes. The findings suggest that it is possible to conduct a stringent, full-scale aeroelastic instability and buckling prediction outside of established commercial packages with accuracy. This open-source application appears to grant structural engineers' greater control over mathematical derivation, providing a highly scalable, repeatable structure for future topological optimisation of marine energy systems.